Conjecture and Question

[Mason Malmuth]

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

[sirio11]

This has been discussed in the past, and I for one, believe this is true. I came up with one example

in this thread

to try to prove why doubling your chips = doubling your expectation can not be true, but the discussion died in that time with no clear answer.

[ZeeJustin]

This just seems obviously true.

1) Every chip you win in a tournament is less valuable than the chip before it.

If your equity is 40k at the start, that does not even come close to implying that your equity at any point is $4 per chip. I think this is obvious, but if needed I will explain this further.

The 40k equity you start with, that includes play for the whole tournament. For example, maybe you make blind level X 60% of the time. Doubling your chip stack will obviously not double your chances of getting that far.

Also, since you are better than the field, it is safe to assume that you will double up early on more than 50% of the time. If this is something that happens more than 50% of the time, and your resulting equity is 80k, that means your starting equity would have to be more than 40k. This logically doesn't follow since the 40k number is a given, therefore, the 80k number would be an overestimate.

I don't know if I explained myself clearly or not, I'll try again later if needed.

Edit: FWIW, even the 75k figure is an overestimate.

[Exitonly]

This is what Atticus was saying, and also what TPFAP says.. the more chips you have the less each are worth.

I think i agree with this, because i think the closer you get to being knocked out, the more important each chip is.

bleh i'm tired, i'll reply to this again in the morning.

[Pat Southern]

The reason I always assumed this to be true (not sure if it is correct) is because when you assume you have a 40k equity at the start of the tournament because you have a certain probability to finish in every position (ie an A% chance to finish 1st, B% to finish 2nd.... X% chance to finish in Xth place) doubling up does not double the probability of each occurrence. Although your % chance to finish in 1st place may be 2A% (it could be more or less than double also), other money finishes will not neccessarily double, and may decrease to make up for your increased likelihood of finishing higher. Not sure if this is correct but thats why I there is a diminishing return of chips. However, as the tournament field increases, I think the gain in $EV increases as well.

[shaniac]

[ QUOTE ]
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

[/ QUOTE ]

When I double up early (not sure why you say "very unusual"), my expectation actually MORE than doubles.

Just one of the benefits of not being a math guy.

[Oatmeal]

***Feel free to disregard this post. I know it is rambling, but I believe I have a better chance of learning something here for having engaged the problem.***

Bravo, Shane, and for what it's worth (not much I'm sure)I agree, but in this hypothetical I am... "a great tournament player. Perhaps one of the best."

With this as the given my instincts tell me doubling on the 1st hand certainly couldn't have more than doubled my expectation and it is probably a bit less than double due to my believing that each chip I win is worth less than the one before.

A guesstimate would put my new expectation between 72500 and 77500, but that is just a feeling which I'm sure doesn't help with Mason's question all that much. Really interested in seeing some more of these replies.

-sloth

[El Diablo]

[ QUOTE ]
When I double up early (not sure why you say "very unusual"), my expectation actually MORE than doubles.

[/ QUOTE ]

I think Mason was just saying you suck at poker, shaniac.

[sirio11]

[ QUOTE ]
When I double up early (not sure why you say "very unusual"), my expectation actually MORE than doubles.



[/ QUOTE ]

Not saying that this happens to you Shane, but usually people saying this, just means they suck at short and middle stack play; so they say they play great with a big stack but most of the time it's just an ilusion created by the skill gap between the player's short and big stack play.

[CardSharpCook]

[ QUOTE ]
[ QUOTE ]
When I double up early (not sure why you say "very unusual"), my expectation actually MORE than doubles.



[/ QUOTE ]

Not saying that this happens to you Shane, but usually people saying this, just means they suck at short and middle stack play; so they say they play great with a big stack but most of the time it's just an ilusion created by the skill gap between the player's short and big stack play.

[/ QUOTE ]

LOL, I thought much the same. My eyes rolled when I read that claim. That someone could have enough skill to overcome the inate disadvantage of having a large stack, yet lack the skill to correctly use a small stack is a little silly.