Conjecture and Question

[ericicecream]

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However, if you are three handed with Negreanu and he goes broke to a complete fish, the value of your stack goes up significantly.


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In the theory, this part should be covered under the "skill advantage" component of the formula, while the "value of the NON-YOU stacks" remains the same. Skill advantage is not a constant, as it would change depending on the remaining opponents and your skill advantage over them in particular. Your advantage over a field involving Negraneau is less than over a field involving the donk. The number of players remaining is a separate component but also taken into consideration in the formula, and is more important as the field thins out.

Also note the "big-stack" concept falls under this skill advantage component also. As you accumulate a big stack, your proportional skill advantage over your opponents should become greater in that situation if playing a big stack is something you do well.

[DonT77]

In Finance they calculate future value as such:

FV = PV x (1+K)^N

Where PV is the present value, K is the interest rate, and N is the number of periods.

Therefore it follows to me that if we double PV, and increase K slightly (due to big stack advantages) - we should get a FV that is more than 2 times our starting FV. (Of course this has limit due to the fixed amount of money in the prize pool.) Somebody please tell me why this shouldn't apply in the first hand of a large MTT...

[Snoogins47]

The one thing this thread brought to mine was my general thoughts I've had fuzzy in my head for some time, about chip value relative to the average stack, for want of a better, more accurate term...

For instance, I've heard analogies trying to explain a decrease in value the more chips you have, something like "when you have $10, finding $1000 is huge. When you've got $100 million, what's a few hundred thousand between friends?"

Take this scenario here though, where everybody at the table has 8kTC left.

Here, I would imagine that having any value >8k for your chip stack is worth significantly more than <8k, but I can't decide if this is a legitimate claim or not. For instance, if everybody has 8k and you have 3k, doubling up has a significant impact on your EV... but if you have 6k, doubling up now seems to provide a much larger boost to your EV: if I had to guess, I'd say it's significantly more than 2x the effect that the shortstack double up has, despite the fact that it's precisely 2x the chips gained. Surely, skill in playing a big stack comes into play, and I've often thought people put way too much faith in the "you gotta survive" mantra, but even having 8001 chips vs your opponent's 8000 would obviously boost the real-money expectation of a hand played for his entire stack, since when you have him covered, the worst case scenario (losing 8kTC) still carries a $EV that's in the black.

Anybody who has thought about this more than I have, or has more capacity with which to do so, have anything to add?

[locutus2002]

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.

[ilya]

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Okay you say, but the guy who started with an $EV of $70 can never get an $EV over $100 because $100 is the most he can win - so are we saying then that because a player is better his $EV can never more than double when his chip EV doubles - even in a 1000 person tournament with escalating payouts and given the advantages that a big stack has?

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Actually, yes, I think that's a very reasonable thing to say. If your skill-adjusted-$EV were to somehow more than double from a double-up, it would have to mean that your skill edge had proportionately increased. But that should not be possible, as the original skill-edge estimate at the beginning of the tournament already takes into account the likelihood of you doubling up & the resultant strategic advantages.
Maybe your unadjusted-$EV might more than double, but that's not your real $EV sorta by definition.

[LearnedfromTV]

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Okay you say, but the guy who started with an $EV of $70 can never get an $EV over $100 because $100 is the most he can win - so are we saying then that because a player is better his $EV can never more than double when his chip EV doubles - even in a 1000 person tournament with escalating payouts and given the advantages that a big stack has?

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Actually, yes, I think that's a very reasonable thing to say. If your skill-adjusted-$EV were to somehow more than double from a double-up, it would have to mean that your skill edge had proportionately increased. But that should not be possible, as the original skill-edge estimate at the beginning of the tournament already takes into account the likelihood of you doubling up & the resultant strategic advantages.
Maybe your unadjusted-$EV might more than double, but that's not your real $EV sorta by definition.

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Even if you would double up eventually, at every point in the tourney your expected chip total is now larger after the double up. i don't think it means your EV more than doubles, but the component of the EV equation that would value the chip accumulating potential of a skilled big stack player has to take into account that he now has that stack earlier, and therefore that he will have greater chip accumulating potential for longer. I think this can outweigh the decreasing marginal cash value of the chips, but it is a piece of the equation.

I like the idea of modeling equity with a logarthmic equation. In terms of relative tourney position, I think it is fair to say as a rough starting point that

10K stack:20K stack as 20K stack:40K stack. If A doubles through B, A becomes B and B becomes A...

This is more appropriate as the blinds get larger, when it is more likely that entire stacks will be on the line. As mentioned, an early double up creates a lot of dead chips in your stack, useful only as a backup plan that alows you to push small edges, but not really that useful (think about rebuy tournaments where you are the only one to rebuy immediately at your table. The chips are dead for a while with blinds that low and no other large stack (the rebuy mentiality of course affects your ability to bully in the rare spot where you could, but the point is those spots won't arise that often early).

Atticus posts on this have fleshed the idea out well, much better than i have attempted.

[El Diablo]

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

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

[Snoogins47]

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The one thing this thread brought to mine was my general thoughts I've had fuzzy in my head for some time, about chip value relative to the average stack, for want of a better, more accurate term...

For instance, I've heard analogies trying to explain a decrease in value the more chips you have, something like "when you have $10, finding $1000 is huge. When you've got $100 million, what's a few hundred thousand between friends?"

Take this scenario here though, where everybody at the table has 8kTC left.

Here, I would imagine that having any value >8k for your chip stack is worth significantly more than <8k, but I can't decide if this is a legitimate claim or not. For instance, if everybody has 8k and you have 3k, doubling up has a significant impact on your EV... but if you have 6k, doubling up now seems to provide a much larger boost to your EV: if I had to guess, I'd say it's significantly more than 2x the effect that the shortstack double up has, despite the fact that it's precisely 2x the chips gained. Surely, skill in playing a big stack comes into play, and I've often thought people put way too much faith in the "you gotta survive" mantra, but even having 8001 chips vs your opponent's 8000 would obviously boost the real-money expectation of a hand played for his entire stack, since when you have him covered, the worst case scenario (losing 8kTC) still carries a $EV that's in the black.

Anybody who has thought about this more than I have, or has more capacity with which to do so, have anything to add?

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After further thought, this is most probably wrong, with the caveat that for a very good player with a large edge, it may be closer to correct, since the value of still having 'some' chips is worth more to you than it would be to most others. Maybe.

[sirio11]

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



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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]

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



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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.

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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.