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  #11  
Old 06-04-2013, 01:48 AM
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Originally Posted by The Chaperone View Post
Win-rate and variance are two entirely different things.
Yes I understand that, and unless we're careful about definitions "volatility" and variance are different things too. My point is that poker players tend to regard volatility emotionally as +/- wins/losses whereas variance occurs about a mean, unless it's being skewed by stop-win and stop-loss limits. Or, at the risk of cross-threading, by someone mashing MAX BET on a machine or going on monkey tilt at a poker table.

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  #12  
Old 06-04-2013, 09:19 AM
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Originally Posted by PokerKat View Post
Hmmm... Well you have the data and I don't, but on general statistical principles and assuming a winning player:

1. Short-stacking reduces your win-rate.

2. A lower win-rate means greater downswings, at least if we define a downswing relative to break-even rather than the variance about the mean.
A lower expectation with the same per-trial standard deviation does lead to greater volatility. But the standard deviation in short-stacking is lower, too. It's lower by a large enough margin to more than compensate for the diminished expectation when it comes to volatility.
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  #13  
Old 06-04-2013, 10:00 AM
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A lower expectation with the same per-trial standard deviation does lead to greater volatility. But the standard deviation in short-stacking is lower, too. It's lower by a large enough margin to more than compensate for the diminished expectation when it comes to volatility.
Actually, this is not entirely accurate. What is true is that bankroll requirements go up for people who have the same standard deviation and lower expectation, but that's not exactly the same as volatility.

Volatility is variance, just in a disguised form. People think of volatility as swings over the course of a day or a week or month, longer term, multi-trial variance. The deviation from expectation per some unit time. But this can just be determined based on single trial variance.

For the case of seeing why it is so obvious that short-stack PLO is less volatile than deep-stack PLO, consider the case of a 20BB player and a 200BB player. The maximum positive or negative theoretical outcome of the hand for the 20BB player is 10x less than that of the 200BB player on any given trial. But consider that volatility over a number of trials increases as the square root of N. Thus, the player with 20BB would have to get his stack in 100 times more frequently than the 200BB player to reach the same level of volatility, which I think anyone who has played PLO knows is far from the case for any competent player. Yes, you get your stack in a lot more as a 20BB short-stacker compared to a 200BB deep-stacker, but nowhere near 100x more. It's closer to 10x more, maybe 20x more for extreme cases.

What's interesting is that this continues to hold for larger and larger stack sizes. Yes, a 100 BB player gets his stack in more frequently than a 1,000 BB player, but 100x more frequently? Probably not. In all cases, playing deeper is more volatile. You may enjoy more EV the deeper you go, but you will have to deal with more volatility, too, though my guess is in the real world both of these quantities increase logarithmically if you assume you are in a good game and can get a good seat.*

This is a simplification and ignores all of the multi-way pots, but also all of the pots as I mentioned before where the deep-stacker gets more BB than the short-stack has in without himself getting his entire stack in, or how the deep-stacked player is going to play more hands in general. The point is that it should be intuitively obvious that deeper stack play in any NL or PL format leads to higher variance and, thus, higher volatility because you get diminishing returns on your EV as you continue to increase your stack and volatility of a multi-trial sample increases as the square root of the number of trials as compared to the variance of a single trial.

*In some games EV diminishes as stack size increases and your only hope of being +EV in the game is to play short. This occurs when the fish to your right has a short stack but the expert to your left has a deep stack. Depending on relative skill levels, it could even occur when both the fish to your right and the expert to your left are deep. You may still be better off playing short.
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  #14  
Old 06-04-2013, 10:22 AM
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Interesting, thanks.
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  #15  
Old 06-04-2013, 11:20 AM
WarDekar WarDekar is offline
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Yeah I agree with CM- as long as the relative skills of players are equivalent anyway.
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  #16  
Old 06-25-2013, 03:05 AM
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Short stacking is more volatile/higher variance if you measure variance in buyins instead of $. So the "short stacking" $300 at 5/10 is not the same as playing $300 at 1/2.

It seems obvious but this is likely what would make one think that "short stacking" is higher variance.
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