Geometric mean in poker?

[SwissPoker]

From "A Mathematician Plays the Stock Market":
John Allen Paulos states, that, given I invest amount P and double it 50% of the time and half it the other 50%, I'm expected to make 25% by arithmetic mean: [100% + (-50%)]/2 = 25%

He further states, that the most likely outcome is to break even and shows this by calculating the geometric mean, the square root of [(1+1)(1-.5)] -1 which results zero.

Has the geometric mean any relevance in poker (i.e. EV calculations)?

Thanks for your answer.

[Orlando Salazar]

Geometric mean is used to calculate PERIODIC "investment" returns over a finite horizon. For one EV calculation, it is irrelevant.
Anyway you must clarify what your period is. Are you calculating % returns per session, hand, 100 hands, week?
And what is your base? Is your initial investment your 100bb buyin, your bankroll, your s&g entry?
The best instance to use geomean is for s&g's or on your total bankroll. For a set of s&g's of varing buyin amounts, take a geomean using each s&g's individual ROI. Unfortunately, this seems meaningless. I just think in terms of opportunity costs. Either, i could make more/hr than a 9 to 5. Or if i invested my bankroll in govt bonds, which has a better modified Sharpe ratio: [Expected Return - Risk Free Return]/(Standard Deviation of Expected Returns - stdev risk free securities). FYI, S&P 500 has a sharpe ratio of ~.50.

[f97tosc]

While there certainly are some mathematical similarities between playing poker and investing, there are also some important differences. One significant difference is that when you invest the rate at which your asset grows is proportional to the magnitude of the asset, i.e., exponential growth.

In poker your win rate typically does not depend on how much you have in the bank, and so the growth pattern is not exponential. For this reason the geometric mean concept is less relevant. An exception could be if you change to higher and lower stakes tables depending on the size of your bank roll.

[kbinder]

I have this book, but read it a while ago. Can you give me the page number or chapter where you found this?

[SwissPoker]

It's in chapter "Average Riches, Likely Poverty" page 95-99.