Optimal Strategy for "Deal or No Deal?"

[Runner Runner]

Yes, people would definitely have more propensity to gamble when they are dealing with a range of cases from $500 to $100K then they would if they had the million case and a few small amounts.

It makes sense that the banker offer would have to be higher to offset their willingness to gamble even though the a zero EV offer would be the same no matter what the circumstance.

[RoundTower]

[ QUOTE ]
I was watching this show earlier this week and noticed that they are now offering more then the fair value of the suit cases for the last 2 offers. For instance, there were 3 suitcases with $500,000, $50,000 and $500, and the offer was over $200,000. Then the offer when there was just a $500,000 and $500 suitcase would of been $300,000!

I would die laughing if a contestant denied one of these ridiculously good offers which not only mitigate risk, but actually have better expected value then the worth of the prize. Now that would be a true gambler.

[/ QUOTE ]
It would be best to turn down one of these "ridiculously good" deals if you expect that the banker will offer you an even better deal with two cases left.

[greg44]

Don't you just add up all the $$$$ and divide by the # of suitcases??? And if the offer is over this # you accept, if it isn't you decline and keep playing?

[Lottery Larry]

I saw this reply by vox, down in the thread:

"One major thing that the above does not consider is the effect the worst case scenario has on the deal. For example, a deal based soley on EV would yield the same for cases totaling $1 million and change, regardless if the cases were the million and lesser amounts, or $500K, $400K, $100K and lesser amounts.

However, picking the $1M case in the former is MUCH worse than picking the $500K case in the latter. On Monday's U.S. episode, where the guy won the most money on the show ever, one deal seemed to consider this. "

I've been driving myself crazy trying to figure out the logic of the low banker offers:

1) Most of the offers, up until the final few suitcases are left, are nowhere NEAR the average case value. Big-time -EV

2) From what I've calculated on the fly over the last few shows I've seen, the offers aren't close to the expected EV even after adjusting for the expected picks that would occur AFTER you turn down the offer.
I've watched a few shows in the last week, and unless my calculation estimates are wrong, the banker is NOT trying to create an offer that is close to the average value if you say "no deal" and then have to pick 4 more cases.

Meaning, the shadow banker isn't calculating "if they turn down this offer, the expected average is $X, so this offer can be %Y lower than $X or Z% lower than the average $/case at the moment"
... and then making an offer close to that calculation.


3) Even paying the million dollars isn't going to put the show in the red- I'm SURE the advertising more than covers any prizes paid out, especially since most people take vastly lower prizes than they should.
The only way the show should EVER have to pay the million is if they have:
- a LAG maniac addicted to the rush, OR
- a situation when the last 2-3 cases are all $300K+ and the player is willing to gamble, knowing that his worst-case scenario is pretty darn nice.


So, is the banker strategy centered around FORCING the players to keep playing, since the odds are the costs won't go up that much with the average $/case... and the show would suck if it went "pick 8 cases, take offer"?

Or are they discounting the even-value offer, knowing that most people are going to fear risk-of-ruin more than loss-of-EV and take cheaper offers?

Or a combo of both?

My wife and I have been arguing about what deal to take (the bald guy's run last night, when he cost himself 190K, scored some points for me), and trying to estimate what the banker's offers are going to be is driving me NUTS!

[gusmahler]

[ QUOTE ]
Don't you just add up all the $$$$ and divide by the # of suitcases??? And if the offer is over this # you accept, if it isn't you decline and keep playing?

[/ QUOTE ]

From a pure math standpoint, you're right. But this isn't math, it's money. As posted earlier, someone had a choice between $75 case, a $1 Million case, and a $355k offer. Obviously, the deal is bad from a math standpoint. But wouldn't $355k make enough of a difference in your life that you would take the $355k deal instead of the chance to "win" $75?

[Scott_Baio]

[ QUOTE ]
[ QUOTE ]
Don't you just add up all the $$$$ and divide by the # of suitcases??? And if the offer is over this # you accept, if it isn't you decline and keep playing?

[/ QUOTE ]

From a pure math standpoint, you're right. But this isn't math, it's money. As posted earlier, someone had a choice between $75 case, a $1 Million case, and a $355k offer. Obviously, the deal is bad from a math standpoint. But wouldn't $355k make enough of a difference in your life that you would take the $355k deal instead of the chance to "win" $75?

[/ QUOTE ]

http://forumserver.twoplustwo.com/showfl...amp;Search=true

[Nottom]

The correct solution to the game depends entirely on whatever your personal marginal utility function for money would be. i.e. how much each additional dollar is worth given how much money you already have. Some people have already alluded to this. For example:

[ 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 ]

If you want to play strictly by +EV than your utility function would just be x.

For most people however 500k isn't twice as valuable as 250k so we use a function to illustrate this point. As a simple example lets assume you have a marginal utility function of f(x)=x^(2/3) so now f(500k)=707 and f(250k)=500 so 500k is worth about 1.4 times as much as 250k. This should be somewhat reasonable for a typical person but will obviously vary based on your own personal value of money.

So now when faced with an offer you can figure the EV of your marginal utility.

For example:

The Bank offers $112k with the following cases remaining:
$1, $300, $10000, $200k, $500k

The True EV is $142060 so as normal its about 20% too low.

Instead of finding the true EV instead find the Marginal EV:
(f(1)+f(300)+f(10k)+f(200k)+f(500k))/5 ~= 255

Now compare this to the Marginal EV of the offer: f(112000)~=335

So based on this utility function you should accept the offer.

[WilliamLowe]

Just did the free one. Got down to 2 cases w/ values 500k and 1mil. The banker offered 532k??? NO DEAL! and I had the 500k case.