variance in $x/$y PLO vs. $2.5x/$2.5y CAP PLO

[pete fabrizio]

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you think wr will be lower in the smaller non-cap game?

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i'm saying that relative to the blinds, both your winrate and variance will be lower. so your wr at 10-20 might be like 8bb/100 with a sd of 80bb/100, while at 25-50 cap i would guess it would be more like 4bb/100 with a sd of 60bb/100. so the bankroll "requirements" of the smaller game would be $96,000, and for the bigger game would be $270,000. The Kelly criteria cutoff point would be around $161,000. however, if your winrate in the bigger uncapped game was also 8bb/100 with an 80bb/100 standard deviation, the bankroll "requirement" would be around $260,000, but the Kelly criteria number drops all the way down to $56,000. the moral of the story is that wr/sd is much more important when you're considering moving up and taking shots than sd alone.

[LA_Price]

Look I wouldn't use the kelly criterion to think about whether I should move up. There's alot of errors that could come to applying it to human decision making.

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The Kelly Criterion

From wikipedia:
The formula specifies the percentage of the current bankroll to be bet at each iteration of the game. In addition to maximizing the growth rate in the long run, the formula has the added benefit of having zero risk of ruin;

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Great certainty! Now I feel all warm and fuzzy.

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The formula will never allow a loss of 100% of the bankroll on any bet.

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True but who makes the decisions about how to bet?
People do, and if there's one thing that is certain that my opponents aren't playing off the assumtions of the Kelly criterion. Perhaps if I programmed a computer to play another computer I would use the Kelly criterion, but in human vs human competition I would think about where it fails to describe reality

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An assumption of the formula is that currency and bets are infinitely divisible, which is not a concern for practical purposes if the bankroll is large enough.

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Another of the hidden assumtions of the Kelly criterion is that each of the bets is independent. This would lead you to believe that your edge at any time is exactly the same. It is not. There are PLO games where if I had the option I would put way more on the table than the Kelly criterion suggests. Not because I think I'm that great, but because other people are making very big mistakes.

What I am saying is that average variance can be misleading. Comparing average variances may not give you a true comparison of the liklihood someone goes off for lots of money or goes bust(which is what I assume most are concerned with). While it may be more likely to lose $2000 on a given hand at 25/50 cap game, the dependent events after losing that hand may differ with those of losing $2000 at the 10/20 game. This is path dependence. Dependent hands take place all the time in PLO. We think about how we're running, or a recent hand against a particular player that may cause us to play differently.


The ability to lose anything you have on the table will skew the distribution between losses and gains. Alternatively if your opponents tilt much more than you do it means that you are less likely to go broke betting a higher percentage of bankroll becasue you will benefit from their dependent tilt.

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The Kelly criterion was originally developed by AT&T Bell Laboratories physicist John Larry Kelly, Jr, based on the work of his colleague Claude Shannon, which applied to noise issues arising over long distance telephone lines

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So you wan't to use a method of finding noise in telephone lines to think about human risk taking? Tell me do noise particles tilt? Do they have a memory?

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the moral of the story is that wr/sd is much more important when you're considering moving up and taking shots than sd alone

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I disagree. I think the moral of the story is think less about how good you play and more about the mistakes your opponents allow you to capitalize on. Think more about how the game structure affects losing players than winning ones. Think more about benefiting from others loss rates and capitalizing on bad decisions than your own winrate over your standard deviation when thinking about moving up. Think about the in the moment deviations and how they affect results. Thinking about risk in PLO should be more like weather forecasting and less like immutable laws of physics.

[pete fabrizio]

I think your criticism of Kelly Criteria/conventional bankroll analysis overstates the case. I generally agree with you that there are a lot of spots that are massive outliers -- e.g. tilt, opponents on tilt, game with big fish, etc -- and that these events are more determinative of the extent of a players "long term" winnings than most people think. However, these are all still evaluable in terms of expected value and expected variance. Risk of ruin/kelly criteria calculations are just the tools we use to make the correct bankroll-maximizing decisions based on those expectations.