PDA

View Full Version : "Deal or No Deal" math


Hopey
04-07-2006, 01:32 PM
I was out for lunch today with some of my co-workers and they were having the following debate:

-You are playing "Deal or no Deal"
-All of the briefcases except for one (and the one you chose initially) have been chosen.
-The two dollar amounts left are $1 million and .01.
-You are given the choice to keep the briefcase that you chose initially, or to switch it with the briefcase that is left on stage.
-What do you do?

I argued that it doesn't matter what you do, you have a 50/50 shot at the $1 million, no matter which briefcase you decide to open. However, a couple of guys were arguing adamantly that you should always choose the briefcase that is left on stage. I argued that the fact that you moved one of the briefcases off the stage initially does not affect the contents of the briefcase, and does not affect the probability that it contains $1 million.

Can someone please put this issue to rest? I feel like an idiot for asking this question, but no matter how much I argued, they kept insisting that I was wrong.

DougShrapnel
04-07-2006, 01:39 PM
You are correct. They are wrong.
it's a 50/50 shot no matter what you choose.
Ask them to figure out the exact chances of each breifcase.

felson
04-07-2006, 01:44 PM
"you should always choose the briefcase that is left on stage."

It sounds like they have confused Deal or No Deal with the Monty Hall problem, which is different. Either that, or they are superstitious.

guesswest
04-07-2006, 01:47 PM
Yes, makes no difference. If you had two briefcases with 1c and one with $1 million, and someone took away one of the 1c briefcases for you after you'd selected a briefcase (and were bound by the rules to do so 100% of the time) - then you should switch.

Hopey
04-07-2006, 01:48 PM
[ QUOTE ]
"you should always choose the briefcase that is left on stage."

It sounds like they have confused Deal or No Deal with the Monty Hall problem, which is different. Either that, or they are superstitious.

[/ QUOTE ]

Yeah, one guy brought up Monty Hall, and I pointed out to him how that show was different.

I just had one of the guys come into my office with a pack of cards to illustrate his point to me. I took the cards from him and did a quick demonstration of how the show works by having him pick a card initially (and not look at it), and then pick each remaining card one at a time until there was only one left. I then asked him to tell me which of the two cards left (the one that he picked initially, or the one that was left) was of a higher denomination. I think he finally got it then.

luckyme
04-07-2006, 01:54 PM
The simplest way to look at it is that initially you picked 2 cases. One you put on the table, the other you left on stage to be opened last.

There are no factors that make one a favorite over the other to hold any specific amount. You could just as well have left all on stage and made the choice of which of the final two to put on the table after there was just the two of them sitting there.

When I run into people like that I try to cajole them into a prop bet.

oh, and math won't help them see it.


gluck, luckyme

guesswest
04-07-2006, 01:55 PM
And another (kinda unrelated thing) is, you should deal! People always want to apply game theory/decision theory to this, and it does ostensibly lend itself to that, but there's no long term expectation attached, you're not going to be in the same situation again.

luckyme
04-07-2006, 02:03 PM
[ QUOTE ]
And another (kinda unrelated thing) is, you should deal! People always want to apply game theory/decision theory to this, and it does ostensibly lend itself to that, but there's no long term expectation attached, you're not going to be in the same situation again.

[/ QUOTE ]

Whenever I've seen the show I've never seen an offer that was worth taking. They always short you on the odds. The only reason to take a deal is because of bankroll considerations if you're out of your league in coin.

Taking the deal is like paying insurance on a big poker pot. It's not +EV, it's simply variance control.

I'd never take their 'deal', luckyme

guesswest
04-07-2006, 02:09 PM
Right, the deal is always less than represents value. But, for instance in the 1c vs $1mil - they'd probably offer you $450,000 or something. So +$500k = +EV and -$500k = -EV, so technically it's a -EV offer. But you're never going to be in that situation again, so you probably should be controlling variance since you have no long term. In exactly the same way you wouldn't sit down with your whole bankroll in a game way bigger than you usually play. Am I missing something?

luckyme
04-07-2006, 02:26 PM
[ QUOTE ]

Right, the deal is always less than represents value. But, for instance in the 1c vs $1mil - they'd probably offer you $450,000 or something. So +$500k = +EV and -$500k = -EV, so technically it's a -EV offer. But you're never going to be in that situation again, so you probably should be controlling variance since you have no long term. In exactly the same way you wouldn't sit down with your whole bankroll in a game way bigger than you usually play. Am I missing something?

[/ QUOTE ]

I can't tell from what you've stated.
I totally agree with the bankroll issue, and most people should take the deal only because they shouldn't be gambling with so much money on one shot.

Your original comment didn't mention bankroll considerations as the reason though --
[ QUOTE ]
People always want to apply game theory/decision theory to this, and it does ostensibly lend itself to that, but there's no long term expectation attached, you're not going to be in the same situation again.

[/ QUOTE ]

Every situation has an expectation attached. Offers that are below that are bad deals, offers that are above that are good deals. It's irrelevant that you'll never be in the same situation again, that applies to virtually every situation we find ourselves faced with.

I used to play backgammon for some serious swag with a friend who made the same claim. He'd lay down to the cube too often with the comment, "sure I know the long-term odds are to take, but we'll never be in this situation again." And he was correct, it was exceedingly unlikely that we would be. That didn't make his folds correct though. Same applies to "Deal or No Deal".

Long-term, smlmong-term.. good deals are odds based.

hope that clarifies what I was commenting on, luckyme

Copernicus
04-07-2006, 02:36 PM
[ QUOTE ]
[ QUOTE ]

Right, the deal is always less than represents value. But, for instance in the 1c vs $1mil - they'd probably offer you $450,000 or something. So +$500k = +EV and -$500k = -EV, so technically it's a -EV offer. But you're never going to be in that situation again, so you probably should be controlling variance since you have no long term. In exactly the same way you wouldn't sit down with your whole bankroll in a game way bigger than you usually play. Am I missing something?

[/ QUOTE ]

I can't tell from what you've stated.
I totally agree with the bankroll issue, and most people should take the deal only because they shouldn't be gambling with so much money on one shot.

Your original comment didn't mention bankroll considerations as the reason though --
[ QUOTE ]
People always want to apply game theory/decision theory to this, and it does ostensibly lend itself to that, but there's no long term expectation attached, you're not going to be in the same situation again.

[/ QUOTE ]

Every situation has an expectation attached. Offers that are below that are bad deals, offers that are above that are good deals. It's irrelevant that you'll never be in the same situation again, that applies to virtually every situation we find ourselves faced with.

I used to play backgammon for some serious swag with a friend who made the same claim. He'd lay down to the cube too often with the comment, "sure I know the long-term odds are to take, but we'll never be in this situation again." And he was correct, it was exceedingly unlikely that we would be. That didn't make his folds correct though. Same applies to "Deal or No Deal".

Long-term, smlmong-term.. good deals are odds based.

hope that clarifies what I was commenting on, luckyme

[/ QUOTE ]

There are several distinctions between the BG situation and Deal or No Deal.

In DoND you have nothing invested other than time, and BOTH offers are +EV. Yes, no deal is greater EV, but there are utility considerations. +450,000 and +1,000,000 are a lot closer for most people than +0 and +450,000, when you will never have either opportunity again.

In BG you are not facing life changing sums of money (or if you are you have invested too much of your bankroll to start with), and while you may not be in the exact circumstances again, you will be in very similar circumstances.

guesswest
04-07-2006, 02:41 PM
I take your point, but I don't mean the 'same situation' like my quad fives won't be up against your quad tens with x pot size again.

I mean Stacy the dental assistant from Boise is getting the opportunity to receive a check equivalent to her salary for 20 years, or toss a coin for 45 years worth, or nothing if she loses. You can still calculate the expectation and value, and I'm not saying it isn't a real calculation, but the 'long term' bit just isn't there. She's never going to be in a situation that's even remotely comparable, such that she could realize long term expectation in a mathematically reliable way. It should be approached like it's the only risk-reward decision she'll ever make. And I'd have a hard time advising her to do anything other than cut and run.

Edit: And lucky - realize you're not saying anything contrary to that. Just clarifying my own position.

KingNeo
04-07-2006, 02:44 PM
Honestly this is the stupidest question ever asked.

Is this even serious?

I suggest you get new friends because they are morons.

Hopey
04-07-2006, 03:05 PM
[ QUOTE ]
Honestly this is the stupidest question ever asked.

Is this even serious?

I suggest you get new friends because they are morons.

[/ QUOTE ]

Yes, it's a stupid question, but I couldn't convince them that they were wrong no matter how much I argued, so I was hoping that someone could give me advice/examples on how to do so.

Even when we came back to the office and did a mock "Deal or no Deal" in my office with a deck of cards, they still weren't totally convinced (though I could tell that they were starting to doubt themselves).

And these aren't my friends, they're my co-workers. And I work for the government...so I'll let you draw your own conclusions about that.

KingNeo
04-07-2006, 03:19 PM
Hopey,

I was not making fun of you, just the people asking the question. I am curious to know what their jobs require them to do if they can't use some logic to determine the answer to your original question. I hope it isn't anything critical.

Hopey
04-07-2006, 03:21 PM
LOL...one of the guys who was arguing adamantly that you need to choose the suitcase on stage just came into my office to tell me that he has thought about the problem some more, and has decided that I was right all along.

Sigh. The sad thing is that we weren't even drinking at lunch, so it's not like he has much of an excuse. He seemed a little sheepish, though.

luckyme
04-07-2006, 03:30 PM
[ QUOTE ]
In DoND you have nothing invested other than time, and BOTH offers are +EV.

[/ QUOTE ]

Interesting. I may learn something again today, because I sure see that situation very differently. I don't think my position is worth $0 ( only time), it was worth more that when I was lined up at the door for the show because I had some chance of winning X amount that was greater that the guy snoozing at home in his lazyboy.

Having reached the stage of having an offer my position is worth, as all positions are, it's expected value. Say it's down to 2 cases, 1c and $1M. My position is worth $500,000.005. They offer me $450K. That is a -EV take, not + EV ??

If you get dealt AA in the big blind in a 100-200 limit HE game. You just sat down. I offer you $100 ( plus your buy-in) to take over your hand. So you have two choices. One puts $100 in your pocket, the other you'll be up or down a lot more. Are both +EV? You barely even have time invested :-)

It seems to me that taking the $100 is -EV, but perhaps I need my head straightened out in that area. It doesn't seem right to compare my situation to before I had AA dealt to me, nor to before I was on stage with an offer on DoND. That situation is of historical interest only and not a factor in the value of my position.

what am I missing, luckyme

chezlaw
04-07-2006, 03:33 PM
[ QUOTE ]
Having reached the stage of having an offer my position is worth, as all positions are, it's expected value. Say it's down to 2 cases, 1c and $1M. My position is worth $500,000.005. They offer me $450K. That is a -EV take, not + EV ??

[/ QUOTE ]
I'd take that deal. The first 450k is worth far more to me than the next 550k.

chez

luckyme
04-07-2006, 03:41 PM
[ QUOTE ]
In BG you are not facing life changing sums of money (or if you are you have invested too much of your bankroll to start with), and while you may not be in the exact circumstances again, you will be in very similar circumstances.

[/ QUOTE ]

I seem incapable of grasping why the number of times I may be in a situation, if ever again or before, has any bearing of it's value.

A guy offers me 100K to play one round of russian roulette with a 6 shooter. Never before, and, hopefully never again. Does that mean I can ignore the 1 chance in 6? That somehow it doesn't apply and that this time my chances or survival are 1 in X because it's a rare or unusualy circumstance.

Really, the 'it rare/unique' approach goes right by me and reading it from two posters on here has me wondering what the heck I've been missing all these years. Help!!

thanks for any clarifying comments, luckyme

luckyme
04-07-2006, 03:46 PM
[ QUOTE ]
I'd take that deal. The first 450k is worth far more to me than the next 550k.

[/ QUOTE ]

Nice framing. That's a neat spin on the 'betting beyond your bankroll' concept.

I've been trying to sort out a couple other issues that came up, though.
1) is taking the deal +EV, OEV or - EV.
2) does it matter in calculating it's value, the fact that it's not a common or recurring situation.

any light shed would be appreciated, luckyme

Copernicus
04-07-2006, 03:49 PM
[ QUOTE ]
[ QUOTE ]
In DoND you have nothing invested other than time, and BOTH offers are +EV.

[/ QUOTE ]

Interesting. I may learn something again today, because I sure see that situation very differently. I don't think my position is worth $0 ( only time), it was worth more that when I was lined up at the door for the show because I had some chance of winning X amount that was greater that the guy snoozing at home in his lazyboy.

Having reached the stage of having an offer my position is worth, as all positions are, it's expected value. Say it's down to 2 cases, 1c and $1M. My position is worth $500,000.005. They offer me $450K. That is a -EV take, not + EV ??

If you get dealt AA in the big blind in a 100-200 limit HE game. You just sat down. I offer you $100 ( plus your buy-in) to take over your hand. So you have two choices. One puts $100 in your pocket, the other you'll be up or down a lot more. Are both +EV? You barely even have time invested :-)

It seems to me that taking the $100 is -EV, but perhaps I need my head straightened out in that area. It doesn't seem right to compare my situation to before I had AA dealt to me, nor to before I was on stage with an offer on DoND. That situation is of historical interest only and not a factor in the value of my position.

what am I missing, luckyme

[/ QUOTE ]

I dont disagree that one option is lower EV than the other, however, the introduction of the "deal" or the offer of $100 introduces a new element to the EV equation, which is the certainty of collecting something (I consider the .01 nothing, shame on me).

Accepting that certainty when it is lower EV is akin to buying insurance. In terms of straight monetary value, buying insurance is -EV. However there is value to no longer facing risks that could significantly impact you.

You would be foolish to buy collision insurance on your $50,000 car if you are Bill Gates, but not so foolish if you only earn $20,000 a year and you need the transportation to even earn that. The $ value of the insurance is exactly the same -EV for both (assuming equal driving abilities, distances etc), but the insurance element has enormous value for one and not the other.

chezlaw
04-07-2006, 04:04 PM
[ QUOTE ]
[ QUOTE ]
I'd take that deal. The first 450k is worth far more to me than the next 550k.

[/ QUOTE ]

Nice framing. That's a neat spin on the 'betting beyond your bankroll' concept.

I've been trying to sort out a couple other issues that came up, though.
1) is taking the deal +EV, OEV or - EV.
2) does it matter in calculating it's value, the fact that it's not a common or recurring situation.

any light shed would be appreciated, luckyme

[/ QUOTE ]
Its the V part that changes. Normally we think of 500k as having more V than 450k. If the values involved were relatively small then normal valuations prevail.

In this case as a one off I would recognise that the values are skewed by the life-changingness of the first 450k.

If I put the value of the first 450k at v1 I would reckon the next 550k is worth about .3v1 to me. That makes taking the deal massively +ev and I would take it like a shot.

chez

Copernicus
04-07-2006, 04:55 PM
[ QUOTE ]
[ QUOTE ]
In BG you are not facing life changing sums of money (or if you are you have invested too much of your bankroll to start with), and while you may not be in the exact circumstances again, you will be in very similar circumstances.

[/ QUOTE ]

I seem incapable of grasping why the number of times I may be in a situation, if ever again or before, has any bearing of it's value.

A guy offers me 100K to play one round of russian roulette with a 6 shooter. Never before, and, hopefully never again. Does that mean I can ignore the 1 chance in 6? That somehow it doesn't apply and that this time my chances or survival are 1 in X because it's a rare or unusualy circumstance.

Really, the 'it rare/unique' approach goes right by me and reading it from two posters on here has me wondering what the heck I've been missing all these years. Help!!

thanks for any clarifying comments, luckyme

[/ QUOTE ]

Independently the number of trials doesnt impact the value, only when you introduce the utility of the prize (the extra value the first 450k has vs the next 550k, as chezlaw put it).

If you have multiple opportunities for a relatively highly probable outcome that also has great utility then there is no value to the "insurance" of taking the lower EV deal the first several times.

Eg if you knew you would be offered the Deal or No Deal situation N times then you can "afford" to refuse the insurance...ie say no deal... N-1 times.

The reason I caveated the hypothetical with "relatively highly probable" is because if it has very low probability of success, waiting till the Nth trial to take the insurance doesnt gain nearly as much. (If the probability of success were 12 million :1 like a lottery, taking the insurance on the first trial doesnt have much -EV compared to taking the insurance on the 10th trial).

luckyme
04-07-2006, 05:27 PM
[ QUOTE ]
Independently the number of trials doesnt impact the value, only when you introduce the utility of the prize (the extra value the first 450k has vs the next 550k, as chezlaw put it).

[/ QUOTE ]

Yes, I thought chezlaw illustrated shifting V nicely. ( I tried to cover it with my "most should take the deal").

My bad. I should have shifted my questions over to the 'Probability' forum. I see I'm out of step with the crowd here.

Essentially, I prefer to calculate the math/finances of a situation and then add any personal considerations to those results. In that way I'm able to refer to the EV as an impersonal, generic reference point, and don't have to have people fill out personal worth statements or risk-aversion personality traits before I do the calc.

As chez has illustrated you can do both at once, but then I can't turn to my lawyer buddy ( who doesn't insure his car or carry life insurance for his wife) and say "this is a +EV situation".

If I was a better poker player, I'd likely be one of those who answers a proposed fearful weak-tight line with "move down in stakes". Again, I'd be separating the 'correct action' from the "for my bankroll" part.

hope that explains why I was so questioning,
thanks, luckyme

Copernicus
04-07-2006, 06:01 PM
[ QUOTE ]
[ QUOTE ]
Independently the number of trials doesnt impact the value, only when you introduce the utility of the prize (the extra value the first 450k has vs the next 550k, as chezlaw put it).

[/ QUOTE ]

Yes, I thought chezlaw illustrated shifting V nicely. ( I tried to cover it with my "most should take the deal").

My bad. I should have shifted my questions over to the 'Probability' forum. I see I'm out of step with the crowd here.

Essentially, I prefer to calculate the math/finances of a situation and then add any personal considerations to those results. In that way I'm able to refer to the EV as an impersonal, generic reference point, and don't have to have people fill out personal worth statements or risk-aversion personality traits before I do the calc.

As chez has illustrated you can do both at once, but then I can't turn to my lawyer buddy ( who doesn't insure his car or carry life insurance for his wife) and say "this is a +EV situation".

If I was a better poker player, I'd likely be one of those who answers a proposed fearful weak-tight line with "move down in stakes". Again, I'd be separating the 'correct action' from the "for my bankroll" part.

hope that explains why I was so questioning,
thanks, luckyme

[/ QUOTE ]

Questioning with good reason..these arent mathematically rigorous concepts, and are personal. Eg chezlaw's .3 waiting for the extra 500k is personal, and would be 1 for Bill Gates and maybe .7 for me.

I never studied utility theory, which I assume gets more rigorous.

luckyme
04-07-2006, 06:46 PM
[ QUOTE ]
Questioning with good reason..these arent mathematically rigorous concepts, and are personal.

[/ QUOTE ]

Whew. thank gawd. I thought I'd stepped thru the looking glass.

So, when we see a poker forum discussing the EV of a situation, we don't have to ask the actual cash value of the BB in order to do the calc. That's where my head was on this topic.

I am risking 450 to win 1,000. It's a 50% chance. Taking the bet is +EV ( impersonal V), not taking the bet ( in this case, taking the deal) is 0EV.

I'm still struggling with the 'both are +EV' angle.

If it should be obvious to me, I won't be offended if you just shrug. thanks, luckyme

Utah
04-07-2006, 07:01 PM
Their thinking has some basis, even though they are wrong. They are thinkng, "the odds were far higher that the $1M case was in the group on the stage versus the singular case you chose" And - they are correct.

However, the odds of any one case in the group being a higher percent of having the $1M case is zero.

The odds of you having the $1M case increases for every negative case until it is 50/50. Now, if you look at it as the Monty Hall problem where the whereabouts of the $1M case is known and this case was intentionally avoided during the revelation process then your co-workers would be correct. However, that is not the case.

Solve and explain the problem with math as it is too hard to get to the answer intuitively. If they still dont get it start hanging out with smarter co-workers /images/graemlins/smile.gif

chezlaw
04-07-2006, 07:07 PM
[ QUOTE ]
[ QUOTE ]
Questioning with good reason..these arent mathematically rigorous concepts, and are personal.

[/ QUOTE ]

Whew. thank gawd. I thought I'd stepped thru the looking glass.

So, when we see a poker forum discussing the EV of a situation, we don't have to ask the actual cash value of the BB in order to do the calc. That's where my head was on this topic.

I am risking 450 to win 1,000. It's a 50% chance. Taking the bet is +EV ( impersonal V), not taking the bet ( in this case, taking the deal) is 0EV.

I'm still struggling with the 'both are +EV' angle.

If it should be obvious to me, I won't be offended if you just shrug. thanks, luckyme

[/ QUOTE ]
There is mathematical rigour but only after you assign values and these are subjective. In probability and poker discussions we usually go with the objective arithmetic values but not always - someone who really wants a bracelet might give up some arithmetic ev to increase their subjective ev.

In the real world the arithmetic values are only important because they often correlate with our subjective values. At extremes this correlation breaks down and its the subjective values that decide the matter.

chez

luckyme
04-07-2006, 09:06 PM
[ QUOTE ]
You can still calculate the expectation and value, and I'm not saying it isn't a real calculation, but the 'long term' bit just isn't there.

[/ QUOTE ]

This has been an interesting thread for me, I seem to have a non-standard way of looking at several issues it has raised. On this one, my statement would be
- "The Long-Term NEVER applies. It is never there."

My view is that when we talk about 'long-term' it's just an analogy to help us visualize 1-time probability, not the other way around. What the heck does, "you have a 37% chance of making a flush by the river" mean to the average bear? He knows you can't make a 37% flush, you either make a 100% one or you don't.

If we explain - "it means if you draw 1000 times you'll make it around 370 times." and he retorts -
"but this is the only hand of hold'em I'm ever going to play, so long-term doesn't apply" he's simply become lost in the analogy.

You don't seem to disagree, sorta ;-) Essentially, it seems you're mixing variance with expectation in a way I don't.

thanks for the comments, luckyme

luckyme
04-07-2006, 09:13 PM
[ QUOTE ]
n the real world the arithmetic values are only important because they often correlate with our subjective values. At extremes this correlation breaks down and its the subjective values that decide the matter.

[/ QUOTE ]

That seems like a lot of work to make a mere 5 letter word like 'value' carry off in a fairly simple calculation.

If we start of calculating the expected valuation in BBs, and end by talking about the value of the BB's to me personally, we're going to need more letters than 'V' to pull that off.

i can't see any disagreement in the overall view, but quite a bit in the way to express it.

thanks for taking the time, chez, luckyme

chezlaw
04-07-2006, 09:23 PM
[ QUOTE ]
[ QUOTE ]
n the real world the arithmetic values are only important because they often correlate with our subjective values. At extremes this correlation breaks down and its the subjective values that decide the matter.

[/ QUOTE ]

That seems like a lot of work to make a mere 5 letter word like 'value' carry off in a fairly simple calculation.

If we start of calculating the expected valuation in BBs, and end by talking about the value of the BB's to me personally, we're going to need more letters than 'V' to pull that off.

i can't see any disagreement in the overall view, but quite a bit in the way to express it.

thanks for taking the time, chez, luckyme

[/ QUOTE ]
If I may, thats not the right way to look at it, ot ar least not what I meant.

Its not start off in BB's then adjust for subjective value. In any real bet the decision is between the subjective upside vs the subjective downside, that is the subjective V if you win vs the subjective V if you lose - thats the only determining factor when evaluating a bet.

It just so happens that in many cases, value measured in BB's is an excellent measure of the subjective value.

chez

Brom
04-07-2006, 09:23 PM
Going off on a bit of a tangent here.

Has anyone here ever figured out exactly how much -EV the deals are? For instance say the EV of all the cases left is $50k, and the banker offers the person $45k. This would mean that he is offering deals that are 90% of true value.

My question is if this 90% number is set for every deal, or if it changes based on the level? It seems to me through rudimentary calculations in my head that the deals turn steadily worse as the show goes on, i.e. the first deal is %90, the next 87%, ... , the last is only 75%. This would mean it is better to take the deals earlir in the show, even though the deals are much smaller, rather than waiting towards the end, when the deals are more -EV yet larger in absolute value.

Anyone else notice this, or care to comment?

luckyme
04-07-2006, 10:40 PM
[ QUOTE ]

If I may, thats not the right way to look at it, ot ar least not what I meant.

[/ QUOTE ]

Boy, I hope it's the latter :-)

[ QUOTE ]
In any real bet the decision is between the subjective upside vs the subjective downside, that is the subjective V if you win vs the subjective V if you lose - thats the only determining factor when evaluating a bet.

[/ QUOTE ]

Hey, what about the elephant!?

Your earlier comment about 'arithmetic value' vs 'subjective value' covered it well. They are two separate concepts, unfortunately sharing the same word and it's the flitting between the uses that I'm questioning.

I have a jar, it has one black bean and X white beans. You pay me $100 and you get to reach in blind for a bean. If it's black you get $10000.

Subjectively, the $100 and the $10000 will have value to you that doesn't necessarily follow their arithmetic 100 to 1 ratio. If you are desperate enough you may pay the $100 regardless of the number of whites in the jar. Odds-smods, I need the money ( loan-sharks rely on this too).

I'll use 'A' of arithmetic value, and 'S' for subjective value. Typically we need to know 'A' to calculate 'S'. At time, like my bean-jar desperation bet, we don't care about 'A'. Other times, as you noted earlier, the 'S' mirrors 'A'. From the other end - We never need to know 'S' to calculate 'A'.

In a poker discussion we assume we're talking about 'A' and we then use our knowledge of it to evaluate 'S'. The concepts of 'shrinking chip value' does not mean that if I ask you to change a black you can give me only 3 blues ( instead of 5).

The 37% of hitting the flush doesn't care about how bad i need to. How bad I need to ( for bracelet or rent due reasons) usually still care about the 37%, bean-jars aside.

It'd be impossible to write a poker book if the author had to cover every "S" odds each rich banker or banglidesh fisherman has to deal with. You lay out the "A", put in a caveat about the "S" and call the printer.

Borodog
04-07-2006, 10:50 PM
First off, it is not true that they never offer +EV deals, or that the relative EV of deals gets progressively worse. It actually (usually) seems to get progressively better, until a point very close to the end (just 3-4 cases left) where they will actually offer a +EV deal. I've seen them do it several times. Like the amounts are $200,000, $1, and $0.01, and they offer a deal of $67,000. Clearly +EV.

But that's not the only consideration, even if you don't take into account the diminishing utility of money (as mentioned above). Take for example this situation. There are 4 amounts left, $200,000, $0.01, $1, and $5. The banker offers you $48,000. Clearly -EV (your EV is ~$50,000). But to pass on the deal, what are you actually doing? You're risking $48,000 not for $200,000, but for something in the neighborhood of $19,000. So 3/4 of the time you win another $19,000, but 1/4 of the time you lose $48,000. Your EV on this decision alone is only $14,250 - $12,000 = $2,250.

Sure, it's positive EV, but are you willing to risk $48,000 when your expectation is only another $2k and change? Add in the diminishing utilities of each dollar (or ten shousand dollars) and it's quite clear than unless you're already rich, taking deals at some point is a smart idea.

luckyme
04-07-2006, 11:08 PM
[ QUOTE ]
There are 4 amounts left, $200,000, $0.01, $1, and $5. The banker offers you $48,000. Clearly -EV (your EV is ~$50,000).

[/ QUOTE ]

ahhhh, I can breath again. I was starting to think I was alone in thinking the $48k offer wasn't +EV. Mind you, I don't see it as -EV, isn't it the 0EV choice ... your stack doesn't change ?? You can keep your $48K stack and fold, or risk it and call ( with +EV).

luckyme

chezlaw
04-07-2006, 11:11 PM
Maybe the problem of working with arithmetic value instead of subjective value is best seen when thinking about your opponent.

[ QUOTE ]
the 37% of hitting the flush doesn't care about how bad i need to

[/ QUOTE ]
True but if you're working out the optimal amount to charge your opponent for the privilege of trying to hit their flush then what matters is how much they are willing to pay (assuming exposed hands for simplicity where only hitting the flush wins). The arithmetic ev only tells you the minimum you should charge, it tells you almost nothing about maximising ev.

Thinking about deal or no deal from the other end, what offer should the banker make in the example you gave? The only way he can optimise the ev of the offer is to take into account the subjective valuations of the competitor. (Here the 'hands' are completely exposed and yet the arithmetic ev only tells the deal maker the maximum they should offer)

chez

luckyme
04-07-2006, 11:46 PM
[ QUOTE ]
The arithmetic ev only tells you the minimum you should charge, it tells you almost nothing about maximising ev.

[/ QUOTE ]

It doesn't even tell me that. The main point, I'm failing to make ;-( is that once you bring subjective value into the discussion we're going to be here a while.

My opponent may be getting frustrated and a huge ATM may leave the game if I take anything major off him right now. I'll just bet Less than the arithmetic break-even, give up a little arithmetic EV to gain the evenings subjective EV. Etc, etc.

To make all these neat subjective choices I'm going to need an accurate arithmetic EV calculation. Sklansky can give me that, only I can add the subjective parts.

Usually, the subjective part is the more interesting step in determining my choice, but it's typically built on solid, boring arithmetical EV calcs.

If somebody is writing about EV, I'm going to assume arithmetical EV. If he's weighing in that the villian is his brother-in-law or employer he has to add that, it's not the default condition.

Your 'arithmetic' vs 'subjective' V covered this well, I not sure we have a disagreement. Perhaps only in my claim that EV=arithmetic unless subjective is overtly added to it.

thanks for the points raised, chez,.. luckyme

luckyme
04-08-2006, 12:19 AM
[ QUOTE ]
(Here the 'hands' are completely exposed and yet the arithmetic ev only tells the deal maker the maximum they should offer)

[/ QUOTE ]

It doesn't even tell him that.
He has to weigh in the value of what will attract viewers. If the competitor needs 130K to save their mother, the viewers may not like a 124K offer, or whatever. Perhaps this competitor has been going through mental torment during the show and the viewers may prefer he is given an easy out rather than more torment.. or vice versa :-)

Arithmetical EV tells us the arithmetical EV. What we do with that information is very subjective but one doesn't fill the role of the other.

I hope I'm not missing something obvious and just being stubborn, luckyme >blush<

chezlaw
04-08-2006, 01:18 AM
[ QUOTE ]
Usually, the subjective part is the more interesting step in determining my choice, but it's typically built on solid, boring arithmetical EV calcs.

[/ QUOTE ]
I agree with that, we are probably saying much the same thing from a slightly different perspective. The point I'm trying to make is that its not always incorrect to make a decision that is a -ev arithmetic choice and that its often a mistake to assume that your opponent is making +ev arithmetic choices (even if they know what it is).

It is, however, always correct to make +ev subjective decision and to assume your opponent is attempting to do the same.

Most of the time, for good poker players in ring games they are the same thing.

Your other post about making the deal or no deal game interesting for viewers is of course true but I was hoping to ignore that aspect. Presumably they don't want someone to accept a deal near the beginning of the show but if it wasn't a show but just a proposition bet (with no audience) the same logic would apply and the optimum deal offer would require an analysis of the subjective values of the player.

chez

bigbrother36
04-09-2006, 02:56 AM
[ QUOTE ]
I'd take that deal. The first 450k is worth far more to me than the next 550k.

chez

[/ QUOTE ]

Bingo! This is called Utility. The deal is -EV to the tune of $50G's. The certainty of the $450G > the -EV of 50G. Deal. Unless $450G is a minor sum to Hero re: his B/R.

chezlaw
04-10-2006, 01:53 PM
I've just watched a whole ********* episode of that ********** program and may never forgive you.

chez

MtDon
04-11-2006, 06:18 PM
I'm not sure whether you are just kiding about thinking that taking a deal is not +EV (Positive Expected Value).

The expected value of the $48,000 deal is (1.0)($48,000) - (your costs of getting on the show) = $48,000 - (your costs of getting on the show).

The expected value of continuing is (1/4)($200,000 + $0.01 + $1 + $5) - (your costs of getting on the show) = $50,001.5025 - (your costs of getting on the show).

Both of these expected values are positive, unless the term "(your costs of getting on the show)" is greater than $48,000.

For deciding which choice is "mathematically" best, it doesn't matter what the value the term "(your costs of getting on the show)" is, because it is the same for both choices.

The basic thing to realize is that each choice has an Expected Value that is independent of the other choices.

- Don

Hopey
04-11-2006, 06:43 PM
[ QUOTE ]
I've just watched a whole ********* episode of that ********** program and may never forgive you.

chez

[/ QUOTE ]

LOL...then you've watched more of it than I have. I couldn't even make it through an entire episode.

Hopey
04-11-2006, 06:56 PM
[ QUOTE ]
Hopey,

I was not making fun of you, just the people asking the question. I am curious to know what their jobs require them to do if they can't use some logic to determine the answer to your original question. I hope it isn't anything critical.

[/ QUOTE ]

There were three of them arguing against me. Two of them were my superiors, and all three were computer programmers. You'd think that a simple math problem such as this would come intuitively to them, but apparently not.

mudbuddha
04-12-2006, 01:48 PM
http://en.wikipedia.org/wiki/Marginal_utility

its an economic theory.. As you have more money, each money adds less utility (happiness) to you. More is better than some but some is much much better than none.

ugh as a economics student i should be able to expalin this better but all i do is play pokah haha

Grisgra
04-13-2006, 06:35 PM
[ QUOTE ]
Going off on a bit of a tangent here.

Has anyone here ever figured out exactly how much -EV the deals are? For instance say the EV of all the cases left is $50k, and the banker offers the person $45k. This would mean that he is offering deals that are 90% of true value.

My question is if this 90% number is set for every deal, or if it changes based on the level? It seems to me through rudimentary calculations in my head that the deals turn steadily worse as the show goes on, i.e. the first deal is %90, the next 87%, ... , the last is only 75%. This would mean it is better to take the deals earlir in the show, even though the deals are much smaller, rather than waiting towards the end, when the deals are more -EV yet larger in absolute value.

Anyone else notice this, or care to comment?

[/ QUOTE ]

The early deals are probably at about 20% of EV, and they progress up to around 60-80% when there's 5-8 cases left, I think. They stay at that level pretty consistently, with the lower %s being there when there's just one big number left. Although I think I saw a couple instances where it was actually closer to 90%.

When it's down to two cases I tend to see almost exactly 100%.

When the person got screwed and there's hardly any good numbers left I've seen slightly above 100% -- at that point they probably want to get the person off the stage because it's no longer interesting.

monroe
04-13-2006, 10:36 PM
I've kept track of 16 Deal Or No Deal games with a spreadsheet. In the list below, the first number is the round, the second number is the average value of the banker's offer (as a percentage of the actual average value of the remaining cases). The third number is the lowest offer made in the games I've observed. The fourth number is the highest offer. The fifth is the number of trials (not every game goes all 9 rounds). Some offers have included other prizes, such as a pony (yeah, a pony) and a new car. I've ignored those offers because I don't know what a pony is worth...

1, 0.12, 0.06, 0.15, 16
2, 0.22, 0.11, 0.35, 16
3, 0.39, 0.17, 0.76, 16
4, 0.56, 0.26, 0.86, 15
5, 0.63, 0.45, 0.85, 16
6, 0.70, 0.49, 0.96, 14
7, 0.86, 0.56, 1.02, 11
8, 0.94, 0.69, 1.12, 9
9, 1.02, 0.94, 1.12, 5

Jordan Olsommer
04-14-2006, 12:20 AM
[ QUOTE ]
I used to play backgammon for some serious swag with a friend who made the same claim. He'd lay down to the cube too often with the comment, "sure I know the long-term odds are to take, but we'll never be in this situation again." And he was correct, it was exceedingly unlikely that we would be. That didn't make his folds correct though. Same applies to "Deal or No Deal".

Long-term, smlmong-term.. good deals are odds based.

[/ QUOTE ]

No one in his right mind would pass up a deal for $450 billion dollars if the two cases remaining were .01 and $1 trillion. I will happily pay a $50 billion premium in that scenario to eliminate variance.

Similarly, there is no [censored] way you are passing up 450k in the .01/$1 mil scenario unless you have several million already in the bank.

luckyme
04-14-2006, 12:45 AM
[ QUOTE ]
[ QUOTE ]
I used to play backgammon for some serious swag with a friend who made the same claim. He'd lay down to the cube too often with the comment, "sure I know the long-term odds are to take, but we'll never be in this situation again." And he was correct, it was exceedingly unlikely that we would be. That didn't make his folds correct though. Same applies to "Deal or No Deal".

Long-term, smlmong-term.. good deals are odds based.

[/ QUOTE ]

No one in his right mind would pass up a deal for $450 billion dollars if the two cases remaining were .01 and $1 trillion. I will happily pay a $50 billion premium in that scenario to eliminate variance.

Similarly, there is no [censored] way you are passing up 450k in the .01/$1 mil scenario unless you have several million already in the bank.

[/ QUOTE ]

My backg point was that you don't need to know dick about 'long-term' to make a decision in any situation, you only need to know the factors at play.

You rebuttal seems to indicate.... hmmm, ok, I gotta say, I don't know where you rebutted that, want to elaborate?

luckyme

Jordan Olsommer
04-14-2006, 09:45 AM
[ QUOTE ]

You rebuttal seems to indicate.... hmmm, ok, I gotta say, I don't know where you rebutted that, want to elaborate?


[/ QUOTE ]

It seemed to me that with that example you were saying that you should reject an offer of $450k in the .01/$1mil scenario because it's -EV, even though you'll never be on that show (or have a chance similar to that) again. If that was not your intention, then I apologize.

luckyme
04-14-2006, 10:17 AM
[ QUOTE ]
[ QUOTE ]

You rebuttal seems to indicate.... hmmm, ok, I gotta say, I don't know where you rebutted that, want to elaborate?


[/ QUOTE ]

It seemed to me that with that example you were saying that you should reject an offer of $450k in the .01/$1mil scenario because it's -EV, even though you'll never be on that show (or have a chance similar to that) again. If that was not your intention, then I apologize.

[/ QUOTE ]

I used it to illustrate that the two topics have no relationship.
a) whether to accept or reject.
b) whether you'll ever step into the same stream again, or be on that show, or have 8 men or the bar vs xyz, or have a green house for sale, etc.

I am in situation X-
if I take action Y I'll be in situation Z some % of the time.
If I take action W I'll be in situation U some percentage of the time. etc.
You know the drill.

I don't need to ask, "Oh, honey, am I ever going to be in this situation again." in order to solve the puzzle. That consideration only arise when the "being in the situation" is the value being weighed. "I'll do it because I'll never get a chance to kiss a bulgarian princess again".

That's not the situation in a straightforward money 'bet'. Assume we know we'll only get this offer once in a lifetime -
You're offered 55-45 on a coinflip for $1
for $100, for $10K, for $100K, for 450K.
In making your choice the 'once in a lifetime' never gets weighed, what does enter into it is bankroll issues and personal philosophy ( I know people who won't bet the $1), I know some who'd take it for their case money ( perhaps they're young and talented), I know some who the $450k is within their bankroll comfort.

"In the situation again" is misguided even on a simple level. If you decide to do it for $10K, knowing you'll be offered it 2 more times that year, you're not in the same situation the second time..you're either $10K richer or poorer for sure never mind any other variables that have changed ( perhaps blonds like you more since you won the first bet ;-).

That is the position you need to rebutt, hope that lays it out better for you ... hop right in, might be fun..

thanks, luckyme

Jordan Olsommer
04-14-2006, 10:37 AM
[ QUOTE ]
That is the position you need to rebutt, hope that lays it out better for you ... hop right in, might be fun..

[/ QUOTE ]

Perhaps, but I'm not rebutting it, because I agree. What I don't agree with is if someone were to say that they would reject paying a $50 billion dollar premium that goes along with accepting a $450 billion dollar deal in a .01/$1 trillion case situation on that principle, if for no better reason than if your case is the one with the penny in it, you can't buy your wife a new car and a new house with Sklanskybucks, and believe me, she is going to kick your ass.* /images/graemlins/tongue.gif


*not to mention the fact that if you were in a situation where you were flipping a coin for a trillion bucks, the incentive for the producers/underwriters/someone on the staff to cheat must be enormous, so you would have to figure that the odds that something shady could be going on behind the scenes to keep you from that trillion bucks is non-zero, and therefore it's no longer a coinflip. The $50 billion premium for the guaranteed $450 billion payout seems very reasonable given the concerns of both bankroll and suspected level of game integrity.

ImBen
04-16-2006, 11:09 AM
A player should accept the deal if...

Offer ^ 2 / (NW + Offer) + Offer > EV

Offer = Banker Offer
EV = Average Value of Remaining Cases
NW = Personal Net Worth

ImBen
04-16-2006, 11:13 AM
As another poster pointed out, the issue in the original post is that the co-workers have confused this situation with the "Monty Hall Problem" taught in every basic probability class.

luckyme
04-16-2006, 11:27 AM
[ QUOTE ]
A player should accept the deal if...

Offer ^ 2 / (NW + Offer) + Offer > EV

Offer = Banker Offer
EV = Average Value of Remaining Cases
NW = Personal Net Worth

[/ QUOTE ]

The NW factor may be useful as a 'in general' statement. In specific cases, chez's "shifting V" approach seems the one that we'd apply on a very individual basis. V is not limited to the money either.

luckyme

ImBen
04-16-2006, 11:08 PM
[ QUOTE ]
[ QUOTE ]
A player should accept the deal if...

Offer ^ 2 / (NW + Offer) + Offer > EV

Offer = Banker Offer
EV = Average Value of Remaining Cases
NW = Personal Net Worth

[/ QUOTE ]

The NW factor may be useful as a 'in general' statement. In specific cases, chez's "shifting V" approach seems the one that we'd apply on a very individual basis. V is not limited to the money either.

luckyme

[/ QUOTE ]

This is a simple Kelly Criterion problem. My post is the solution.

Rev. Good Will
04-17-2006, 12:55 AM
to everyone throwing around the term "-EV" in this thread


on a show such as deal or no deal where they give you money, you cannot lose anything, therefore it is impossible by definition, to have a -EV deal on the show. What you guys are talkign about is the optimal choice

SossMan
04-17-2006, 01:43 AM
This thread got me thinking.....

What is the lowest offer you would accept?

madnak
04-17-2006, 01:56 AM
Definition of 0 EV is relative. There was a thread on this recently. If I have a guarantee of $400,000, and I give that up in order to earn an average of about $350,000, it's most useful for me to consider that a -EV option.

chezlaw
04-17-2006, 08:05 AM
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
A player should accept the deal if...

Offer ^ 2 / (NW + Offer) + Offer > EV

Offer = Banker Offer
EV = Average Value of Remaining Cases
NW = Personal Net Worth

[/ QUOTE ]

The NW factor may be useful as a 'in general' statement. In specific cases, chez's "shifting V" approach seems the one that we'd apply on a very individual basis. V is not limited to the money either.

luckyme

[/ QUOTE ]

This is a simple Kelly Criterion problem. My post is the solution.

[/ QUOTE ]
The kelly criterion applies to repeated gambles doesn't it and is about maximising growth rates. Almost the opposite of the problem here.

chez

jason1990
04-17-2006, 10:46 AM
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
A player should accept the deal if...

Offer ^ 2 / (NW + Offer) + Offer > EV

Offer = Banker Offer
EV = Average Value of Remaining Cases
NW = Personal Net Worth

[/ QUOTE ]

The NW factor may be useful as a 'in general' statement. In specific cases, chez's "shifting V" approach seems the one that we'd apply on a very individual basis. V is not limited to the money either.

luckyme

[/ QUOTE ]

This is a simple Kelly Criterion problem. My post is the solution.

[/ QUOTE ]
The kelly criterion applies to repeated gambles doesn't it and is about maximising growth rates. Almost the opposite of the problem here.

chez

[/ QUOTE ]
As I understand it, what you are doing when you apply a Kelly betting system is maximizing your expected utility, where you take for your utility function

U(x) = int_1^x y^{-1/k} dy.

(Here, k is the Kelly number.) Stated in this way, it has nothing to do with repeated gambles. However, it does presuppose a specific utility function. If an individual has a different utility function, then the Kelly system will not maximize his/her expected utility. Since utility functions differ from person to person, the bet amount recommended by the Kelly formula is not optimal in any objective sense.

On the other hand, it is apparently the case that the Kelly system with k=1 generates the largest long-term bankroll growth rate among a certain family of utility functions. Again, though, if your personal utility function is not a member of that family, or if you're not concerned about long term bankroll growth, then this is hardly relevant.

ImBen
04-17-2006, 10:51 AM
Correct. Anyone playing Deal Or No Deal who wishes to maximize the growth of his/her personal wealth should use the formula for offer acceptance which was posted. Anyone with any other goal for the game should jump off the nearest bridge.

The Kelly Criterion applies to any situation where there is risk. A person on Deal Or No Deal is taking just a few among a large series of risks he/she will take throughout life.

chezlaw
04-17-2006, 11:13 AM
[ QUOTE ]
Correct. Anyone playing Deal Or No Deal who wishes to maximize the growth of his/her personal wealth should use the formula for offer acceptance which was posted. Anyone with any other goal for the game should jump off the nearest bridge.



[/ QUOTE ]
I'll take the $450,000 thanks. You can jump off a bridge if you choose.

[ QUOTE ]
The Kelly Criterion applies to any situation where there is risk. A person on Deal Or No Deal is taking just a few among a large series of risks he/she will take throughout life.

[/ QUOTE ]
That's simply wrong. There aren't enough such big risks especially if you're not that young anymore. $450,000 might secure a non-young persons financial position for the rest of their left (under reasonable assumptions). Risking that for some additional money is not covered by the kelly criterion and is not close to being worth it at near 1-1 odds.

chez

ImBen
04-17-2006, 11:17 AM
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
A player should accept the deal if...

Offer ^ 2 / (NW + Offer) + Offer > EV

Offer = Banker Offer
EV = Average Value of Remaining Cases
NW = Personal Net Worth

[/ QUOTE ]

The NW factor may be useful as a 'in general' statement. In specific cases, chez's "shifting V" approach seems the one that we'd apply on a very individual basis. V is not limited to the money either.

luckyme

[/ QUOTE ]

This is a simple Kelly Criterion problem. My post is the solution.

[/ QUOTE ]
The kelly criterion applies to repeated gambles doesn't it and is about maximising growth rates. Almost the opposite of the problem here.

chez

[/ QUOTE ]
As I understand it, what you are doing when you apply a Kelly betting system is maximizing your expected utility, where you take for your utility function

U(x) = int_1^x y^{-1/k} dy.

(Here, k is the Kelly number.) Stated in this way, it has nothing to do with repeated gambles. However, it does presuppose a specific utility function. If an individual has a different utility function, then the Kelly system will not maximize his/her expected utility. Since utility functions differ from person to person, the bet amount recommended by the Kelly formula is not optimal in any objective sense.

On the other hand, it is apparently the case that the Kelly system with k=1 generates the largest long-term bankroll growth rate among a certain family of utility functions. Again, though, if your personal utility function is not a member of that family, or if you're not concerned about long term bankroll growth, then this is hardly relevant.

[/ QUOTE ]

If you're willing to sacrifice optimal growth of your wealth in exchange for a reduced risk of experiencing short-term loss, set 0 < k < 1 to satisfy your risk tolerance. Also, do not confuse optimal with maximal. The Kelly Criterion is inherently risk averse, so watering it down just unnecessarily reduces growth.

Note that reducing k is done in practice when applying the Kelly Criterion to situations involving uncertainty rather than risk, whereby a precise +EV cannot be determined. In the case of Deal Or No Deal, all of the variables are explicitly known.

ImBen
04-17-2006, 11:19 AM
[ QUOTE ]
[ QUOTE ]
Correct. Anyone playing Deal Or No Deal who wishes to maximize the growth of his/her personal wealth should use the formula for offer acceptance which was posted. Anyone with any other goal for the game should jump off the nearest bridge.



[/ QUOTE ]
I'll take the $450,000 thanks. You can jump off a bridge if you choose.



[/ QUOTE ]

What is the specific situation you're talking about?

ImBen
04-17-2006, 11:24 AM
That's simply wrong. There aren't enough such big risks especially if you're not that young anymore. $450,000 might secure a non-young persons financial position for the rest of their left (under reasonable assumptions). Risking that for some additional money is not covered by the kelly criterion and is not close to being worth it at near 1-1 odds.



[/ QUOTE ]

Umm, did you even plug the numbers into the formula for whatever situation you're referring to?

I would hazard a guess that it would tell you to accept, and that you're arguing simply because you don't grasp what I'm explaining to you.

luckyme
04-17-2006, 11:30 AM
[ QUOTE ]
Umm, did you even plug the numbers into the formula for whatever situation you're referring to?

[/ QUOTE ]

the formula doesn't have slots for all the factors that matter. NW is only one of many. So even if it did give the right answer it wouldn't be a "True,justified answer" :-)

luckyme

chezlaw
04-17-2006, 11:37 AM
[ QUOTE ]

That's simply wrong. There aren't enough such big risks especially if you're not that young anymore. $450,000 might secure a non-young persons financial position for the rest of their left (under reasonable assumptions). Risking that for some additional money is not covered by the kelly criterion and is not close to being worth it at near 1-1 odds.



[/ QUOTE ]

Umm, did you even plug the numbers into the formula for whatever situation you're referring to?

I would hazard a guess that it would tell you to accept, and that you're arguing simply because you don't grasp what I'm explaining to you.

[/ QUOTE ]
You would hazzard wrongly and unless net worth includes a componant of age (in which case it is just hiding the issue behind the words 'net worth') then it must be wrong.

Just imagine being 90 with no needy dependents and compare with same net worth but being 20.

chez

ImBen
04-17-2006, 01:13 PM
[ QUOTE ]
[ QUOTE ]
Umm, did you even plug the numbers into the formula for whatever situation you're referring to?

[/ QUOTE ]

the formula doesn't have slots for all the factors that matter. NW is only one of many. So even if it did give the right answer it wouldn't be a "True,justified answer" :-)

luckyme

[/ QUOTE ]

???

Noone was even talking to you.

luckyme
04-17-2006, 01:27 PM
[ QUOTE ]
???

Noone was even talking to you.

[/ QUOTE ]

Well, somebody posted it in a public forum, perhaps thinking they were in pm mode. In your 1st post on this thread, how did you tell they were talking to you? ... how do we tell?

If you going to post questionable material, heck, even rock solid material on a public forum I don't like your chances of regulating who respconds, but good luck with it.
( I'm not offended in the least if you or anyone places me on ignore, if that solution works for you better than private messaging)

luckyme

ImBen
04-17-2006, 01:41 PM
[ QUOTE ]
[ QUOTE ]

That's simply wrong. There aren't enough such big risks especially if you're not that young anymore. $450,000 might secure a non-young persons financial position for the rest of their left (under reasonable assumptions). Risking that for some additional money is not covered by the kelly criterion and is not close to being worth it at near 1-1 odds.



[/ QUOTE ]

Umm, did you even plug the numbers into the formula for whatever situation you're referring to?

I would hazard a guess that it would tell you to accept, and that you're arguing simply because you don't grasp what I'm explaining to you.

[/ QUOTE ]
You would hazzard wrongly and unless net worth includes a componant of age (in which case it is just hiding the issue behind the words 'net worth') then it must be wrong.

Just imagine being 90 with no needy dependents and compare with same net worth but being 20.

chez

[/ QUOTE ]

You obviously have no concept of how the optimal formula works, and until you at least make some attempt to understand it, it's worthless conversing with you. For some reason, you have it in your narrow mind that the formula causes you to make reckless gambles which couldn't be farther from the truth.

Someone unusually risk averse can adjust the k value in the Kelly formula downward as previously mentioned. However, this is not the case with the vast majority of people. If you watch the show, you will see how greed-driven and risk-loving people really are. Make a lowball estimate of someone's worth during the next show and see how many offers which should be accepted that are turned down.

chezlaw
04-17-2006, 04:55 PM
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

That's simply wrong. There aren't enough such big risks especially if you're not that young anymore. $450,000 might secure a non-young persons financial position for the rest of their left (under reasonable assumptions). Risking that for some additional money is not covered by the kelly criterion and is not close to being worth it at near 1-1 odds.



[/ QUOTE ]

Umm, did you even plug the numbers into the formula for whatever situation you're referring to?

I would hazard a guess that it would tell you to accept, and that you're arguing simply because you don't grasp what I'm explaining to you.

[/ QUOTE ]
You would hazzard wrongly and unless net worth includes a componant of age (in which case it is just hiding the issue behind the words 'net worth') then it must be wrong.

Just imagine being 90 with no needy dependents and compare with same net worth but being 20.

chez

[/ QUOTE ]

You obviously have no concept of how the optimal formula works, and until you at least make some attempt to understand it, it's worthless conversing with you. For some reason, you have it in your narrow mind that the formula causes you to make reckless gambles which couldn't be farther from the truth.

Someone unusually risk averse can adjust the k value in the Kelly formula downward as previously mentioned. However, this is not the case with the vast majority of people. If you watch the show, you will see how greed-driven and risk-loving people really are. Make a lowball estimate of someone's worth during the next show and see how many offers which should be accepted that are turned down.

[/ QUOTE ]
I was responding to this post of yours:

[ QUOTE ]
A player should accept the deal if...

Offer ^ 2 / (NW + Offer) + Offer > EV

Offer = Banker Offer
EV = Average Value of Remaining Cases
NW = Personal Net Worth

[/ QUOTE ]

Not many k's to adjust.

You must realise that if you introduce a 'k' that allows you to adjust for subjective values then you've agreed with what I've been saying.

Why you make this abusive is a mystery.

Edit: and you're agreeing with what luckyme was saying. The k allows you to take account of all the other factors.

chez

jason1990
04-17-2006, 05:22 PM
[ QUOTE ]
[ QUOTE ]
As I understand it, what you are doing when you apply a Kelly betting system is maximizing your expected utility, where you take for your utility function

U(x) = int_1^x y^{-1/k} dy.

(Here, k is the Kelly number.) Stated in this way, it has nothing to do with repeated gambles. However, it does presuppose a specific utility function. If an individual has a different utility function, then the Kelly system will not maximize his/her expected utility. Since utility functions differ from person to person, the bet amount recommended by the Kelly formula is not optimal in any objective sense.

On the other hand, it is apparently the case that the Kelly system with k=1 generates the largest long-term bankroll growth rate among a certain family of utility functions. Again, though, if your personal utility function is not a member of that family, or if you're not concerned about long term bankroll growth, then this is hardly relevant.

[/ QUOTE ]

If you're willing to sacrifice optimal growth of your wealth in exchange for a reduced risk of experiencing short-term loss, set 0 < k < 1 to satisfy your risk tolerance. Also, do not confuse optimal with maximal. The Kelly Criterion is inherently risk averse, so watering it down just unnecessarily reduces growth.

Note that reducing k is done in practice when applying the Kelly Criterion to situations involving uncertainty rather than risk, whereby a precise +EV cannot be determined. In the case of Deal Or No Deal, all of the variables are explicitly known.

[/ QUOTE ]
It seems like you've missed the point of my post. When you use the Kelly Criterion, you are simply maximizing your expected utility under the utility function log(x). If log(x) does not accurately describe my personal preferences, then using the Kelly Criterion does nothing for me. The claim that the Kelly Criterion maximizes bankroll growth is, in a sense, irrelevant. Bankroll growth is a red herring. In the presence of a utility function, it is the growth of the utility of the bankroll which is important. (See this post (http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=5463316&an=0&page=1#Post 5463316).) You said

[ QUOTE ]
Anyone playing Deal Or No Deal who wishes to maximize the growth of his/her personal wealth should use the formula for offer acceptance which was posted. Anyone with any other goal for the game should jump off the nearest bridge.


[/ QUOTE ]
The player's goal should be to maximize the growth of the utility of his/her personal wealth. How he/she does this depends on his/her personal evaluation of utility, which is a subjective matter. You are suggesting that using the formula you posted, which is a conseuqence of the Kelly system, is the only reasonable way to play Deal or No Deal. This is not true. In fact, using that formula would be unreasonable if your utility function is anything other than log(x).

Tater10
04-17-2006, 07:11 PM
I enjoy the show for all the reasons in this thread.

Everyone at some point will displace risk for security. the 1M vs .01 is high risk for most (me included).

The bank doesnt use straight X% of fair value for any given round, I believe they have a formula that uses the risk involved.

Example:
2 cases left: 500k and 250k, EV=375k, bank offer is 350k. What % of participants would take that deal?

2 cases left: 750k and .01. EV=375k (again), but if the bank offer is 350k, I would expect more particpants to take this deal. The bank formula explains this and lowers the offer.

(i hate comming to a large thread late, excuse me if i'm treading on ground already discussed)

LogicSequence
05-06-2006, 05:55 AM
Hello everyone, i've been searching online for some kind of formula the banker uses to calculate his offers. So far i've not found one, but i did find something that i think can lead to one. You can actually play deal or no deal online on the NBC website, the game is a flash based game, and has the same rules as the show, and obviously, the deals are calculated by the game. So i pulled the flash file and opened up the source code. YAY, now, who can pull a formula out of that?? It's all right in front of me, but i must admit i didn't exactly advance in programming classes past basic C++ in college. So would anyone care to take a look and see how the offers are calculated? Obviously it is a SET formula and not adhoc.

<font class="small">Code:</font><hr /><pre> function clockIs(ticking)
{
if (ticking)
{
clock.start();
}
else
{
clearInterval(si);
} // end else if
} // End of the function
function SendVars(cmdName, objFunction, strFunction)
{
if (!processing)
{
processing = true;
friendlyMessage = "";
cleanUpVars("Result", "Round", "BoxesToOpen", "Amount");
_level0.resetKicker();
vars.dond = cmdName;
vars.onLoad = objFunction;
vars.sendAndLoad(tUrl, vars, "POST");
} // end if
} // End of the function
function cleanUpVars()
{
var _loc2 = arguments;
for (var _loc1 = 0; _loc1 &lt; _loc2.length; ++_loc1)
{
if (vars[_loc2[_loc1]] != null)
{
delete vars[_loc2[_loc1]];
} // end if
} // end of for
} // End of the function
function moneyFormat(a)
{
var _loc2 = a.toString();
var dot = _loc2.indexOf(".");
var cents = "";
if (dot &gt; -1)
{
cents = _loc2.substring(dot + 1, _loc2.length);
if (cents.length == 1)
{
cents = cents + "0";
} // end if
_loc2 = _loc2.substring(0, dot) + ",";
} // end if
var _loc3 = new Array();
var j = 0;
var _loc1 = _loc2.length;
while (_loc1 &gt; 0)
{
_loc3[j] = _loc2.substring(_loc1 - 3, _loc1);
_loc1 = _loc1 - 3;
++j;
} // end while
_loc2 = "";
for (var _loc1 = _loc3.length - 1; _loc1 &gt;= 0; --_loc1)
{
_loc2 = _loc2 + _loc3[_loc1];
if (_loc1 &gt; 0)
{
_loc2 = _loc2 + ",";
} // end if
} // end of for
if (_loc2 == ",")
{
_loc2 = "0";
} // end if
return (_loc2 + cents);
} // End of the function
function disableBoxes()
{
var _loc2 = _root;
for (var _loc1 = 0; _loc1 &lt;= totalBoxes; ++_loc1)
{
_loc2["box" + _loc1].enabled = false;
} // end of for
boxesDisabled = true;
} // End of the function
function enableBoxes()
{
var _loc2 = _root;
for (var _loc1 = 0; _loc1 &lt;= totalBoxes; ++_loc1)
{
_loc2["box" + _loc1].enabled = true;
} // end of for
boxesDisabled = false;
} // End of the function
function alert(msg)
{
processing = false;
var _loc1 = vars.Result.toLowerCase();
switch (_loc1)
{
case "broken session":
{
friendlyMessage = friendlyMessage + "Verbinding verbroken";
return;
}
case "wrong status":
{
friendlyMessage = friendlyMessage + "Er is iets misgegaan";
return;
}
case "wrong pin code or validation server unreachable":
{
friendlyMessage = "Verkeerde code, controleer je code en voer hem nogmaals in";
return;
}
} // End of switch
tmpMsg = tmpMsg + (msg + ": " + unescape(vars) + "\n\n");
friendlyMessage = tmpMsg;
} // End of the function
function restartGame()
{
playAgain();
} // End of the function
function createVarsObject()
{
calls = calls + "createVarsObject\n";
serverCalls = "";
vars = new LoadVars();
vars.Round = 1;
vars.Username = _level0.vars.Username;
vars.SessionID = _level0.vars.SessionID;
vars.SessionPassword = _level0.vars.SessionPassword;
tUrl = _level0.tUrl;
vars.ResponseType = "pair";
vars.cmd = "firstgeneration";
processing = false;
} // End of the function
function showrandoms()
{
for (var _loc1 = 0; _loc1 &lt; rands.length; ++_loc1)
{
} // end of for
} // End of the function
function shuffle()
{
rands = new Array(totalBoxes);
populateRands(1);
} // End of the function
function populateRands(i)
{
var _loc2 = i;
if (_loc2 &lt; amnts.length)
{
var _loc1 = Math.floor(Math.random() * totalBoxes) + 1;
if (rands[_loc1] == null)
{
rands[_loc1] = _loc2;
populateRands(++_loc2);
return;
} // end if
populateRands(_loc2);
} // end if
} // End of the function
function setRands(minNr, maxNr, maxNrs)
{
var _loc1 = new Array();
var j = 0;
var randMax;
var _loc3;
var rnds = new Array();
for (var _loc2 = minNr; _loc2 &lt;= maxNr; ++_loc2)
{
_loc1[j++] = _loc2;
} // end of for
for (var _loc2 = 0; _loc2 &lt; maxNrs; ++_loc2)
{
randMax = _loc1.length;
_loc3 = Math.floor(Math.random() * randMax);
rnds.push(_loc1[_loc3]);
_loc1.splice(_loc3, 1);
} // end of for
return (rnds);
} // End of the function
function init()
{
var _loc1 = _root;
XML.prototype.ignoreWhite = true;
System.useCodepage = true;
debugMessage = "";
dealMade = false;
finalAmount = "";
fAmount = "";
fr = new Array("preliminaries", "load anim", "game start", "round start", "deal or no deal");
amnts = new Array("0", ".01", "1", "5", "10", "25", "50", "75", "100", "200", "300", "400", "500", "750", "1,000", "5,000", "10,000", "25,000", "50,000", "75,000", "100,000", "200,000", "300,000", "400,000", "500,000", "750,000", "1,000,000");
amntsReal = new Array(0, 1.000000E-002, 1, 5, 10, 25, 50, 75, 100, 200, 300, 400, 500, 750, 1000, 5000, 10000, 25000, 50000, 75000, 100000, 200000, 300000, 400000, 500000, 750000, 1000000);
ratios = new Array(5.000000E-002, 1.500000E-001, 2.500000E-001, 4.000000E-001, 5.000000E-001, 6.000000E-001, 7.000000E-001, 8.000000E-001, 9.000000E-001);
sumPercentages = new Array(5, 7, 9, 13, 17, 20, 25, 33, 50, 50, 50, 50);
variablePercentages = new Array(6, 11, 16, 21, 26, 31, 41, 51, 61, 71, 81, 91);
currentBoxes = 26;
totalBoxes = 26;
tFullName = level0.tFullName;
user = tFullName.substring(0, tFullName.indexOf(" "));
user = user.charAt(0).toUpperCase() + user.substring(1, user.length).toLowercase();
nrOfBoxesToRemove = 6;
boxesRemoved = 0;
roundNr = 0;
soundSet = false;
categoriesAreStored = false;
shuffle();
oldTab = "";
tScore = "day";
clock = new Sound(_loc1);
clock.attachSound("clock");
doorSlide = new Sound(_loc1);
doorSlide.attachSound("doorSlide");
machineSlide = new Sound(_loc1);
machineSlide.attachSound("machineSlide");
boxRowPang = new Sound(_loc1);
boxRowPang.attachSound("boxRowPang");
myBoxWoosh = new Sound(_loc1);
myBoxWoosh.attachSound("myBoxWoosh");
boxSelectCling = new Sound(_loc1);
boxSelectCling.attachSound("boxSelectCling");
boxSelectCling.setVolume(20);
amountSelectClick = new Sound(_loc1);
amountSelectClick.attachSound("amountSelectClick");
sndWrong = new Sound(_loc1);
sndWrong.attachSound("wrong");
sndRight = new Sound(_loc1);
sndRight.attachSound("right");
mxml = new XML();
mxml.load("lines.xml");
mxml.onLoad = readXML;
} // End of the function
function readXML()
{
var _loc2 = _root;
base = this.childNodes[0].childNodes;
for (var _loc1 = 0; _loc1 &lt; base.length; ++_loc1)
{
if (base[_loc1].attributes.value != "HTML")
{
_loc2[base[_loc1].attributes.id] = unescape(base[_loc1].attributes.value);
continue;
} // end if
_loc2[base[_loc1].attributes.id] = base[_loc1].childNodes.toString();
} // end of for
gotoRUReady();
_loc2.logoMC.gotoAndStop(language);
} // End of the function
function gotoRUReady()
{
gotoAndStop("r u ready");
startGameButton.enabled = true;
startGameButton.onPress = startGame;
} // End of the function
function startGame()
{
_root.setupBoxes();
} // End of the function
function setupBoxes()
{
var _loc1 = _root;
var _loc2 = this;
processing = false;
gotoAndStop("game start");
v2;
v3;
amountHolder = _loc1.ahLeft.ah;
v1 = 1;
for (j = 0; v1 &lt;= totalBoxes; j++)
{
if (v1 &gt; 13)
{
amountHolder = _loc1.ahRight.ah;
} // end if
v3 = amountHolder["amount" + (j % 13 + 1)];
v3.amount = euro + amnts[v1];
v3.amountNr = v1 - 1;
v3.removed = false;
v3.gotoAndStop(1);
v2 = _loc1["box" + v1];
v2._visible = false;
v2.enabled = false;
v2.gotoAndStop(v1 + 1);
v2.boxNr = v1;
v2.onPress = function ()
{
openSuitcase(this);
};
++v1;
} // end of for
doorSlide.start();
ahLeft.gotoAndPlay(2);
ahRight.gotoAndPlay(2);
bxNr = 0;
boxesInRow = 6;
si = setInterval(showBoxRow, 300);
} // End of the function
function showBoxRow()
{
var _loc3 = _root;
var _loc2;
if (bxNr &lt; 22)
{
boxRowPang.start();
for (var _loc1 = 1; _loc1 &lt;= boxesInRow; ++_loc1)
{
_loc2 = _loc3["box" + (_loc1 + bxNr)];
_loc2._visible = true;
} // end of for
bxNr = bxNr + boxesInRow;
boxesInRow = 5;
return;
} // end if
clearInterval(si);
enableBoxes();
} // End of the function
function openSuitcase(suitcase)
{
var _loc1 = suitcase;
disableBoxes();
globalSuitcase = _loc1;
vars.Box = _loc1.boxNr - 1;
trace (roundNr);
if (roundNr == 0)
{
_root.openSuitcase2(_loc1);
return;
} // end if
if (roundNr == 1 &amp;&amp; !soundSet)
{
myBoxWoosh.onSoundComplete = function ()
{
amountSelectClick.start();
};
soundSet = true;
} // end if
_root.openSuitcase2(_loc1);
} // End of the function
function openSuitcase2(suitcase)
{
amountSelectClick.start();
var amount;
var amountNr;
var _loc1;
var _loc2;
processing = false;
myBoxWoosh.start();
if (roundNr == 0)
{
roundNumber = "";
++roundNr;
gotoAndStop("round start");
box0.gotoAndStop(globalSuitcase.boxNr - 1 + 2);
box0.boxNr = suitcase.boxNr;
globalSuitcase._visible = false;
animateOwnBox(globalSuitcase.boxNr);
return;
} // end if
_loc2 = rands[suitcase.boxNr];
_loc1 = _loc2 &lt;= 13 ? (_root.ahLeft.ah["amount" + _loc2]) : (_root.ahRight.ah["amount" + (_loc2 - 13)]);
if (++boxesRemoved &lt; nrOfBoxesToRemove)
{
globalSuitcase._visible = false;
_loc1.gotoAndPlay(2);
_loc1.removed = true;
explainRound(false);
return;
} // end if
if (boxesRemoved == nrOfBoxesToRemove)
{
globalSuitcase._visible = false;
_loc1.gotoAndPlay(2);
_loc1.removed = true;
si = setInterval(gotoDealOrNoDeal, 1000);
if (nrOfBoxesToRemove != 1)
{
nrOfBoxesToRemoveNextRound = nrOfBoxesToRemove - 1;
} // end if
if (nrOfBoxesToRemoveNextRound == 1)
{
casesString = "case";
return;
} // end if
casesString = "cases";
} // end if
} // End of the function
function gotoDealOrNoDeal()
{
clearInterval(si);
fadeBoxes(true);
updateUser(false);
gotoAndStop("deal or no deal");
machineSlide.start();
si = setInterval(checkSum, 4000, true);
} // End of the function
function dealOrNoDealEnd(boxNr)
{
myAmountNr = rands[box0.boxNr];
trace ("box0: " + box0.boxNr + " - myAmountNr: " + MyAmountNr);
if (!dealMade)
{
fAmount = amntsReal[myAmountNr];
trace ("fAmount: " + fAmount);
} // end if
var _loc1 = myAmountNr &lt;= 13 ? (_root.ahLeft.ah["amount" + myAmountNr]) : (_root.ahRight.ah["amount" + (myAmountNr - 13)]);
_loc1.gotoAndPlay(2);
_loc1.removed = true;
updateUser();
} // End of the function
function updateUser(inbetween)
{
if (inbetween)
{
updateMain = line05;
return;
} // end if
currentBoxes = currentBoxes - boxesRemoved;
boxesIn = currentBoxes;
boxesOut = totalBoxes - currentBoxes;
finalAmount = euro + moneyFormat(fAmount);
if (roundNr &lt; 10)
{
if (!dealMade)
{
updateMain = line06_A + boxesOut + line06_B + boxesIn + line06_C + line06_D + nrOfBoxesToRemoveNextRound + line06_E + casesString + line06_F;
}
else
{
updateMain = line07_A + boxesOut + line07_B + boxesIn + line07_C + finalAmount + line07_D;
} // end else if
return;
} // end if
if (roundNr == 10)
{
if (!dealMade)
{
updateMain = line08;
box0._x = 360;
box0._y = 450;
box0.onRelease = function ()
{
_root.dealOrNoDealEnd(this.boxNr);
};
}
else
{
updateMain = line09_A + finalAmount + line09_B;
box0._x = 360;
box0._y = 480;
box0.onRelease = function ()
{
_root.dealOrNoDealEnd(this.boxNr);
};
} // end else if
myBoxWoosh.start();
boxMessage = "";
box0._yscale = 200;
box0._xscale = 200;
box0.enabled = true;
++roundNr;
return;
} // end if
if (roundNr == 11)
{
var _loc2 = line19;
var _loc1 = line04;
if (vars.Rank &gt; 0)
{
if (_level0.isGuestLogin)
{
_loc2 = line23_B;
}
else
{
_loc2 = line23_A + vars.Rank;
} // end else if
_loc1 = line20;
} // end if
trace (_loc1);
if (!dealMade)
{
updateMain = _loc1 + line24_A + moneyFormat(fAmount) + line24_B + moneyFormat(fAmount) + line24_C + _loc2;
}
else
{
updateMain = _loc1 + line24_A + moneyFormat(amntsReal[myAmountNr]) + line24_D + finalAmount + line24_B + moneyFormat(fAmount) + line24_C;
trace (line24_C);
} // end else if
playAgainButton._visible = true;
playAgainButton.onRelease = playAgain;
box0._visible = false;
++roundNr;
} // end if
} // End of the function
function explainRound(timed)
{
nrOfBoxesLeftToRemove = nrOfBoxesToRemove - boxesRemoved;
if (timed)
{
clearInterval(si);
} // end if
roundNumber = roundText + " " + roundNr;
if (nrOfBoxesLeftToRemove != 1)
{
roundMessage = line13_A + nrOfBoxesLeftToRemove + line13_B;
}
else
{
roundMessage = line14;
} // end else if
enableBoxes();
} // End of the function
function fadeBoxes(out)
{
var _loc3 = out ? (80) : (100);
var v3 = out ? (80) : (0);
var _loc2;
for (var _loc1 = 1; _loc1 &lt;= totalBoxes; ++_loc1)
{
_loc2 = _root["box" + _loc1];
_loc2._alpha = _loc3;
_loc2.fade._alpha = v3;
} // end of for
} // End of the function
function dealAccepted()
{
clockIs(false);
fAmount = dealAmount;
trace ("fAmount: " + fAmount);
_root.deal();
} // End of the function
function nodeal()
{
if (!dealMade &amp;&amp; roundNr &lt; 10)
{
updateUser(true);
si = setInterval(backToGame, 2500, true);
}
else
{
backToGame();
} // end else if
processing = false;
} // End of the function
function continueGameAfterDeal()
{
gotoAndStop("deal or no deal");
backToGame();
} // End of the function
function backToGame(timed)
{
if (timed)
{
clearInterval(si);
} // end if
boxesRemoved = 0;
++roundNr;
if (nrOfBoxesToRemove != 1)
{
--nrOfBoxesToRemove;
} // end if
if (roundNr &lt; 10)
{
fadeBoxes(false);
explainRound(false);
gotoAndStop("round start");
enableBoxes();
}
else
{
dealMachine._visible = false;
updateUser(false);
} // end else if
} // End of the function
function deal()
{
processing = false;
fadeBoxes(true);
updateMain = line15_A + euro + moneyFormat(fAmount) + line15_B + moneyFormat(fAmount) + line15_C;
gotoAndStop("deal");
dealMade = true;
continueAfterDealButton.onRelease = continueGameAfterDeal;
continueAfterDealButton.enabled = true;
} // End of the function
function dealDeclined()
{
clockIs(false);
_root.nodeal();
} // End of the function
function checkSum(timed)
{
var _loc3 = _root;
globalTimed = timed;
var lowSum = 0;
var _loc2 = 0;
trace ("box0.boxNr: " + box0.boxNr + " -&gt; " + amntsReal[rands[box0.boxNr]]);
for (var _loc1 = 1; _loc1 &lt;= totalBoxes; ++_loc1)
{
amount = rands[_loc1] &lt;= 13 ? (_loc3.ahLeft.ah["amount" + rands[_loc1]]) : (_loc3.ahRight.ah["amount" + (rands[_loc1] - 13)]);
if (!amount.removed)
{
if (amntsReal[rands[_loc1]] &lt; 100000)
{
lowSum = lowSum + amntsReal[rands[_loc1]];
continue;
} // end if
_loc2 = _loc2 + amntsReal[rands[_loc1]];
} // end if
} // end of for
lowSum = lowSum * sumPercentages[roundNr] / 100;
_loc2 = _loc2 * sumPercentages[roundNr] / 100;
_loc2 = _loc2 * variablePercentages[roundNr] / 100;
trace (sumPercentages[roundNr]);
trace (variablePercentages[roundNr]);
var sum = Math.round(lowSum + _loc2);
trace (sum);
_loc3.checkSum2(sum);
} // End of the function
function checkSum2(sum)
{
processing = false;
dealAmount = sum;
dealMachine.dealAmount = euro + moneyFormat(dealAmount);
boxSelectCling.start(4.700000E+000);
if (globalTimed)
{
clearInterval(si);
if (roundNr &lt; 10)
{
if (!dealMade)
{
dealMachine.gotoAndStop("deal");
}
else
{
dealMachine.gotoAndStop("play on");
} // end if
} // end else if
globalTimed = false;
} // end if
} // End of the function
function animateOwnBox(boxNr)
{
var _loc1 = _root;
var _loc2 = boxNr;
endX = _loc1.box0._x;
endY = _loc1.box0._y;
endXscale = _loc1.box0._xscale;
endYscale = _loc1.box0._yscale;
endRotation = _loc1.box0._rotation;
startX = _loc1["box" + _loc2]._x;
startY = _loc1["box" + _loc2]._y;
startXscale = _loc1["box" + _loc2]._xscale;
startYscale = _loc1["box" + _loc2]._yscale;
startRotation = _loc1["box" + _loc2]._rotation;
xDiff = startX - endX;
yDiff = startY - endY;
xScaleDiff = endXscale - startXscale;
yScaleDiff = endYscale - startYscale;
rotDiff = endRotation - startRotation;
nrOfSteps = 10;
animStep = 10;
xStep = xDiff / animStep;
yStep = yDiff / animStep;
xScaleStep = xScaleDiff / animStep;
yScaleStep = yScaleDiff / animStep;
rotStep = rotDiff / animStep;
_loc1.box0._x = startX;
_loc1.box0._y = startY;
_loc1.box0._xscale = startXscale;
_loc1.box0._yscale = startYscale;
_loc1.box0._rotation = startRotation;
si = setInterval(animateOwnBox2, 10);
} // End of the function
function animateOwnBox2()
{
var _loc1 = _root;
if (nrOfSteps-- &gt; 0)
{
_loc1.box0._x = _loc1.box0._x - xStep;
_loc1.box0._y = _loc1.box0._y - yStep;
_loc1.box0._xscale = _loc1.box0._xscale + xScaleStep;
_loc1.box0._yscale = _loc1.box0._yscale + yScaleStep;
_loc1.box0._rotation = _loc1.box0._rotation + rotStep;
return;
} // end if
clearInterval(si);
boxMessage = line02;
roundMessage = line03;
si = setInterval(explainRound, 2000, true);
} // End of the function
function stopGame()
{
getURL("javascript: window.close()");
} // End of the function
function getCategories()
{
answerPicked = false;
if (categoriesAreStored)
{
catNr = cat.length - 1;
machineSlide.start();
gotoAndStop("categories");
}
else
{
cat = new Array();
catId = new Array();
catsAndIds = vars.CategoryList.substring(0, vars.CategoryList.length - 1).split("#");
cleanUpVars("CategoryList");
var _loc1 = 0;
for (var _loc2 = 0; _loc1 &lt; catsAndIds.length; ++_loc2)
{
catId[_loc2] = catsAndIds[_loc1];
cat[_loc2] = catsAndIds[_loc1 + 1];
_loc1 = _loc1 + 2;
} // end of for
catNr = cat.length - 1;
categoriesAreStored = true;
} // end else if
updateMain = line16;
} // End of the function
function getQuestion(timed)
{
if (timed)
{
clearInterval(si);
} // end if
catNr = catNr % cat.length;
vars.Category = catId[catNr];
SendVars("question", showQuestion);
} // End of the function
function showQuestion()
{
if (vars.Result.toString() == "Ok" &amp;&amp; vars.dond == "question")
{
processing = false;
cleanUpVars("Category");
gotoAndStop("questions");
playAgainButton._visible = false;
updateMain = line17;
answerSuccessText = "";
if (answerButs.length == 0)
{
answerButs = new Array("", questionMachine.q.a, questionMachine.q.b, questionMachine.q.c);
} // end if
with (questionMachine.q)
{
qTxt = vars.Question;
aTxt1 = vars.a1;
aTxt2 = vars.a2;
aTxt3 = vars.a3;
} // End of with
cleanUpVars("Question", "a1", "a2", "a3");

} // end if
tt = 0;
si = setInterval(showTime, 1000);
} // End of the function
function showTime()
{
tt = tt + 1;
if (tt &lt; 13)
{
clock.start();
questionMachine.q["d" + tt].play();
}
else
{
clearInterval(si);
answerId = -1;
vars.Answer = "a1";
si = setInterval(delayedAnswerCall, 1000);
} // end else if
} // End of the function
function delayedAnswerCall()
{
clearInterval(si);
SendVars("answer", showAnswer);
} // End of the function
function selectAndShowAnswer()
{
var _loc1 = _root;
var _loc2 = this;
if (!_loc1.answerPicked)
{
clearInterval(_loc1.si);
_loc2.ring.gotoAndStop(2);
_loc1.vars.Answer = _loc2.answerId;
_loc1.answerId = _loc2.answerId.substr(1, 1);
_loc1.questionMachine.q["aBG" + _loc1.answerId].gotoAndStop(4);
_loc1.SendVars("answer", showAnswer);
_loc1.answerPicked = true;
} // end if
} // End of the function
function showAnswer()
{
if (vars.Result.toString() == "Ok" &amp;&amp; vars.dond == "answer")
{
processing = false;
if (vars.Correct == "true")
{
sndRight.start();
answerButs[Number(vars.CorrectAns)].gotoAndStop(3);
questionMachine.q["aBG" + answerId].gotoAndStop(3);
if (roundNr &lt; 10)
{
updateMain = line18;
continueButton._visible = true;
continueButton.onRelease = function ()
{
_root.backToGame(false);
};
} // end if
}
else
{
sndWrong.start();
updateMain = line21;
answerButs[Number(answerId)].gotoAndStop(2);
questionMachine.q["aBG" + answerId].gotoAndStop(2);
si = setInterval(hideMachine, 2000);
} // end else if
}
else if (vars.Result.toString() == "Time Exceeded")
{
sndWrong.start();
updateMain = line22;
si = setInterval(hideMachine, 2000);

} // end else if
cleanUpVars("Answer", "Correct", "CorrectAns", "TimeToAns");
} // End of the function
function hideMachine()
{
clearInterval(si);
questionMachine.play();
updateMain = line25;
playAgainButton._visible = true;
playAgainButton.onPress = reInit;
si = setInterval(reInit, 5000);
} // End of the function
function reInit()
{
clearInterval(si);
playAgain();
} // End of the function
function gameOver()
{
clock.setVolume(50);
si = setInterval(decreaseAmount, 10);
} // End of the function
function decreaseAmount()
{
clock.stop();
var _loc1;
if (fAmount &gt; 0)
{
clock.start();
if (fAmount &gt;= 1000000)
{
fAmount = fAmount - 100000;
}
else if (fAmount &gt;= 100000)
{
fAmount = fAmount - 10000;
}
else if (fAmount &gt;= 1000)
{
fAmount = fAmount - 100;
}
else if (fAmount &gt;= 100)
{
fAmount = fAmount - 10;
}
else if (fAmount &gt;= 1)
{
--fAmount;
}
else
{
fAmount = 0;
} // end else if
_loc1 = fAmount;
finalAmount = euro + " " + moneyFormat(_loc1);
return;
} // end if
clearInterval(si);
answerSuccessText = "GAME OVER";
questionMachine.play();
playAgainButton._visible = true;
playAgainButton.onPress = init;
} // End of the function
function playAgain()
{
init();
} // End of the function
stop ();
bLoaded = 0;
stop ();
init();
</pre><hr />

bearly
05-06-2006, 08:32 PM
find some folks to have lunch w/ who aren't "out to lunch"...................b

Silent A
05-07-2006, 05:11 AM
[ QUOTE ]
You can actually play deal or no deal online on the NBC website, the game is a flash based game, and has the same rules as the show, and obviously, the deals are calculated by the game.

[/ QUOTE ]

I tried the flash game out and there's something wrong with the code. I got it down to 2 suitcases. One is 400K abd the other 200K. What's the bank's offer?

213K

WTF?

Then again, they didn't give me the option of switching cases, and my case had the 200K.

I also got an offer of $775 when the last 3 cases were 300, 500, and 750.

And finally I managed to get it down to the ultimate: 1 cent or $1 million. The offer was 355K and my case had 1 cent.

Gunner
05-08-2006, 07:35 PM
Yeah I had a situation where I got down to two cases (200K and 400K) and my offer was 175K or something. Obviously there is no benefit to taking the offer... Didn't make any sense.

Klompy
05-09-2006, 08:03 AM
Man do I hate that show, but I was forced to watch it last week because I knew someone on the show.

3rdEye
05-09-2006, 09:49 AM
In economic terms, it depends on your level of "risk aversion." In other words, the unbiased, "rational" choice might not always be the one that gives you the most utility, given that you might be so averse to risk that the chance of losing the money offered would not be worth it.

3rdEye
05-09-2006, 09:55 AM
http://people.few.eur.nl/vandenassem/files/wall%20street%20journal%20europe%2012-01-06%20(small).pdf

[ QUOTE ]
I was out for lunch today with some of my co-workers and they were having the following debate:

-You are playing "Deal or no Deal"
-All of the briefcases except for one (and the one you chose initially) have been chosen.
-The two dollar amounts left are $1 million and .01.
-You are given the choice to keep the briefcase that you chose initially, or to switch it with the briefcase that is left on stage.
-What do you do?

I argued that it doesn't matter what you do, you have a 50/50 shot at the $1 million, no matter which briefcase you decide to open. However, a couple of guys were arguing adamantly that you should always choose the briefcase that is left on stage. I argued that the fact that you moved one of the briefcases off the stage initially does not affect the contents of the briefcase, and does not affect the probability that it contains $1 million.

Can someone please put this issue to rest? I feel like an idiot for asking this question, but no matter how much I argued, they kept insisting that I was wrong.

[/ QUOTE ]

Copernicus
05-09-2006, 08:02 PM
[ QUOTE ]
In economic terms, it depends on your level of "risk aversion." In other words, the unbiased, "rational" choice might not always be the one that gives you the most utility, given that you might be so averse to risk that the chance of losing the money offered would not be worth it.

[/ QUOTE ]

Whats interesting is that the link in the post after yours (and maybe still immediately before this), cites studies that show that utility itself changes over relatively short time frames, and contestant behavior varies based on whether they lost large briefcases early in their game or not.

It would seem to have application to poker. A player who has lost early might be more inclined to gamble later, even if hes already recovered his early losses.