[pzhon]

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Generally speaking, I am very surprised that so few readers are not deeply offended by, and rabidly opposed to, my assertion that EV alone is NOT the best basis for totally evaluating a given poker situation.

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You are attacking a straw man. The objections people have are not that E$ is the only thing that matters. There are contexts in which a different combination of E$ and risk is more appropriate than the Sharpe ratio. Please don't assume that anyone who disagrees with you is saying that only E$ matters.

The OP pointed out a context in which E$ is much more important than the standard deviation. As your bankroll grows, maximizing E$ is relatively more important than minimizing variance for the purpose of maximizing expected utility. If you are underbankrolled, you may want to be more conservative than the Sharpe ratio would suggest. According to polls, 2+2ers tend to be overbankrolled, so the Sharpe ratio should tend to overemphasize managing risk while underemphasizing E$.

Rather than consider only EV/SD, you can consider (EV^n)/SD. For any n, you get a risk vs. reward ratio, and only n=1 corresponds to the Sharpe ratio. The most appropriate n to use depends on both your Kelly fraction and your bankroll.

There are other objections to the Sharpe ratio, such as that the shape of the distribution of results about the mean matters. To a slightly favorable coinflip, it is possible to add a purely favorable gamble which decreases the Sharpe ratio because it increases the variance much more than it increases the expected value, e.g., a 1/1,000,000 chance to win $10,000 adds a penny to EV, but adds about as much variance as a coin-flip for $100. This might ruin the Sharpe ratio of someone crushing low stakes games, but it would be nothing to fear. Less obviously, buying lottery tickets is not the same as selling lottery tickets.

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“Poker plays are best evaluated on a risk-adjusted basis, rather than simply considering Expected Value alone.”

Don’t you find it kind of interesting that so few 2+2 readers are actually challenging this statement?


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Not really. Perhaps your expectations are off. You underestimated your audience.

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The player with the better Sharpe Ratio is the better player...

Finance guys know for a fact that Sharpe ratio, Sortino ratio and other reward/risk ratios ...


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Stop right there. If the Sharpe ratio is everything, why would there be other measures like the Sortino measure? The answer is that the Sharpe ratio isn't everything, which is intuitive for many poker players who don't know the finance terminology. The Sharpe ratio is inappropriate for many situations, such as the one the OP brought up. That strongly suggests that your assertion, that a better Sharpe ratio means you are a better player, is wrong.

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I assert that, if you choose to turn a blind eye to Sharpe and continue to play by EV alone, you are sure to be taking the worst of it relative to opponents who truly understand how to apply Sharpe’s work to poker.

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You are attacking a straw man. We aren't saying EV is everything. We're saying something more complicated that your assertion that the Sharpe ratio is everything.

It is possible to ignore the Sharpe ratio and not to be taking the worst of it in any serious sense. E$ is roughly zero sum, but variance is not. If I evaluate my risks in a different consistent fashion from the way you do, that doesn't mean I lose, and it doesn't mean you gain from playing me.