Re: The Wotmog theory
 

This is really well thought out. Curious though, why is it called "the Wotmog theory"? I tried googling it but didnt find anything so I'm thinking its just something you thought of?

Re: The Wotmog theory
 

Yes, I would also like to say, that was maybe one of the best posts I have ever read. It's up there with Shania. Really simple, really smart. It will help me out a lot.

-Jason

Re: The Wotmog theory
 

This post has been added to our "Anthology of Wisdom". Thanks to all who contributed. Mason, I know others would join me in thanking you for getting this going in the first place and hoping other thought provoking questions follow.

Re: The Wotmog theory
 

[ QUOTE ]
I just wanna chime in to repeat what has already been said (just because some people are prone to discount posts from "lesser-known" posters). Very nice post.

[/ QUOTE ]

I find interesting how we have came a long way since

this thread


If somebody dare to read that thread (I think it's a very good one), you'll find how I was critiziced for basically trying to prove what Mason is saying in this post.

I was a "lesser-known" poster then.

Re: Conjecture and Question
 

It depends on the expected number of hands played to the end of the tournament, but it would be a similar situation to buying in for the standard price, but getting double chips, and arriving one hand late, except everyone at the table has seen you play one hand.

Re: Conjecture and Question
 

i'm no mathguy, and i've only read the posts on the first page, most of which takes some effort to grasp.
However, this is my proof that your conjecture is right.
Say 100 entrants in tourney, so total chip value is $1.000.000 of which yours are worth $40.000. So, remaining 990.000 chips are worth $960.000. Then 10.000 chips you just won were only worth $9.697. You expect to handle them with 4x efficency, so $38.788+$40.000=$78.788

Re: The Wotmog theory
 

[ QUOTE ]
I find interesting how we have came a long way since

this thread


If somebody dare to read that thread (I think it's a very good one), you'll find how I was critiziced for basically trying to prove what Mason is saying in this post.

I was a "lesser-known" poster then.

[/ QUOTE ]

I'm still waiting for your reply to this post in that thread, sirio. [img]/images/graemlins/cool.gif[/img]

Later,
Che

Re: The Wotmog theory
 

[ QUOTE ]
This is really well thought out. Curious though, why is it called "the Wotmog theory"? I tried googling it but didnt find anything so I'm thinking its just something you thought of?

[/ QUOTE ]

You googled "wotmog"? LOL

No, I was just thinking of a name for my theory and I came up with the "Where'd the money go theory" (WTMG) and made it wotmog so it could be pronounced.

Thanks for the compliments, all. Glad I can contribute something back as I have gotten alot out of many of the posts I've read on the forum.

Re: Conjecture and Question
 

I am new to hold em and i am reading a few books by you .... this all seems greek to me with the expected chip value and convex ev and all this other stuff .... is this covered in books or is it common knowledge .... im curious to know

Re: The Wotmog theory
 

[ QUOTE ]
[ QUOTE ]
I just wanna chime in to repeat what has already been said (just because some people are prone to discount posts from "lesser-known" posters). Very nice post.

[/ QUOTE ]

I find interesting how we have came a long way since

this thread


If somebody dare to read that thread (I think it's a very good one), you'll find how I was critiziced for basically trying to prove what Mason is saying in this post.

I was a "lesser-known" poster then.

[/ QUOTE ]

Sirio, please let me know next time they get on you and I will beat them down!

Re: The Wotmog theory
 

[ QUOTE ]
I find interesting how we have came a long way since

this thread


If somebody dare to read that thread (I think it's a very good one), you'll find how I was critiziced for basically trying to prove what Mason is saying in this post.

I was a "lesser-known" poster then.

[/ QUOTE ]

am i the only one who sees a connection between this, and nobody great posting here ???


seriously guys, i've only been playing MTTs for a few months, but i've already made the decision to mostly just lurk now. i was already going to after my redzone math formula post got zero intelligent replies, but i thought i'd try one more time to approach the stack size theory in this post

i thought both topics were quite interesting, however nobody was interested at all in actually thinking about the ideas. all people want to do is make sarcastic, insulting remarks. and come up with horribly inappropriate annalogies to show how smart they are by proving others wrong. then when one of the "clique" leaders comes up with a witty (however faulty it may be) rebuttal, all the sheep jump on with the quote post. here's an idea. THINK FOR YOURSELf

if you insist on always being correct, and pointing out flaws in others' ideas without actually thinking about them, and thats what you all really want to do, then fine. continue to follow your heros' words as gospel, and viciously attack any new ideas that go against what the "top posters" say. just don't expect any independantly thinking, good players to stay here too long. ever.

Re: Conjecture and Question
 

Spee said: So let's say Tiger is roughly 2:1 or 2.5:1 to win the event (as he usually is rated by the bookies here in the UK). He then promptly goes out and eagles the first hole to take a two shot lead on the field. Does that increase his expectation? Maybe a little but not too much.


The Tiger Woods analogy holds up well. If Tiger eagles the first hole, it is already factored into his favorite status. An eagle with 71 holes to go should not affect anything. Similarly, a double-up, or even a triple-up early on should not affect expectation at all since top palyers are expected to double up several times thoughout the tourney. (I doubt they will get their stacks from 10K to 10 million, by just picking up blinds here and there.)

If anything, should a top player fail to double up fairly early (when the cannon fodder is still hanging around)his/her expectation should drop. I think we can all agree that it's easier to take chips from a decent amateur than from a world-ranked pro later on.

For what it's worth, that's my take, any comments?

Re: Conjecture and Question
 

I imagine that the 40K equity developed for the start of a tournament has taken into account occurrences of extreme variance, ie. Doubling up or busting out on the first hand. Therefore it is easy to assume that your equity will rise, but as far as it doubling is definitely an overestimate.

Re: Conjecture and Question
 

I am not sure about the first double specifically, but it seems correct since if you carry it out (if you somehow doubled up every hand) your expectation would decrease proportionally, since at the end you would end up with only a fraction of the money even though you had all the chips.

Re: Conjecture and Question
 

I would say it doesn't come even close to doubling.

While you, of course, need chips to play; the player's positive expectation is not due to the chips. It is due to his skill.

If his expectation were proportional to chips, then losing a quarter of his stack would decrease his expectation by $10,000. This is not the case. Again, his skill is the main difference here.

I would say that to double his expectation would require an increase in chips several-fold.

Re: Conjecture and Question
 

Suppose you are a great tournament player. Perhaps one of the best. You enter a $10,000 buy-in tournament and when the first hand is dealt, since you're such a great player your expectation is $40,000 even though you only have $10,000 in tournament chips. Now a very unusual first hand takes place and you double up. That is you now have $20,000 in tournament chips. My conjecture is that your expectation does not double even though your chip count has. So instead of having an expectation of $80,000 it may only be $78,000, or $75,000, or some other number less than $80,000, but it will definitely be less than $80,000.


Hi

Being English and new to tournament poker I have found myself thinking about this quite a lot so apologies if this is too long or is somehow a result of my complete poker ignorance. I just do not think the question has been answered properly, so I will have another go. I hope I am not covering ground that everyone has worked through before.

I can promise a small Tiger Woods analogy and Sir Isaac Newton gets a mention too.

The reason that I don’t think the question has been answered properly is that the conjecture mixes up two things – chips and expected value. They are very different things but we tend to use chips as a proxy for expected value in order to protect our sanity.

OK – we know that we start with $40,000 EV and $10,000 chips so clearly they are not the same. We get a transfer of chips to us of $10,000. Cool. We know where it came from – the first guy out of the tournament, the chips make it easy to follow the money – the total number of chips is unchanged and we know where they all are. Now the total expected value of all current competitors added together has also stayed the same (it equals the prize pool) but we don’t know where it all is now. We could try recalculating our EV but I think it is probably better if we look at it another way and try recalculate the expected value of all he other players and see what is left for us.

The poor sap who is currently wondering how to get to the car park without anyone noticing has generously donated to the remaining players all of his expected value. We have two possible extremes here. We could have just knocked out another great player with an EV of $40,000 or we could have knocked out some eccentric, rich (I wish) English bloke who has only ever played two online free rolls with an EV of approximately $0.01.

As the chips are not the EV – just a proxy for it – we know that the EV has not all just switched over to us – we do know though that the total EV remains unaltered overall.

Let’s start with the unluckiest pro ever. We have just knocked out one of the people we expected to take prize money – how cool is that? Our EV has gone up quite a bit - but so has everybody else’s EV. This guy, by the form book, was destined to be the nemesis for a lot of players and as he was at our table we were a prime candidate. Taking him out has helped everyone else at our table as well as us. Imagine it two of the best at your table – nightmare.

Ok we know that our EV has gone up but not by all of this guy’s $40,000 - the others in the whole tournie and the others at this table got some of the extra EV vested in him as a great player (as an aside maybe they are just getting back some of their EV that they lost the moment two superstars were seated with them).

Now let’s look at the English guys $0.01 of EV – where did that go? Well nobody much cares really but we do care where his chips went. They are with us. Lovely. I don’t think our EV has only gone up a cent, I think it is quite a bit more. We are now the table chip leader, we have in our stack the price of one bad beat. Fantastic. We can think about bossing the table and some of the EV from the other players near me has just come to me, more than this some of the EV from the guy who will join our table soon has come to me, and the guy we will be playing in an hour. Everyone really.

We can see how the proxy of chips measures the affect on everyone’s EV if we look at average stack size. Before the English guy left for the airport the average stack was $10,000 now everyone else has $10,000 and we have $20,000 – everyone else has a below average stack. This is a proxy measure of everyone else’s EV going down a bit. As the EV taken from the English guy was so insignificant this transfer of EV from everyone else is the more important bit here.

Ok to sum up – the total of chips and the total EV for all players remains the same. Some chips have moved in a very simple way but the EV calculation is much more subtle and complex and it has affected everyone in the tournie not just us and the guy with the red face.

Here is the Newton/Einstein bit. Instead of golf balls think about gravity.

The greater the mass the greater the gravitational force being applied to all other objects in the universe. In our case we have a closed universe of all the participants and their chips. When we got the extra $10,000 in chips our gravitational pull increased quite a bit having an effect on all other players and their chips – including a much greater affect on those closest to us.

When our closed universe was created we came to it with a greater gravitational pull than most because of our skill (density?), now we have more mass, more force. By beating an expert player we relieved some of the forces pulling on everyone else (and us) by beating Englishman the significant affect is just our greater pull on everyone else as we have a greater mass of chips.

There is also the whole Einstein time thing to ponder upon now that we have bent the space time continuum a bit (maybe another sleepless night) but for now what does this make me conclude about the conundrum……………. Well it might be right and it might not!

In general I think it is right that it will be less than $40,000 EV that I get from the $10,000 in chips. Certainly if the EV of the tearful one is only $0.01 I cannot possibly have gained $40,000 of EV. If however the one I knocked out was the absolute nuts the Tiger Woods circa 2000/2001 of poker then pheww how much EV did that guy have? Maybe I gained a bit more than $40,000 even when everybody else has had a bit of his EV too.

Ok I think that is about it except to say that I think the rules are a bit different for poor players. Let’s assume that the English guy won the first hand! Now he started out with $0.01 EV and by taking out the man with $40,000 he must have more than doubled his EV – he probably added more than $0.01 to everyone else’s EV too!

Anyway this may not have helped you but here in the UK it is nearly 2am and I need to stop thinking about this so goodnight.


PS Wotmog theory is, as of today, a google whack.

Re: Conjecture and Question
 

I think you conjecture is intuitively obvious, and almost certainly correct for reasons that others have no doubt stated.

However I think the key point is quantifying the effect. For instance is the effect so small that you should not change your strategy on account of it?

Computer simulation is a good way of getting a feel for things. I did some tests a while back although I assumed equal skill, maybe I will go back and rework them.

The other important question is what is our great player going to do if he gets knocked out of the tournament? Is there a great $500/$1000 NLH game to get back to? Are there several $10000 buy in comp starting online in the next few hours. In other words what exactly is your objective.

I think the question is dangerous, in the sense that a casual reader might get the impression your conjecture applies to them in the tournaments they typically enter. I think the TCEV<>$EV is the most abused concept in tournament poker.

Re: Conjecture and Question
 

I think you have supplied insufficient information to formulate a response to your hypothesis. How many seats (in addition to this one) does our hero have in the tourney? 3? 4?

Re: Conjecture and Question
 

<i>I think you have supplied insufficient information to formulate a response to your hypothesis. How many seats (in addition to this one) does our hero have in the tourney? 3? 4? <i>

It was not my hypothesis - I blame some Malmuth guy whose book of poker essays I am ploughing through for some light relief from Harrington doing my head in with hand scenarios.

My assumption is that it is a closed tournament - 1 seat per participant, no rebuys nadir.

Re: Conjecture and Question
 

Most of the comments agree with your assessment. And in a sense I do as well, although I doubt proof is possible. I would suggest that a portion of the original 30k extra equity has been realized in the first hand so the added value is slightly less than the initial buy in. The amount less would be based on the number of opponents. The new value would be 2 x (n-1)/n where n is the number of original participants. This assumes that the player was average. If the player was poor the value would be less because more of his buy-in was already included in your starting equity. If the player was better than you it would be greater (some of your buy-in was included in his equity). To tell the truth I think the ability to make more moves (and survive losses) as an early table leader more than compensates for one less bad player in the tournament. Therefore, double equity is a reasonable estimate.

Re: Conjecture and Question
 

I remember when this thread first came up. I didn't get it then, and really don't get it now. A lot of thought has gone into the replies of many.

Why?

I know I'm not very bright, and numbers isn't my bag, but to what purpose is even trying to figure out an answer? (Never understood the purpose of climbing Everest, either, but that's as close as some of the analogies I've read that make my hair hurt.)

Has anyone EVER won a tournament based on their EV before it began? If someone has a huge +EV before the tournament, should I be scared?

Re: Conjecture and Question
 

This may have been mentioned, but following the doubling chips = double expectations if you won all the chips what would your expectation be according to the formula? It seems your expectation would quickly be more then it's possible to win.

-f

Re: Conjecture and Question
 

How did Richas not get more response?

just looking at other players EV rather than your own was a great inuitive leap.

The rest of the post is just gravy. I mean clearly he's wrong about how much it matters to you about which guy you knocked out, but it's pretty clear proof that there are distinctly non-linear relationships between chips/EV/skill.

Re: Conjecture and Question
 

WTF

Re: Conjecture and Question
 

Why the bump? i know everyone has seen it, but i think we have a lot more to talk about.

Re: Conjecture and Question
 

[ QUOTE ]
I remember when this thread first came up. I didn't get it then, and really don't get it now. A lot of thought has gone into the replies of many.

Why?



[/ QUOTE ]

because if the chips are of a different value depending upon who has them then this should affect how you bet.

We can see this when the big stack is happy to call with rubbish as the consequences of losing to a 10bb push are so low compared to wiping the guy out and building the stack with the 10bb and the dead money.

That is later on but if the chips have differing values at the begining when everyone has the same number it could be that it is right to call the push from the best player in the tournie and take the coin flip but absolutely wrong for you to call a similar push if you are the best/better player.

Once the chips are in the middle they don't belong to either the good or bad player involved in the hand. The expected value they represent is different again. When the best player pushes pre flop and is called the extra ev in the chips he owns has changed, each chip is worth the same as the worst player in the world with the same hand it is only when the hand is resolved that the ev is known as either 0 or what the pot is worth in your stack.

Re: Conjecture and Question
 

I do not believe you can use a math model to determine if your expectation is more/less than double.
If you are a good player, who, when the *correct* odds of you placing in the top 3 of an event are X, you MUST increase your stack size as the tournament progresses, in order to retain that X expectation, just like everyone else has to increase their stacks.
There will be aberrations in the growth of your stack and the extremities of those aberrations will cause a temporal adjustment of X.
There is an IMMEDIATE and DEFINITIVE increase in table command, when the best player at the table, doubles his chips on the 1st hand.
When that situation occurs, the last thing on the player's mind: How much did doubling up just now, increase my X?

I may be simple minded........however..........I do not believe that MATH can be used to determine the odds of one's ability to place in the money when there are so many variables involved in a tournament.

Re: Conjecture and Question
 

[ QUOTE ]
I conclude that the one factor model (chips only) is inadequate to estimate EV, since we know a great players EV is about his/her long run ROI: lets say $40K.

If the EV of T10,000 starting chips must be below $1300 for any player, then other aspects such as skill, etc must comprise the remaining ~$40K. Some skills may be based on the quanitity of chips, but the main conclusion is still that doubling the stack size early does not affect EV that much. A first order affect on the additional EV of chips alone would be an increase of less than $1300 for T20,000.

[/ QUOTE ]

I believe that if Raymer, or any other intelligent pro, doubles his chips on the 1st hand, at a table of average players, that his EV increases by more, because his command of the table increases by more. I would think it would be less, only if he has stiff competition at his table.

Re: Conjecture and Question
 

[ QUOTE ]
Hi Everyone:

I have a conjecture that I believe is true and I have reasons for believing that this is true. But I'm hoping that others can explain the reasons a little better than I can, or perhaps explain why my conjecture is wrong. Here it is:

Suppose you are a great tournament player. Perhaps one of the best. You enter a $10,000 buy-in tournament and when the first hand is dealt, since you're such a great player your expectation is $40,000 even though you only have $10,000 in tournament chips. Now a very unusual first hand takes place and you double up. That is you now have $20,000 in tournament chips. My conjecture is that your expectation does not double even though your chip count has. So instead of having an expectation of $80,000 it may only be $78,000, or $75,000, or some other number less than $80,000, but it will definitely be less than $80,000.

So if my conjecture is correct, I would like to hear good reasons why this is the case. If it's not correct, I want to hear those reasons as well.

This should make for a good discussion and thanks in advance for the help.

Best wishes,
Mason

[/ QUOTE ]

Now I see that this was a trick question! You're asserting that the player expects to win $40,000.00 in the event.
You are saying he has $10,000.00 in tournament chips because that is what he paid for the T10,000.
It's obvious that everytime he doubles his chip count, his expected winnings is not going to double......even if he takes 1st place with all of the chips, he isn't going to get all of the money...........

All of those posts........in an attempt to make a trick question a logical one.

Re: Conjecture and Question
 

The total expectation of the entire tournament is $40K. The fact that you double the first time on the first hand instead of the 50th hand actually lessens you expectation for the entire tournament because as a better player you would be expected to have more chips to double with on a later hand.

Re: Conjecture and Question
 

yes its true mason you damn newb

Re: Conjecture and Question
 

Seems to me it's not that simple a model if you start considering the extreme possibilities. Yes, if you take the premise that more chips == less value per chip initially, that answers your question, but I think there is perhaps an effect where the more chips you acquire, the slower thr rate of value drop is.

Example:
10,000 chips, and chips are worth 1 unit each
20,000 chips, and chips are worth .9 unit each
30,000 chips, and chips are worth .8 units each? I doubt it (and that's without taking into account the use a good player can put a big stack to).

It's like a ski-slope graph perhaps, where the chip-value drop is fastest as you move upwards from 10K, but the chip-value drop starts to decelerate and then plateau the more and more you get.

Is there a point where you have so many chips you can just all-in with every hand and beat the field to death with that? (not necessarily by winning that much, but by inducing an all-or-nothing game from opponents, and eliminating players/allowing slightly bigger stacks to build, which you'll suck out eventually anyway...)? It certainly happens in STTs sometimes.

Maybe. And at that point the chips may even start appreciating in value, as the brute-force of your play draws the money to you, or to others who'll end up giving it to you...

At that point you've got a sort of bathtub effect in terms of chip value, with a big drop/rise at each end of the scale, and a valleyed plateau in the middle.

This is all stream-of-consciousness speculation though, and is probably way off beam. I'll think on it more, and return about it.

EDIT: Yes, I realise this doesn't address your questions at all.

Re: Conjecture and Question
 

I think its possible for your EV to up by more than double if the person you are doubling up on is most skilled.
heres an example:
1 players EV is 2
your EV is .8
and 4 other players ev is .8
so if everyone pays a 100 dollar entry fee, and strats with 100 chips. you should get back 80 dollars
but the pro whoose ev is 2 will get 200 dollars soooo
if you double up on him and knock him out at the same time and assuming everyone elses stacks stays the same. you have 33% of all chips in play, and everyone same skill you ev is now $198 which is more than double you starting ev.

Re: Conjecture and Question
 

If I have 10K, but an expectation of 40K, then the rest of the field's expectation must be collectively reduced by 30K. Whoever I double through is most likely someone with a below-10K expectation for two reasons.
1.Excluding me, the field is below average.
2.If this player was KO'd early on, it is more likely that they are a below-average player.
The gain in expectation--for me & for the field--can't be very large when dead money meets its inevitable end.

If I am so good that with 10K I have an expectation of 40K, aren't we basically assuming that I'll more than double up with great frequency? And when I do, won't I have to deal with a much greater proportion of Phil Ivey's than of Dmitri Nobles?

Re: Conjecture and Question
 

I'll have a stab at disproving it. Well, "proof" would be too strong a word, but anyways ...

This borrows stuff from eric and also richas and probably loads of others on various threads linked to here - I'm just trying to piece it together. Some of this also borrows from discussions on the STT forum.

I think the key is the skill edge. This will change when the stack sizes change - it will change because of our skill at playing different stack sizes against the stack sizes on our table(s), and because of the way in which other people respond to your stack size and how you play it (affecting your edge even if you are equally skilled with all stack sizes). It will also change relative to the field depending on who you knocked out. If I'm up against Ivey and Danneman and I get to choose who to take a coinflip against, I want to take Ivey out - the same applies when there are still hundreds of players left. So, theoretically at least, I think it is possible to more than double $EV early on by doubling your chips.

Last time I was around the STT forum there were similar discussions and talk of getting some data together and looking at the ITM/ROI stats for tourneys where people doubled up in the first couple of levels vs not doubling up so early - with a view to empirically determining how much of an edge you needed to take the coinflip. IIRC, there were some convincing arguments for calling as a slight dog, let alone a slight favourite. There were certainly posters with some data suggesting that doubling up early more than doubled their ROI, and for STTs that makes loads of sense (even without factoring in hourly rate, which is a more significant factor for an STT specialist I guess). I'll see if I can find any data on the forum, but it's such a different animal that it might not be useful for MTTs.

You'd need an awful lot of MTT data, preferably hundreds of tourneys for each player involved, to even begin to get an empirical idea - although it might be possible to categorise playing styles/strategy to group players in the hope of getting a big enough data set to test the idea that for at least some players doubling chips could more than double $EV - or showing that it probably doesn't.

It's also been pointed out that if you double up early on, you won't be eliminated on the next coin flip (assuming that your second opponent hasn't doubled up yet - and, erm, that you're offered a lot of coin flips for your whole stack early on - which would include making a 50-50 AI push/call on the river). If we take a really simplified game where the starting stacks are 10BB - and so it's just a pre-flop AI-fest from the getgo - then doubling up on a coinflip early on allows you to lose the next coin flip without being any worse off if you lose it than you would have been had you passed on the first coinflip. Assuming they're both 50-50s we have the same chance of donking out early regardless of whether we take both or only the second coin-flip. But if we take both we have a 1 in 4 chance to quadruple up, 1 in 4 to double up and 1 in 2 to donk out - the best case if we pass it up first time around is doubling up half the time.

Or think of it this way. We play a tournament where the button gets the first decision - push blind (without looking at the cards) or fold. If he folds, the player to his left gets to push blind or fold, and so on until someone pushes and nominates someone else to call them. You'd be nuts not to push AI every time you get the button - allowing yourself to get even slightly shortstacked would be a killer in this game - your only protection is having a bigger stack so that noone chooses to take you on.

So taking the first coin flip is like taking out insurance for the second - we're no more or less likely to get knocked out of the tournament this way, but we're in a much more favourable position on average if we take both (or, in fact, every opportunity where we believe we're a coinflip against their range, on any street). This might be another mechanism whereby doubling up could more than double $EV. Furthermore, if your opponents are taking coinflips and therefore cover you, you're more likely to get called in a close situation - meaning you're more likely to get knocked out and, if you win, you only got half as many chips off the opponent as you could have done had you also doubled up earlier.

Apologies for the ramblingness. Interesting thread (and links to other threads). [img]/images/graemlins/smile.gif[/img]

Re: Conjecture and Question
 

Surely your $40K theoretical equity at the start already includes the X% of the time you will double up?

Obviously your equity in this tournament goes up but not by much depending on what % of the time your $40k theoretical includes an early double up.

Re: Conjecture and Question
 

[ QUOTE ]
Surely your $40K theoretical equity at the start already includes the X% of the time you will double up?

Obviously your equity in this tournament goes up but not by much depending on what % of the time your $40k theoretical includes an early double up.

[/ QUOTE ]
Yes, but your equity calculation after doubling up excludes all the possible scenarios considered for the pre-tourney calculation where you did not double up and/or had donked out early, so it goes up a lot*. And your chip stack is not the only variable that has changed in the calculation compared to pre-tourney - depending on what happens to relative skill level and how play changes when there is a big stack hanging around.


* Mason's estimate was an upper limit of 70% probability that a top pro will double up at least once in any given tourney. So after doubling up, we get to eliminate 30% of the pre-tourney scenarios, all of which had $0 as the outcome. That is a pretty big difference!

Re: Conjecture and Question
 

E2A: In addition to losing the 30% of tournies where we never double up (EV=$0) we also lose the large percentage of tournies where we don't manage to double up until later when we're shorter-stacked relative to the blinds - while it's possible to do well from this position, we're much more likely to be crawling ITM or bubbling if we've been struggling to keep a shortstack alive.

If 15% of the field get paid and our hero cashes considerably more frequently than the average player and/or finishes higher when he does cash such that he earns an average of 4 buy-ins over all tournaments - eliminating the 30% + ?% of tournaments where he never doubled up or only managed it as a micro stack later on ...that really does suggest that expectation could more than double.

It seems much much more likely that LAGs could get a more than doubling of $EV compared to TAGs. The LAGs game is high variance, and as long as he has a +EV skill level the high variance is exactly what will get you the money in an MTT. Depending on the payout structure, you need to crawl into the money 10 times or more in order to get anywhere close to a single win or couple of high finishes. The LAG tries to eliminate those unprofitable crawl into the money finishes by taking risks to get a big stack in return for also busting out more often. It'd be interesting to see the stats for someone like Ted Forrest in terms of double up early% vs donk out early% and crawl into the money vs make the final table.

I'm sure this could be done with a computer simulation - different playing styles, %VPIP and skill edges to model what happens to a chipstack over time and what the final cash outcomes are. It'd be really interesting to compare a LAG style - smaller edges applied more often - against a TAG - bigger edges applied less often (preferably also modelling propensity to get called, I guess).

Re: Conjecture and Question
 

Let's do some math:

You have a function f with a variable x that represents your initial chip count and f(x) is your expected value. In your example you have f(10,000) = 40,000.

We know that every additional chip that you earn in a tournament has a little less value than the average value of your original chips, so the given function has the property: f(x1 + x2) < f(x1) + f(x2)

Now it's easy:
f(20,000) = f(10,000 + 10,000) < f(10,000) + f(10,000) < 40,000 + 40,000 = 80,000.