Variance in different forms of poker

[henrikrh]

It seems like variance is a relaly misused term around here, SNGers say SNGs have high variance, limt players say variance is higher in limit than in NL and NL players say the opposite. So I was hoping someone who understands it very well could make it crystal clear...

1) What is variance in the context of poker?
2) Which form of poker has the highest variance and why?
3) Which has the lowest and why?

[AaronBrown]

Variance is a measure of the dispersion of profit, usually measured per hour or per 100 hands. People actually talk about standard deviation, which is the square root of variance, more than variance itself.

One way to think about it is about 2 times out of 3, your results will be within one standard deviation of your long-term expectation. So if you are a +2 BB/hour player with a standard deviation of 20 BB/hour, about 1 time in 6 you'll lose more than 18 BB in an hour, 1 time in 3 you'll be between -18 BB and +2 BB, 1 time in 3 you'll be between +2 BB and +22 BB, and 1 time in 6 you'll win more than 22 BB in an hour.

Low variance is good because you can play at higher stakes for the same bankroll, and you can know your expected win rate more precisely.

There's no one-size-fits-all answer to which kind of poker has the highest or lowest variance. It doesn't depend only on the table and limit structure, it depends on the playing styles of the people. In no limit, it also depends on the size of stacks relative to the blinds.

Your first thought would be no limit variance is higher, due to the occassional very large pot. But the potential for large pots means people take fewer chances. In the no limit games I play variance is generally higher than limit games, but I wouldn't extrapolate that to all games.

[Zetack]

[ QUOTE ]
Variance is a measure of the dispersion of profit, usually measured per hour or per 100 hands. People actually talk about standard deviation, which is the square root of variance, more than variance itself.

One way to think about it is about 2 times out of 3, your results will be within one standard deviation of your long-term expectation. So if you are a +2 BB/hour player with a standard deviation of 20 BB/hour, about 1 time in 6 you'll lose more than 18 BB in an hour, 1 time in 3 you'll be between -18 BB and +2 BB, 1 time in 3 you'll be between +2 BB and +22 BB, and 1 time in 6 you'll win more than 22 BB in an hour.

Low variance is good because you can play at higher stakes for the same bankroll, and you can know your expected win rate more precisely.

There's no one-size-fits-all answer to which kind of poker has the highest or lowest variance. It doesn't depend only on the table and limit structure, it depends on the playing styles of the people. In no limit, it also depends on the size of stacks relative to the blinds.

Your first thought would be no limit variance is higher, due to the occassional very large pot. But the potential for large pots means people take fewer chances. In the no limit games I play variance is generally higher than limit games, but I wouldn't extrapolate that to all games.

[/ QUOTE ]

A much simpler way to explain variance is to simply say its about swings. A game with a lot of variance has big swings up and down.

So if you have say a winrate of 1.8 BB/100 and you play 500,000 hands over the next year, you can say with pretty good confidence that you'll be pretty close to a certain number of BB's up at the end of the year. But because of variance you may be hugely down or hugely up over some small subsection of hands during that stretch.

People tend not to be wild about varience because nobody likes the downswing side of varience.

Having said that, I have no idea what form of poker is innately swingier.

--Zetack

[soko]

I like the way AaronBrown said it. He explains how even if you are a +BB/100 player using your standard deviation you can see the chances of having a bad run or a good run in x number of hands and that the lower your variance the more precisely you can figure out your true winrate.

[Mason Malmuth]

Hi Aaron:

Your variance at no limit almost always has to be higher due to the fact that you win or lose a very large pot every now and then. However, if you're an excellent player, this is more than compensated for by your win rate (assuming typical weak opponents in either limit or no limit) also being much higher.

Best wishes,
Mason

[soko]

to answer your question about what has more/less variance, it has to do mainly with the number of cards being delt, for example, in 5 card draw, less cards are being delt out therefore there are less combinations of cards that can be delt out in each hand therefore the decisions are much easier to make because there are less posibilities of what your opponent is holding and less betting rounds to let your opponent draw out on you

In a game like hold-em there are up to 25 cards from the deck being delt out, with 4 betting rounds, there is an eponential growth in the number of possible combinations of hands that can be delt compared to draw. Is it any coincidence that the most popular game is the game that deals half the deck? giving you a good balance of variance and complexity, it's the perfect poker game.

Then in a game like omaha, the whole deck is almost dealt out which has an INSANE number of combinations possible making everything ive already said even more great.

[winky51]

nicely put

[threeonefour]

[ QUOTE ]
to answer your question about what has more/less variance, it has to do mainly with the number of cards being delt,

[/ QUOTE ]

this statement is pretty misguided imo. the number of players, the betting structure, and other rules all play a huge roll.

compare razz, 7stud, 7studhilo. now compare each of these heads up vs 8 handed.

now think of some crazy variants of poker, 10 card stud with one betting round vs 7 card stud with 5?

[AlanBostick]

In an 8-handed game of 5-card draw there are 40 cards dealt out before the draw and another five or so afterwards, for a total of about 45 cards dealt. In a 10-handed hold'em game there are twenty cards dealt out before the flop and an additional five cards dealt out on the board, for a total of 25 cards dealt. Therefore, by your reasoning, 5-card draw should have rather more variance than hold'em.

Have you ever played 5-card draw in a cardroom?

There's a REASON why hold'em pretty much took over California in 1987.

[DCWildcat]

[ QUOTE ]
In an 8-handed game of 5-card draw

[/ QUOTE ]

has 5 card draw ever been played 8 handed? [img]/images/graemlins/smile.gif[/img]