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Poker Efficient Frontier

poker

YES – it actually exists! At the beginning it was a jaw-dropping, but then I realized that I have looking for this so it was kind of expected. Damn, it is still cool! Stop the geeky excitement and go step-by-step!

If you do not know/remember what the Efficient Frontier is, here is the sum from Wiki:

The efficient frontier is a concept in modern portfolio theory introduced by Harry Markowitz and others. A combination of assets, i.e. a portfolio, is referred to as “efficient” if it has the best possible expected level of return for its level of risk (usually proxied by the standard deviation of the portfolio’s return). Here, every possible combination of risky assets, without including any holdings of the risk-free asset, can be plotted in risk-expected return space, and the collection of all such possible portfolios defines a region in this space. The upward-sloped (positively-sloped) part of the left boundary of this region, a hyperbola, is then called the “efficient frontier”.

Markowitz_frontier

I got some historic data from a friend of mine that is working on really cool poker-related project (cannot tell what though, unless you are investor) and jumped to check if Efficient Frontier exists in Poker and found that giving Nobel Prize to Markowitz was really a good idea.

I’ve taken the history of games (hundreds of thousands) for many of top players, calculated their annual average weekly profits & stddevs (from what I call “The production stage”) and plotted one versus another. This is what I’ve got:

poker efficient frontier

poker efficient frontier – each letter is player; Y-axis is Average Weekly Gain (in %); X-axis is Standard Deviation of the gain

If you would think about it, this is kind of expected since there are players that got higher stdev (take more risks by their nature/game strategy) than others and good players succeed to leverage this risk  into higher gains. Most of year-by-year movement of players was towards lowering the risk (and profits) – we all become more cautious with the time )))

Beautiful.

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