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

I hope the title is clear, although I concede it might not be.

so: I haven't played much CAP plo (the version on FTP where you can only commit 40bb to a pot at a time) and so I'm really not that sure how it plays, but seeing the 25/50 going regularly has got me thinking: How much would the 'variance' (pardon my impercise usage) in a game like this differ from a game of 10-20 PLO, given that the most you can 'buyin' for, on a given hand, is always going to be just $2000? What sort of impact would this have on the standard deviation, in $$s?

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

I haven't done any math regarding bankroll requirements in these games, but I generally consider them to have have significantly more variance than a typical uncapped game.
I crushed the 5/10 capped game over the summer, but saw 10 cap bet buyin downswings in a session rather frequently. I always played this game with at least 60 cap bets in my roll and felt better with 100 cap bets. I personally wouldn't play the 25/50 seriously with less than a 150k roll, and a big part why that is is psychological. You are going to need to commit 2k far more frequently than in 10/20 and you cant afford to be gunshy.

That said, I am sure there is a ton of money to be made in that game and if you can handle it financially and emotionally I would definitely advise playing it. Cap games often draw some really weak competition and can be very juicy. Additionally, if you are trying to work your way up to normal 25/50 games this is a great transition game.

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

I agree. Assuming the level of play is at the same level or higher than the 10/20 game, I think you're variance is going to be much higher for the 25/50 capped game money wise.

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

I am currently working on a way of thinking about risk in PLO. It requires an understanding of philosophy and mathematics instead of the blind application of models taken from regular casino games.

It require a pretty long explanation, the paper I'm working on is already over 10 pages. It is a work in progress but I am always looking for people to sample and critique. PM your email address if you're interested in reading.


As far a cap game and variance are concerned, it would depend how people respond to the change. The jumps in win/loss per hand will of course be smaller, but it could be that people bet more money overall(by getting into all-in coups more often) which could actually raise the magnitude of the overall swings, while still maintaining the lower per hand swings. This doesn't have to happen of course, it is merely a possibity. Expectation is of course the amount bet x the equity edge that you get in with. At 25/50 you may be able get in with a smaller edge twice as often which would yield a higher expectation. The more frequent jumps may also be more "tilt inducing" which, if you don't tilt as much as your opponents, could be better off for you.

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

I'm also sort of curious as to how my winrate will change playing cap games, where you never get to experience the deep-stacked spots that are a huge source of EV in uncapped games.

my intuition is that the larger flop pots (relative) combined with felting lightly will lead to higher variance vs. the smaller game, but then not having the huge 200+bb pots will keep some of the larger swings in line. Maybe.

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

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I'm also sort of curious as to how my winrate will change playing cap games, where you never get to experience the deep-stacked spots that are a huge source of EV in uncapped games.

my intuition is that the larger flop pots (relative) combined with felting lightly will lead to higher variance vs. the smaller game, but then not having the huge 200+bb pots will keep some of the larger swings in line. Maybe.

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these guys are crazy. the variance in the smaller game is definitely much lower. however, your winrate will also definitely be lower, so your wr/sd may not be much better, if at all.

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

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

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

Is there a difference between playing in a cap game and playing short in normal ring game? I guess because everyone else is also short? Or does the name cap bring out the gamblor in everyone?

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

well in a cap game you don't have the advantage of having deep stacks betting each other out of multiway pots on later streets, which is a not-insignificant advantage of PLO short-stacking.

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

The problem is that poker results are path dependent. Let me explain. Standard deviation does not differentiate between a series of small changes or a single very large change. Pete isn't quite understanding the question, and the underlying assumtion of standard deviation. It could be he is right that the swings in the 25/50 cap game could be bigger, but for the wrong reasons.

The limiting amount for the 25/50 40BB cap game and the 10/20 100BB+ game, the monetary amount $2000, could be viewed differently by the player in each game. The 25/50 players may think "hey, I only lost 40BB", while the 10/20 could think "damn, I just lost 100+BB" even though they are betting the same amount. There is an undefinable element to the 10/20 game that isn't contained in the cap game. Losses are not capped, which can benefit players who tilt alot less. Other players tilt is a very big part of any PLO players winnings.

The larger relative swings(in BB) per hand of the 10/20 game could induce people to play worse, or perhaps the more frequent(and possibly lower expecation per all-in) swings of the 25/50 game will induce people to play worse. It could also be neutral, I don't know. If I was cmyr I would think about the mistakes that players can make in each game, and play whichever game the weakest relative players were in.

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

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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.

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

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.

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

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.