How bout An Actual Poker Problem

[David Sklansky]

This was posted elsewhere but I've gotten curious as to what the analysts on this forum would say about the following words regarding no limit holdem tournaments that have gotten down to two equally skilled players with highly unequal stacks.

Those who are not fully familiar with expert holdem strategy need not feel that they are disqualified from the discussion.

"An equal-skill tournament analysis would lead us to believe that if only two players remained at a final table, with one player holding 90% of the chips and the other holding 10%, the player with 10% would still have a 10% chance of winning the event. In fact, if these players were flipping coins to determine the winner, that would be true. But it’s not true if the player with the bigger chip stack is a skilled tournament player who understands how to use his chips. In this case, the player with only 10% of the chips has almost no chance of winning, even if that player with 10% of the chips matches the skill level of his opponent.

We saw a perfect example of this in a televised final table a few years back, when Paul Phillips and Dewey Tomko were heads up at the end, with Phillips holding most of the chips and Tomko extremely short-stacked. Hand after hand, Dewey Tomko pushed all-in, doing his best to give himself at least a coin-flip chance of winning. Unfortunately for him, Paul Phillips had so many chips that he didn’t have to flip coins. He just let Dewey take the blinds until he found a premium starting hand, then he called Dewey’s all-in bet. It’s not a coin-flip situation if one player is betting everything on any two random cards and the other player is playing selective strong hands. Dewey had almost no chance of winning this tournament against Phillips’ strategy. And I’m not criticizing Tomko’s all-in-on-every-hand strategy. In fact, with his desperately short chip stack, this was his most intelligent strategy. He knew he had second-place prize money locked up if he ended up with zero chips, and he knew his short stack chips weren’t worth squat. But he had no intention of waiting for premium cards—a strategy that would almost invariably lead him to going out with a whimper. He could not afford to give up the blinds, nor could he afford to play poker. His chips had no utility value at all, and the poker skills he possessed were crippled without the chips to play."

[madnak]

Sounds good to me. A lot of things are like that. It would depend on the function, but even something as simple as utility=(stack size)^2 would result in this kind of scenario.

I don't have any clue what the relative utility function might actually be, I'm neither an advanced player nor a tournament player.

[FortunaMaximus]

Disqualified for this one. Steamroll principle. Thanks for the invite.

[IronUnkind]

David:

I don't play tournaments very often, but the quote is obviously false. I'll let others elaborate.

[Darryl_P]

If it's true that the low stack couldn't afford to lose blinds, then the blinds must have been a reasonable chunk of his stack. In that case, it would be a huge mistake for the large stack to wait for a premium hand.

In any case, if I were in a heads-up situation at the end of tournament, I'd like to have the writer of this piece as my opponent.

[Phil153]

Let me preface this by saying I know virtually nothing of tournament strategy. That said, the quote is completely false, and even manages to contradict itself, saying:

[ QUOTE ]
In fact, if these players were flipping coins to determine the winner, [the 10%-90% chance rule] would be true."

[/ QUOTE ]

If the players are equal skill, then the contest is essentially a series of coin tosses.

<u>Looking purely at the chance of doubling up vs the chance of losing, the tournament is identical to one where they both start with equal stacks of the short stack's size.</u> Thus, with equal skills, and if the short stack is a fearless opponent who understands tournament strategy, the short stack has a 50% chance of doubling up, which he has to do slightly more than 3 times to win. This gives the short stack an almost exactly 10% chance of winning.

For people who can't see this, let's examine a few scenarios.

1. Where the the blinds are large relative to the short stack.
In this case, then the optimal strategy is pushing almost every hand. The big stack cannot afford to wait, and must call fairly often, meaning he will never have greater than an average of about a 60/40 advantage each time he calls. Combined with the average extra blinds picked up the short stack, this means that the short stack has to win about 3 of these in a row, which is 6.4%. Of course, after winning two (&gt;16%, probably 20ish with the extra blinds), he is on equal footing with the big stack, and should abandon the pushing strategy. So the number here is damn close to 10%. On the other hand, if the big stack does wait for a better advantage (AA,KK,QQ,JJ), the short stack will on average grow a significant amount before and between showdowns, necessitating only 1.5 70/30 matchups to be on equal footing.

2. Where the blinds are small relative to short stack
In this case the short stack shouldn't push every hand. But once again, if the players are of equal skill, the short stack has a 50% chance of doubling up and a 50% chance of losing his remaining stack. Looking purely at the chance of doubling up vs the chance of losing, the tournament is identical to one where they both start with equal stacks of the short stack's size. So, his chance of doubling up twice (25%) puts him on a nearly equal footing with the large stack, and the chance of winning is 10%

CONCLUSION: The author of the quote is clearly wrong.

[Phil153]

holy crap, just read the original thread. The confusion in that thread is amazing.

[fluorescenthippo]

[ QUOTE ]
Hand after hand, Dewey Tomko pushed all-in, doing his best to give himself at least a coin-flip chance of winning. Unfortunately for him, Paul Phillips had so many chips that he didn’t have to flip coins. He just let Dewey take the blinds until he found a premium starting hand, then he called Dewey’s all-in bet. It’s not a coin-flip situation if one player is betting everything on any two random cards and the other player is playing selective strong hands. Dewey had almost no chance of winning this tournament against Phillips’ strategy.

[/ QUOTE ]

based upon this description it sounds like dewey had a much higher than 10% chance of winning. unless you are leaving something out, phillips was playing far too tight, lowering his 90% chance to win. or maybe its just a bad example idk.

it should be more like a coinflip situation if played corectly. paul should still be pushing allin with the same percentage of hands dewey is since the effective stack is obviously the same. this will reverse the 40/60 edge the pusher may have when called and average out to a 50/50 flip.

so basically, phillips should still be "flipping coins" by making unexploitable pushes and calls, he is just less likely to bust first.


edit: im also assuming at least one shallow stack here based upon the description

[David Sklansky]

"holy crap, just read the original thread. The confusion in that thread is amazing."

Feel free to go over there and tell them what you think.

[FortunaMaximus]

[ QUOTE ]
holy crap, just read the original thread. The confusion in that thread is amazing.

[/ QUOTE ]

Yeah, and it was a fun thread. /images/graemlins/tongue.gif

[PrayingMantis]

This is wrong.

[r3vbr]

often if the big stack waits more than 1 or 2 hands for a "premium hand", the blinds the small hand will win will be significant in relation to his stacksize

in FT HU situations its rare to fold over 2 hands in a row to this strategy..

this cant be right David..

[wheeler]

David,

You cover this in one of your books (don't remember which one). Suppose two players both use the same strategy and this strategy is independent of their stack size. Then each player's probability of winning is in proportion to his/her stack size.

The part in bold is important. For example, suppose both players use the following strategy:

If I have less than half the chips, fold; otherwise go all-in.

Then they are "equally skilled players", i.e., they're both pretty dumb, but now the player with more than 50% of the chips wins with probability 100%.

But what about two good players? Unfortunately, it's also not true that the optimal strategy is independent of stack size. For example, imagine two players are playing a hand of heads-up hold-em with blinds $1 and $2. In one case they start with stacks of $2; in the other, with stacks of $2000. The optimal strategy in the two cases is different.

What is true, however, is that the optimal strategy depends only on the size of the smaller stack. This reinstates the conclusion in your book: If two expert players ("expert" in the game-theoretic sense, not in the sense of a poker pro!) are playing heads-up, then each player's probability of winning is proportional to their stack size.

[SNOWBALL]

Am I the only one that has a feeling that the author of this piece plays martingales?

[FortunaMaximus]

[ QUOTE ]
Am I the only one that has a feeling that the author of this piece plays martingales?

[/ QUOTE ]

lol. Tried a fibonacci variation once. Silliest thing I ever did.

[valenzuela]

"An equal-skill tournament analysis would lead us to believe that if only two players remained at a final table, with one player holding 90% of the chips and the other holding 10%, the player with 10% would still have a 10% chance of winning the event. In fact, if these players were flipping coins to determine the winner, that would be true. But it’s not true if the player with the bigger chip stack is a skilled tournament player who understands how to use his chips. In this case, the player with only 10% of the chips has almost no chance of winning, even if that player with 10% of the chips matches the skill level of his opponent."


This is false, lets play HU poker I start with 10x the BB u ( yes u!) start with 90x the BB, what odds do you give me?
I havent played poker in 8 months, I beated the 22 SNGs and I once won a 200 ppl 10 dollar buy-in tournament.

I think I can get to 3% chances of winning by simply using a push/ fold strategy.

[soon2bepro]

I'm almost sure it's a false statement, because:

Yes the large stacks selects hands so when they do play, it may be 80-20 or whatever, but they're NOT playing every hand, and meanwhile the short stack's stack keeps growing. Unless both player's M are ridiculously high (even when one of them only has 10% of the chips in play) in which case it's very wrong to be going all in on every hand.

[valenzuela]

[ QUOTE ]
I'm almost sure it's a false statement, because:

Yes the large stacks selects hands so when they do play, it may be 80-20 or whatever, but they're NOT playing every hand, and meanwhile the short stack's stack keeps growing. Unless both player's M are ridiculously high in which case it's very wrong to be going all in on every hand.

[/ QUOTE ]

QFT

[Jim T]

That can't be right, because Doyle Brunson was heads up a couple of years ago with a huge chip lead vs some bearded guy (Skanski or something?), and ended up losing.

The fact that Doyle didn't use the author's prefered method (even though he ultimately lost) would seem to put the kibosh on the theory also. Is Paul Phillips so much more skilled than Doyle that he used an almost unbeatable strategy that Doyle wasn't aware of?

[51cards]

It was sort of said just a few posts ago, and should have ended the thread I think.

Neither player has the ability to wager more chips than the small stack has. So as far as the play of one hand is concerned their options are identical. If they are playing the same strategy it's totally coinflips.

End thread. Right?

[Jim T]

[ QUOTE ]
It was sort of said just a few posts ago, and should have ended the thread I think.

Neither player has the ability to wager more chips than the small stack has. So as far as the play of one hand is concerned their options are identical. If they are playing the same strategy it's totally coinflips.

End thread. Right?

[/ QUOTE ]

While the author was wrong, he is talking about the two players playing DIFFERENT strategies. Short stack is going all-in about every hand, while the big stack is waiting on a big hand.

[David Sklansky]

"While the author was wrong, he is talking about the two players playing DIFFERENT strategies. Short stack is going all-in about every hand, while the big stack is waiting on a big hand."

But he was claiming they were both right in using those strategies. Anyway its over now. When it comes to poker, or general gambling concepts it is obvious that Snyder should not be taken seriously

[Victor]

someone link original thread pls?

[FortunaMaximus]

[ QUOTE ]
someone link original thread pls?

[/ QUOTE ]

Link (http://forumserver.twoplustwo.com/showflat.php?Cat=0&amp;Number=7764649&amp;an=0&amp;page=0#Post 7764649)

It's a long read though.

[siegfriedandroy]

[ QUOTE ]
"While the author was wrong, he is talking about the two players playing DIFFERENT strategies. Short stack is going all-in about every hand, while the big stack is waiting on a big hand."

But he was claiming they were both right in using those strategies. Anyway its over now. When it comes to poker, or general gambling concepts it is obvious that Snyder should not be taken seriously

[/ QUOTE ]

do you disagree with much of his blackjack stuff? i used uston apc back in the day, but i know snyder was well respected among top bj players. probably the next book i would have read (had i not abandoned bj for poker /images/graemlins/smile.gif) was his shuffle tracking work, which wong's site recommended. never did learn to track well, but was dam good w/ uston's system. won 12 of my last 15 trips to vegas- s.d. smiled on me. well enough about my broken blackjack dreams /images/graemlins/smile.gif good luck w/ snyder, DS! jk peace