Thread: Variance
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Old 01-15-2007, 04:59 PM
sweetjazz sweetjazz is offline
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Default Re: Variance

[ QUOTE ]
Mike,

NL is only different because in most games a great NL player can have a much greater edge than a great limit player can. In the super high stakes NL games with all decent players, the great NL player's edge can drop to one more similar to a limit player's and then everything Gabe is saying is exactly the same for both players.

-DeathDonkey

[/ QUOTE ]

DD, there are two features about NL that make the associated variance different from limit. First, the unlimited betting tends to give the better player at a table a bigger edge. Thus a player's winrate at various tables would be more sensitive to who is playing at the table in NL than in limit. This works to the advantage of the very best players (who would keep bigger edges in NL than limit) and works against the very good players who insist on playing in bad games where the very best are sitting. In other words, it should be easier for a very good but not world-class limit player to minimize how much he loses to Schneids than it should be for a similarly talented NL player to minimize his losses to aba, and that's entirely due to the structure of the game being played. To this extent, aba's points have some more merit in NL than they do in limit games.

OTOH, the pots in NL get much bigger in relation to the blinds than in limit. If an optimal strategy requires taking/forcing a lot of coinflips (and I don't know enough about NL to speak with much, or even any, authority here), then the variance is going to be brutal. As the game evolves and toughens up, the edges may become small enough that luck is a major factor in who succeeds and who does not.

My basic intuition with regard to no limit is that in short stack games played close to optimally, the variance will be huge because aggressively jamming will be the best strategy. In bigger stack games, the best strategy is more likely to combine aggressive pot building and stealing with trapping, and I don't know how this compares with the possibility of the pots getting really big. (Note: All of the above is likely to be severely flawed thinking.)

As far as limit, the fact that large downswings can occur once your winrate drops to the 1 BB/100 or so area or below is mathematical fact. Indeed, in the limiting case where your winrate is exactly 0 BB/100, you would experience arbitrarily large downswings (and similarly arbitrarily large upswings). No matter how far down you were, if you kept playing long enough you'd eventually get back to even; conversely no matter far up you got, if you kept playing long enoguh you'd eventually drop below zero. This is the result of simple mathematical analysis of a random walk.
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