Response to Sklansky's article "Chips Changing Value in Tournaments"

[mornelth]

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but is the bullet that lets you make a peripheral assault *marginally* more valuable than the last bullet you have in your gun with the bad guy bearing down on you?



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If I have a chance - I'd rather NOT be in a situation where I have 1 bullet and a bad guy charging on me since there's always a possibility of a misfire. I'd rather have a TON of bullets to be able to take multiple shots around the corner (or whatever). If I get lucky - I'll shoot the guy before he gets close, if not - I'll save the last bullet...

In that sense having a LOT of bullets has value.

Ok, getting away from the bullets - as I stated elsewhere, and you yourself did - there are a LOT of excellent tournament pros these days that are much more aligned with Snyder's tournament strategy. Therefore there MUST BE something valueable in ideas presented both in Snyder's articles and the book.

I think it would be to the benefit of all readers to try and emotionally detach themselves from PESONALITIES involved and actually evaluate for themselves the ideas presented and decide how/if those ideas should affect their tournament strategy. I fully subscribe to the idea of Chip Utility Value and I do a lot of my thinking of tournament situations and moves and such in terms of CUV. Actually, anyone who ever said or thought something like "Fold, you still got a playable stack" is doing the same thing without CONCIOUSLY recognizing the fact that they are considering CUV of the situation rather than just cEV.

FWIW - I do believe that Snyders articles have more emphasis then necessary on DISPROVING any or all ideas expressed or held by MM and DS alike.

[jackaaron]

But, if you want to prove people wrong who think mathematically, you have to provide them with the math that will show them that they are wrong. Thus far, Snyder has not provided that to Mason or David. If he wishes to disprove their theories (which some people disagree with since Mason and David didn't start with a tournament mentality, but a cash game mentality, and obviously those are two separate and different games), he will have to show how their math is wrong. Other than that, he's just p'ing in the wind.

[mornelth]

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But, if you want to prove people wrong who think mathematically, you have to provide them with the math that will show them that they are wrong. Thus far, Snyder has not provided that to Mason or David. If he wishes to disprove their theories (which some people disagree with since Mason and David didn't start with a tournament mentality, but a cash game mentality, and obviously those are two separate and different games), he will have to show how their math is wrong. Other than that, he's just p'ing in the wind.

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What I get from the article is that Snyder thinks that the MATH is right - the PREMISES upon which the math is based are WRONG, or at least not applicable to real-world tournaments of today.

How do I explain this.

If I have 10 apples and I give you 4 of them, I'll have 6 left. However, since I do not like you (for the purposes of the example) - I'm not going to give you any apples, so at the end of the day you go hungry, even though the math is perfectly correct.

[BigAlK]

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But, if you want to prove people wrong who think mathematically, you have to provide them with the math that will show them that they are wrong. Thus far, Snyder has not provided that to Mason or David. If he wishes to disprove their theories (which some people disagree with since Mason and David didn't start with a tournament mentality, but a cash game mentality, and obviously those are two separate and different games), he will have to show how their math is wrong. Other than that, he's just p'ing in the wind.

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If Snyder's goal is for DS and MM to come out and say, "you're right, we're wrong" then I doubt that's going to happen under any conditions, with math or without.

I'm not a mathmetician, however my day job (that I'm ignoring right now [img]/images/graemlins/wink.gif[/img] ) is in software development. Mathmatical proofs, testing, and attempting to consider all possible scenarios is my normal mode. However I was struck by this statement near the beginning of Snyder's article:

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Mathematicians want to put numbers on everything. As a professional gambler, I understand the desire to figure out things like odds, advantages, and probabilities. But just because we may want to come up with these numbers doesn’t mean we should find some way to force them when there is no practical and accurate way to generate them.

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IMO modeling all the relevant factors in a poker tournament would be akin to building a weather prediction model (remembering to factor in the butterfly that causes the tornado that's always mentioned in chaos theory discussions). The considerations that go beyond the current hand or even the current street on the current hand are real, but tough to put an accurate number on their impact.

For an example of a concept that is tough to put a number on read the "Hammer of Future Bets" chapter of NLHT&P. In the example you think you might have the best hand on the turn (top pair, king kicker) however your opponent could possibly have a hand that you're way behind and unlikely to catch up (a straight or set are both possible). The chance that to get to showdown you'll have to call both this bet and a larger river bet make this a difficult situation. If your opponent's turn bet put him all in this would be an easier decision. This "hammer" is obviously an example of the utility value of chips that Snyder discusses. I assume that David believes this hammer has value since it is discussed in a book he co-authored. But how do you put a number on the value of your opponent's hammer (or the value of having the hammer if you're the opponent)?

Al

[Shandrax]

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I think players that adhere to Snyder's strategy, and 2+2ers should play in Trout like tournaments on Stars which would prove once and for all.....absolutely nothing.

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A lot of excellent tournament players from 2+2 play very much the strategy that Snyder advocates.

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Absolutely true and I'd say Fossilman is a prime example for it. Anyways, arguing with David Sklansky about poker, math or logic is not something I would like to do for a living. You simply gotta know when you are outmatched.

The only compromise I see here would be to acknowldege that Snyder's style of play is specifically designed to exploit the 2+2 style of play. This doesn't mean that it's a correct way to play by itself. If everyone would play like that it couldn't work, because they would push each other all-in with random hands. It's only correct if your opponents stick to the gap concept and let you get away stealing more than your fair share of pots. Reminds me of some sort of prisoneer's dilemma where one guy is constantly cheating the other guy and the other guy let's him always get away with it, because he sticks to certain principles.

[BigAlK]

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The only compromise I see here would be to acknowldege that Snyder's style of play is specifically designed to exploit the 2+2 style of play.

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It's designed to exploit tight play. Mason has said numerous times that 2+2 doesn't recommend tight play so that ain't gonna happen.

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This doesn't mean that it's a correct way to play by itself.

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Any style that maximizes your expectaton against the mix of players you're playing against is correct. Any style that doesn't isn't correct (or at least isn't most correct). No style is the "correct way to play by itself" under all conditions. As with lots of poker decisions the optimal style is always situational and therefore the answer as to the optimal style to play is "it depends."

[trojanrabbit]

To me this seems like the right strategy for the wrong reasons. The reason that a big stack is valuable is because you can waste a few chips and it won’t affect your equity. If we assume that as our stack gets bigger, each chip becomes less valuable, our equity will look like this as a function of chips.

If we accept Snyder’s view, that each chip becomes more valuable as our stack gets bigger, our equity will look like this.

If that were true, Snyder should be advocating careful, cautious play with a big stack since each chip is so precious that we shouldn’t be throwing them around at stacks who don’t value their chips as much. If a small stack doesn’t value their chips as much (since each chip is worth less in a small stack) they should be eager to play against the big stack. Just doesn’t make sense to me. The reason a big stack can be a bully and push everyone else around is because of the small value of chips to the big stack. He can spew a few chips and he won’t slide down the equity curve that much. If Snyder were correct then a big stack losing 100 chips would be a bigger loss to that stack than a small stack losing 100 chips. What?!?

Naturally you don’t have a smooth equity curve at any case when you get down to just a few blinds, but there has to be some relation that holds true for bigger stacks. Look back a Snyder’s curve that is continuously sloping up. Where does it stop? Your stack can’t be worth more than 1st place prize. But think about it. Snyder says that chips having more value in a bigger stack is true even if everyone is equal skill. That means that at the start of the tournament everyone has an equity equal to an equal share of the prize pool. And the slope of the equity curve at the starting point must be 1:1. If the equity curve actually slopes up, like Snyder says, then that means the slope must always be >1 with a larger stack. That means your chips will equal the value of the first place prize before you have all this chips!

Tysen

[mornelth]

Neither is correct, IMO.

here's my version :



When you are SEVERELY shortstacked your chips have very little value.

As you get more and more chips their value increases (and along the steepest portions of the curve - it increases MORE than just the straight-up dollar value). As you go upwards through Harrington's zones and you add more and more options to what you can do wit your stack - the value of your stack grows.

Later in the graph (when you have a LOT of chips) - you will eventually reach the point where ADDITIONAL chips have little value BY THEMSELVES, they only add value to you because you can afford to lose a coinflip with a smaller stack without significantly impacting your chances of winning or you can slow down and wait if the cards / conditions do not cooperate.

[BigAlK]

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here's my version ... <graph>


When you are SEVERELY shortstacked your chips have very little value.

As you get more and more chips their value increases (and along the steepest portions of the curve - it increases MORE than just the straight-up dollar value). As you go upwards through Harrington's zones and you add more and more options to what you can do wit your stack - the value of your stack grows.

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As a believer in Snyder's contentions this graph is almost exactly what I've envisioned. Although he hasn't made it clear in his articles it isn't possible for the value of chips to increase indefinitely since the total valuation of all chips, regardless of how this valuation is derived, can't exceed the amount remaining in the prize pool. The added utility of additional chips past a certain point is marginal, however this point is fairly high in comparison with other stack sizes. At a minimum, for those who agree with mornelth's graph, I wouldn't expect the chip value increase to slow down significantly until you're at least the chip leader at your table (possibly chip leader of the tournament).

[Mason Malmuth]

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Mathematicians want to put numbers on everything. As a professional gambler, I understand the desire to figure out things like odds, advantages, and probabilities. But just because we may want to come up with these numbers doesn’t mean we should find some way to force them when there is no practical and accurate way to generate them.


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Hi Al:

This statement of Snyder's is very inaccurate and he knows this. First off, the type of theory that all of gambling comes under is statistical. Again, going back to my Gambling Theory book, here's a quote from page 12:

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Incidentally, and this is important, all successful gamblers are statisticians, not mathematicians.

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This is from the essay titled "Non-Self-Weighting Strategies." It shows why mathematical thinking is wrong and why a different type of statistical thinking is correct.

Best wishes,
Mason