Re: Conjecture and Question
 

By the way, the easiest way to see that cEV does not equal $EV, even in a winner-take-all tourney, is to look at an extreme example. Let's say you're in a 100-person tourney, winner-take-all. Your skill is such that you have a 2% chance of winning (Twice the odds of an average player.)

On the first hand you're offered a 100-way allin, where you have precisely a 1.5% chance of winning. Furthermore, the other players won't take the bet unless you come along. Clearly this is a highly +cEV opportunity. It's even a +$EV play (meaning you'll profit over time from your buyin). However, based on your skill expectation, you should decline, as its $EV is 25% less than the $EV you'd get from playing. (This ignores hourly rate, of course, but you get the idea.)

Re: The Wotmog theory
 

Gregery,

I want to say that I think that according to this formula there are only two relevant values. The value of your chips, and the value of the chips you don't have. I guess you'd take into account someone like Negreanu in the field (IE, your chips worth less, chips you don't have are worth more), and that this value can obviously change throughout the competition. However, any chip you make is a chip you make, regardless of where you got it from. If you are in a field of 1000 players and you stack Negreanu, you probably will not be able to change the value of the chips you now hold because the difference in the field is basically unchanged.

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

That's how I think you should approach it.

This was a really really really really good post.

-Jason

Re: Conjecture and Question
 

[ QUOTE ]
Tiger Woods analogy....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. He is after all quite a bit better than even money to finish in the top 10. But it is also very early in the tournament.


[/ QUOTE ]

The problem with this analyogy is that in golf, once you finish one hole, the next one you start from scratch and you are both just as likely to get a good score as on the last hole.

But in poker, if you just doubled your chips, then you have more weapons in your arsenal. It would be more like if Tiger got an eagle on the first hole, then he gets to use 1 additional club in his bag until someone else catches up to him on the leaderboard.

Basically, having a big stack would not be any better if you just redeemed your chips at that point in time. But you don't -- you play on, and having a big stack ends up in reality meaning your ability to acquire more chips goes up faster than linearly.

-g

Re: Conjecture and Question
 

[ QUOTE ]
It would be more like if Tiger got an eagle on the first hole, then he gets to use 1 additional club in his bag until someone else catches up to him on the leaderboard.

[/ QUOTE ]

At the risk of sounding like a complete nit, I would like to offer that a better analogy would be he gets to play from the ladies' tees until someone catches up to him.

Re: The Coinflip Game!
 

[ QUOTE ]
Let's say instead of poker, you're playing the coinflip game. You have a really good coin that wins 60% of the time. This is where your edge comes from.

Your equity is 40k. 60% of the time, you will win your first flip and double up. 40% of the time you will lose your flip and be out.

Since your initial equity was 40k, your equity after the first flip (with undetermined results) will also be 40k. If you lose the flip, your equity is 0.
.4x+.6y = 40,000
x=0
.6y=40,000
y= 66,667

In this scenario, after your first flip, assuming you win, your equity is $66,667

Although this is not poker, the parallels to the given example should be obvious.

[/ QUOTE ]

I’m not sure I agree with this. If it’s early in a poker tournament, wouldn’t the correct analogy be “I’m going to flip my 60% favorite coin for 5% of my stack repeatedly with you, and after 100 flips, lets see what the average chip count is for both of us”?

I don't think you can just freeze your equity at one point in time because you are not accounting for your future chip stream in that model.

For example, let's say you and I invest in 2 companies. They are worth $100 now. Your company earn $1 a year, mine earns $2 a year. After one year (ie. flip), you've made $1 and I've made $2. But you can't then say that your That doesn't mean our equity in the companies is now $101 and $102.

-g

Re: The Coinflip Game!
 

[ QUOTE ]
[ QUOTE ]
Let's say instead of poker, you're playing the coinflip game. You have a really good coin that wins 60% of the time. This is where your edge comes from.

Your equity is 40k. 60% of the time, you will win your first flip and double up. 40% of the time you will lose your flip and be out.

Since your initial equity was 40k, your equity after the first flip (with undetermined results) will also be 40k. If you lose the flip, your equity is 0.
.4x+.6y = 40,000
x=0
.6y=40,000
y= 66,667

In this scenario, after your first flip, assuming you win, your equity is $66,667

Although this is not poker, the parallels to the given example should be obvious.

[/ QUOTE ]

I’m not sure I agree with this. If it’s early in a poker tournament, wouldn’t the correct analogy be “I’m going to flip my 60% favorite coin for 5% of my stack repeatedly with you, and after 100 flips, lets see what the average chip count is for both of us”?

I don't think you can just freeze your equity at one point in time because you are not accounting for your future chip stream in that model.

For example, let's say you and I invest in 2 companies. They are worth $100 now. Your company earn $1 a year, mine earns $2 a year. After one year (ie. flip), you've made $1 and I've made $2. But you can't then say that your That doesn't mean our equity in the companies is now $101 and $102.

-g

[/ QUOTE ]

Your analogy does not apply. I am factoring in future scenarios, while you are not. I am including the original 40k estimate in my formula, while you are not using any such original estimate in your formula.

Re: Conjecture and Question
 

Hi,

Your conjecture that expectation does not double even though your chip count has is true and is probably understated. It’s more likely that twice the chips has the same EV for a player early on, than twice the EV.

Every players plot of EV to chips is going to have several characteristics that are identical.
1) EV(zero chips) = 0
2) EV (55M chips or 100%) = $7.5M or 100% of the chips
3) EV(chips) is a convex function: this is intuitively obvious since the payout structure is goes to the top 10% in increasing amounts, chips won at the end are much more valuable in $ than chips won in the beginning (percentage wise). The proof for this is like the proof for iso-utility lines in economics.

The implications are far reaching:

1) Players EV functions are ALWAYS convex, if they weren’t they would cross other players EV functions at some point and the better player would have lower EV for the same number of chips.

2) All players are below the WOTMOG line ~ 1 (for large field size). Definition of convex. This implies that even the greatest player in the world; lets say Greg Raymer, has an EV less than $1363 with a stack of T10,000 at the beginning of the tournament. (based on 55M chips and $7.5M 1st place.)

3) Somewhere around the bubble is where the slope of the convex function > 1 for most players when chips won are more valuable than chips lost EV(2XT) > 2 X EV(T)

Maybe someone talented with math can draw some graphs.

Re: Conjecture and Question
 

Quick aside....

It seems pretty obvious that in a winner-take-all tournament with Mason's parameters, as

total_prize_pool --> $40,000 ==> value_of_doubling_up --> $0,

but isn't it also true that as

total_prize_pool --> $INF
==> value_of_doubling_up --> $40,000 ?

My point is just that Mason's conjecture may seem intuitively correct because $40,000 equity in a $10,000 buy-in seems like a large edge.

What seems intuitively correct to me is that your expectation comes closer and closer to doubling as your edge represents a smaller and smaller % of the winner-take-all prize, no matter how huge that edge seems relative to the buy-in.

Re: Conjecture and Question
 

If your expectation did not go down, then you could theoretically keep doubling up and end up cashing 4x the tournament prize pool. The smaller field and the closer to the money, the less your expectation increases with each chip.

Everett

Re: Conjecture and Question
 

Quick (& extreme) counter example-

Let's say you're playing heads-up and you both put in $50 and play winner takes all. Your opponent is stronger than you, so his expectation is $70 and yours is $30. You double-up the first hand. Now your $EV went from $30 to $100 in one hand (over 3x$EV, by doubling).

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?

Re: The Wotmog theory
 

[ QUOTE ]

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


[/ QUOTE ]

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.

My most convincing argument yet
 

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...

Re: The Wotmog theory
 

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?

Re: Conjecture and Question
 

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.

Re: Conjecture and Question
 

[ QUOTE ]

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?

[/ QUOTE ]

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.

Re: Conjecture and Question
 

[ QUOTE ]
[ QUOTE ]

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?

[/ QUOTE ]

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.

[/ QUOTE ]

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.

Re: Conjecture and Question
 

[ 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.

Re: The Wotmog theory
 

[ QUOTE ]
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?

[/ QUOTE ]

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.

Re: Conjecture and Question
 

[ 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.

Re: Conjecture and Question
 

[ 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.

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 ]

It really is a shame that people blatently ignore your posts. Although, I am not sure you arent, in fact two different people. The guy who writes gems like these, and the guy who throws out short phrases about being a "push-monkey".


anyway, NP

Re: Conjecture and Question
 

[ QUOTE ]
[ 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 ]

It really is a shame that people blatently ignore your posts. Although, I am not sure you arent, in fact two different people. The guy who writes gems like these, and the guy who throws out short phrases about being a "push-monkey".


anyway, NP

[/ QUOTE ]

I don't understand how your equity is only $1300. This is based on multiplying the first prize by your percentage of chips in play? But you are playing for the entire prize pool. Could locutus or someone else explain?

Re: Conjecture and Question
 

Hi Everett:

What you say is also easy to show late in a tournament because of the impact of the prize pool. But here I'm talking about the very first hand.

Best wishes,
mason

Re: Conjecture and Question
 

Hi Don:

First off, and I didn't state this in my original post, I do agree that a marginal player's expectation will behave differently from that of a very good player. I'm only interested in what happens to the EV of a very good player when he doubles his chips early on.

Best wishes,
Mason

Re: Conjecture and Question
 

Hi ilya:

The problem here is that in the two person tournament doubling up is impacted by the end game -- the tournament is over. In my question, the impact of the endgame is negligible (I think).

Best wishes,
Mason

Re: Conjecture and Question
 

Hi TV:

I don't think so. Using Harrington terminology, there is no question that when your M is 10 you have playing advantages over opponents whose M is 5. But when your M is 80, I don't believe you have any advantages over someone whose M is 40.

Best wishes,
Mason

Re: Conjecture and Question
 

Hi locutus:

I just read your post quickly. While I agree with what you say, that effect should be negligible right at the beginning of a tournament. late inb a tournament it should be huge, but my question concerns the first hand.

best wishes,
mason

Re: Conjecture and Question
 

Hi Atticus:

Your example may not be relevant since it effectively ends the tournament. In my question knocking one person out and you having double the chips really has no impact.

best wishes,
mason

Re: Conjecture and Question
 

Hi Atticus:

Great post. At the very least I think this is part of the answer.

best wishes,
Mason

Re: Conjecture and Question
 

[ QUOTE ]
Hi TV:

I don't think so. Using Harrington terminology, there is no question that when your M is 10 you have playing advantages over opponents whose M is 5. But when your M is 80, I don't believe you have any advantages over someone whose M is 40.

Best wishes,
Mason

[/ QUOTE ]

Sure he does. For one thing, a guy with an M of 80 can stack a guy with an M of 60. 40 can't. I'm not saying it's necessarily a big advantage, because it doesn't come up often, but it is an advantage.

Edit: A second point I think is important, which someone else made, is that the larger stack is further away from having to worry about going broke. Because he's betting less valuable chips, he's freer to make close chip EV+ plays.

Of course, whether to take a 50/50 to double up early is a key part of the question. I don't have answers, just thoughts. Good thread.

P.S. This has definitely been talked about here a few times before. Still a good revisiting of it.

Re: The Wotmog theory
 

Hi eric:

Great post.

Best wishes,
mason

Re: The Wotmog theory
 

Hi Zoot:

I disagree. To play a successful "big stack game" you need opponents whose stacks are starting to put them in jeapordy (but not yet tiny). After the first hand of the tourney, this won't be the case.

Best wishes,
Mason

Re: Conjecture and Question
 

[ QUOTE ]
Even though chips were issued at a 1chip = $1 scale, they don't pay that way.

[/ QUOTE ]


This is why.


It doesn't need to be big and mathematically funky, with odd proofs and analogies.


edit: make it a SNG. You go all-in with all but one other player and win....you have 9 tenths (or 8 ninths) of the chips but only a max of one half of the prize pool equity (actually a bit less).

Reedit: Doh! one half not one third.

Re: My most convincing argument yet & the \"time\" factor
 

After pondering this some more, I think the Finance Equation for Future Value is more applicable in a winner-take-all type of format where cEV is closer to $EV at the end of the tournament - because getting all the chips does not get you all of the money in most large MTTs where the winner usually only gets ~25% of the prize pool.

I think the Future Value formula might have some merit when it comes to projecting the size of ones stack say mid-way through a tournament, but once the blinds get bigger and the pots get bigger and variances get larger and the payout get nearer - I think it loses most of its validity.

In other, more simplified words, we can use the FV equation for cEV but not for $EV.


One other factor that has not been mentioned yet is the 'time' factor. In a MTT, it is the person who lasts the longest who wins the most money - and the longer you last the more money you make. By having more chips, you not only have the big stack benefits already mentioned, but you also have more 'time' - time to survive, time to wait for better situations or bigger hands, time to setup plays, time to change gears, etc. Note that in the FV equation the n - factor is the number of periods. In an MTT this could be hands, levels, hours, or whatever - but the more periods you are alive for and the larger your stack and the larger your growth rate - the larger you future stack should be and the more money you should make.


So how does all this relate to Mason's question - I think that by doubling up the first hand you can more than double your chip expectancy for midway through the tournament, but I don't think that it approaches doubling your $ expectancy at the end of a tournament.

It would be interesting if we hand enough hand histories, to figure out at what point a player doubled his initial stack and how that actually relates to his $EV.

Re: Conjecture and Question
 

The great player’s increased expectations implies that he will, over a sufficient sample set of tournaments, increase his chip count faster than an average player. Therefore, during the early and middle stages of a tournament, he is expected to have a larger than average stack. Doubling through an average stack will result in a stack that is still less than double his expected stack at that stage of the tournament.

Steve

Re: Conjecture and Question
 

My post will contain random statements. They might mean abosoluely nothing.

1)lets suppose that everyone has 10k, the blinds are 50k-100k with 10k antes, the pro has an expectation of 10k.
lets suppose that everyone has 10k, the blinds are 500-1000, the pro has an expectation of 13K.

2)lets suppose that everyone has 10k, the blinds are 25-50 the, pro has an expectation of 40K...however the pro will only have 39.96K of expectation if he folds the first hand, after every hand the pro expectation decreases a tiny bit unless he increases his stack.

3)lets suppose the pro can win 50 chips in every 25-50 hand he plays with a stack of 10k. Its obvious that the pro will be able to win >50 chips in every 25-50 hand with a stack of 20k.( unless nobody has more than 10k)

IMO the flaw in everybody who agree with the statement is theyre not taking into account the loss on the pro expectation after every hand that goes by without chip profit.( im talking about early stages )

Re: Conjecture and Question
 

I've tried to read everyone's posts, and I'm gonna try to throw in my own thoughts on this.

My thesis here is: After the tournament starts, there's no way to know what your expectation is. I think once you make your judgement at the start of the tourney, that's all you have, and obviously that's shaky in itself, here's why I think this:

1. I look at trying to re-evaluate your expectation as analogous to the comment I occasionally see fish make. You're both all in preflop, you have Ak and he has a pair, you hit your A on the river. The fish says "nice river", or "river saved you". We all know this isn't the case, you had 5 chances to hit and you did.

I think this is the same as the situation we're talking about. Before the tournament starts, you somehow made a judgement as to your expectation, which theoretically should have considered every possible outcome. On avg, you expect to be up x amount. Doubling up in the first hand should have already been considered as one of these. You can't make any sort of new judgements, because you already have. I think you're basically being results oriented when you start trying to re-evaluate your expectation.

So basically what I'm saying is, this specific outcome doesn't matter.

2. I like the Golf analogy. However, I'd like to make a football analogy. Similar, but a little distinct, and a little more extreme, and therefore I think fits better.

Pretty much any football game, the halftime score isn't that important most of the time. That is, if you tell me USC is beating Bama by 7-0 at halftime, you're basically telling me *nothing* about the outcome. I'd say this is probably going to be the case up to around a 17 point difference. Witness UT coming back against LSU this year, and UT has had a horrible season.

So, what I'm saying is, doubling up early on is pretty useless. I mean, it's nice, it feels good, but ultimatly, in the grand scheme of information that you're talking about, it's really not important, at all. Anything could happen, the next hand you could lose with AA against AK AI PF. You could get moved to a table with all pros and be at the ONE table without bad players.

If say in the first 5 hands you have doubled up each time, yeah, then it starts to matter. But until you can really say you have a *dominating* chip stack, I dont think your expectation changes significantly. Having twice everyone else's stack just isn't that big a deal. Things will be evened out in an hour.

3. Furthermore, I think expectation calculations are pretty much useless. As they say in commercials for mutual funds, past performance does not indicate future success. but nevermind that, even if your ROI is a certain number of a lot of tournaments, I just view it as useless to try to calculate expectation. You play the best game you can and hope to do well.

Re: Conjecture and Question
 

Hi Mason:

[ QUOTE ]
Hi TV:

I don't think so. Using Harrington terminology, there is no question that when your M is 10 you have playing advantages over opponents whose M is 5. But when your M is 80, I don't believe you have any advantages over someone whose M is 40.

Best wishes,
Mason

[/ QUOTE ]

I strenuosly disagree with this. If nothing else having and M of 80 allows you to win twice as many chips as a player who's M is 40. Also, while this might not make itself apparent in any individual hand, the player with an M of 80 will be able to play more speculative hands until the blinds go up or his stack bleeds away than the player with the M of 40 will. So, he in effect has twice as many opporunities to flop a big hand and win a big pot and further grow his stack. Those are the two issues that come to mind immediately but there may be more.

Best wishes,
Mike

Re: The Wotmog theory
 

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.

Re: Conjecture and Question
 

[ QUOTE ]
Hi Atticus:

Your example may not be relevant since it effectively ends the tournament. In my question knocking one person out and you having double the chips really has no impact.

best wishes,
mason

[/ QUOTE ]

It says little about your particular problem, that's true. I just use it to illustrate the notion that the relationship between your stack size and your $EV is not a straight linear one, even in a WTA tourney.