parappa
09-05-2004, 04:19 AM
I'm going to do my best. I think this issue gets hinted at from time to time on the single table board, but ignored because either 1) the answer is obvious 2) it's seen as the mournful lament of a player on tilt (which is probably true) or 3) no one knows.
Anyhow, here's my best formulation:
It seems to be true that a good player has a positive expectation over bad players at the low limits but that low limit ring games have a high variance because of the way in which low limit players play. So, a good player can be expected to win at a certain rate, but can expect bigger fluctuations in his bankroll than a player with the same advatange who is playing in a lower variance game. To achieve the same results in a higher variance game a player's bankroll must be larger in order to withstand increased fluctuations. But, if his bankroll is long enough he will withstand the fluctuations and ultimately have a positive expectation.
First attempt to ask the question: Can't certain SNG structures invoke the other half of that idea? If his bankroll is too short, he may often at some point go broke before his results begin to conform to his expectation. And since SNGs are independent trials, doesn't it make more sense to think of SNGs in terms of a series of independent "lifetimes" in which a player could possibly play on a series of short bankrolls, but his results could never "even out" over time? In the context of SNGs, it doesn't matter if his chip count over all the SNGs evens out, it matters how many times his bankroll gets to zero chips, because when that happens, he's out, and the cards breaking even later won't rescue that result.
Next Try: Take, for instance, an SNG in which each player starts with 100 chips and blinds start at 10/20. Does a good player actually have the same positive expectation over his opponents that he would in an adequately bankrolled ring game? He may have the same theoretical positive chip expectation against a group of bad players over a long series of trials, but an SNG is an independent series of short run trials. If a player ever loses more than 100 chips, he's out. While with an unlimited bankroll he'd win, but doesn't the variance of typical low-limit play, coupled with a series of artificially short bankrolls and the "go broke-you're out" structure make it just as likely that he will hit zero chips and lose, over and over again, until his results become just slightly better than random, his ability to take higher EV bets with his cards "watered down" (for lack of a better term)?
In this situation, can't increased variance actually decrease overall profitability? If so, wouldn't there have to be a combination of SNG structure and player profiles which must be inherently unprofitable?
Next attempt: Chip EV and Tournament EV are not always the same thing. Mustn't there be a threshold where variance, although not affecting chip EV over all the hands in all the tournaments, can, due to the independent nature of the "go broke, you're out" nature of SNGs, reduce Tournament EV from positive to negative over many tournaments?
Next attempt: It is commonly said that your variance will be higher at party but that if you are playing your cards better than your opponents, your results will even out over time. But does this actually make sense? I understand that your "lifetime chip count" will even out over time, but I don't see why this assumption applies to a series of tournament results. I think that if the same phenomenon is true, it needs a stronger explanation than the one relying on chip variance that makes sense in ring games.
Anyhow, that's three tries at it. Does anyone know the answer to this? Please tell me if you do; I really don't know how to even think about it. /images/graemlins/smile.gif
And if the way that I've put the question doesn't make any sense, please tell me that and I'll try again. /images/graemlins/smile.gif
Anyhow, here's my best formulation:
It seems to be true that a good player has a positive expectation over bad players at the low limits but that low limit ring games have a high variance because of the way in which low limit players play. So, a good player can be expected to win at a certain rate, but can expect bigger fluctuations in his bankroll than a player with the same advatange who is playing in a lower variance game. To achieve the same results in a higher variance game a player's bankroll must be larger in order to withstand increased fluctuations. But, if his bankroll is long enough he will withstand the fluctuations and ultimately have a positive expectation.
First attempt to ask the question: Can't certain SNG structures invoke the other half of that idea? If his bankroll is too short, he may often at some point go broke before his results begin to conform to his expectation. And since SNGs are independent trials, doesn't it make more sense to think of SNGs in terms of a series of independent "lifetimes" in which a player could possibly play on a series of short bankrolls, but his results could never "even out" over time? In the context of SNGs, it doesn't matter if his chip count over all the SNGs evens out, it matters how many times his bankroll gets to zero chips, because when that happens, he's out, and the cards breaking even later won't rescue that result.
Next Try: Take, for instance, an SNG in which each player starts with 100 chips and blinds start at 10/20. Does a good player actually have the same positive expectation over his opponents that he would in an adequately bankrolled ring game? He may have the same theoretical positive chip expectation against a group of bad players over a long series of trials, but an SNG is an independent series of short run trials. If a player ever loses more than 100 chips, he's out. While with an unlimited bankroll he'd win, but doesn't the variance of typical low-limit play, coupled with a series of artificially short bankrolls and the "go broke-you're out" structure make it just as likely that he will hit zero chips and lose, over and over again, until his results become just slightly better than random, his ability to take higher EV bets with his cards "watered down" (for lack of a better term)?
In this situation, can't increased variance actually decrease overall profitability? If so, wouldn't there have to be a combination of SNG structure and player profiles which must be inherently unprofitable?
Next attempt: Chip EV and Tournament EV are not always the same thing. Mustn't there be a threshold where variance, although not affecting chip EV over all the hands in all the tournaments, can, due to the independent nature of the "go broke, you're out" nature of SNGs, reduce Tournament EV from positive to negative over many tournaments?
Next attempt: It is commonly said that your variance will be higher at party but that if you are playing your cards better than your opponents, your results will even out over time. But does this actually make sense? I understand that your "lifetime chip count" will even out over time, but I don't see why this assumption applies to a series of tournament results. I think that if the same phenomenon is true, it needs a stronger explanation than the one relying on chip variance that makes sense in ring games.
Anyhow, that's three tries at it. Does anyone know the answer to this? Please tell me if you do; I really don't know how to even think about it. /images/graemlins/smile.gif
And if the way that I've put the question doesn't make any sense, please tell me that and I'll try again. /images/graemlins/smile.gif