Poker Essays by Mason Malmuth

[gtrunner57]

I noticed that on page 88, Malmuth writes "Even though it is true that the standard deviation is larger in no-limit hold'em, the real expert will also have a much larger win rate, meaning that he probably won't need as much money to ensure survival."

However, Malmuth's formula for a bankroll requirement as a function of standard deviation and win rate on page 59 has the standard deviation being squared over the win rate. This would imply that the standard deviation has a larger effect on the bankroll requirement, assuming similar changes in standard deviation and win rate.

I have been very impressed by the analysis and reasoning that Malmuth uses throughout his arguments in <u>Poker Essays</u>. I am just trying to figure out his reasoning on this issue. Is it because the standard deviation does not increase very much compared with a large increase in win rate when comparing limit to no-limit hold'em? Even if it does not increase proportionally as much, any increase would seem to have a large effect since the standard deviation itself is much larger than that of win rate.

I am hoping for someone to clear this up for me. Thanks for any replies.

[npc]

[ QUOTE ]
I am just trying to figure out his reasoning on this issue. Is it because the standard deviation does not increase very much compared with a large increase in win rate when comparing limit to no-limit hold'em? Even if it does not increase proportionally as much, any increase would seem to have a large effect since the standard deviation itself is much larger than that of win rate.

[/ QUOTE ]

When I made the move from playing predominantly limit games to no-limit, one thing that was a big shock to me was how *low* my standard deviation was in big bet games. So, my short answer to the question you pose in the second sentence is, "yes".

Here are some real examples from my own records. My hourly standard deviation playing 9-18 limit Hold'em in 2002 was very similar to my houly standard deviation playing 2-5 NL Hold'em in 2005 (within 20%). My hourly earn rate in the 2005 2-5 NL games was about 45% higher than it was playing 9-18 limit in 2002.

Issues regarding poker popularity, relative skill of opponents, sample size, etc. all have an effect on this data, so this single example cannot be considered conclusive. Nonetheless, I expect that many big bet players' records would produce qualitatively similar results. In any case, my results certainly support Mason's assertion.

[uDevil]

Unless Mason himself responds, you are more likely to get good mathematical responses in the probability or theory forums, where pzhon, BruceZ, AaronBrown, et. al. may see it.