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Old 12-09-2005, 08:16 AM
henrikrh henrikrh is offline
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Default Variance in different forms of poker

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?
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  #2  
Old 12-09-2005, 09:19 AM
AaronBrown AaronBrown is offline
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Default Re: Variance in different forms of poker

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.
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Old 12-09-2005, 10:24 AM
Zetack Zetack is offline
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Default Re: Variance in different forms of poker

[ 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
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Old 12-09-2005, 11:23 AM
soko soko is offline
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Default Re: Variance in different forms of poker

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.
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Old 12-09-2005, 11:32 AM
soko soko is offline
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Default Re: Variance in different forms of poker

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.
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Old 12-09-2005, 02:42 PM
winky51 winky51 is offline
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Default Re: Variance in different forms of poker

nicely put
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Old 12-09-2005, 03:01 PM
threeonefour threeonefour is offline
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Default Re: Variance in different forms of poker

[ 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?
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  #8  
Old 12-09-2005, 03:16 PM
AlanBostick AlanBostick is offline
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Default Re: Variance in different forms of poker

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.
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  #9  
Old 12-09-2005, 05:07 PM
ohnonotthat ohnonotthat is offline
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Default Re: Variance in different forms of poker

Varience alone is not the best way to choose a game (your ambition should be to balance your win rate with your varience) but since you asked I'll give you the best answer I can.

Assuming you are equally proficient at both limit and NL holdem (proficient in this case refers to an equal win rate in games with equal blinds) limit has a smaller varience.

A 10-20 limit player who wins at a rate of $40 per 100 hands (or an equivelent hourly rate if you prefer to measure in this manner) will see smaller and fewer swings than will someone who wins the same amount at 5-10 blind NL.

I'm not sure what a 10-20 stud player's varience will be (same $40/100hand win rate) but I'm guessing it will definitely be smaller but probably won't be MUCH smaller.

(If the ante were larger 10-20 stud would move closer to 10-20 holdem in terms of varience).

A 10-20 high draw player (lol - good luck finding such a game) with this same win rate will have a very small varience; this may be the least volatile form of poker other than some obscure types found in home games. (It will be smaller still if he plays Jacks-or better with the bug but even "anything opens" draw is a very stabile game).

A 10-20 low draw player with this win rate will have a huge varience; this explains why this game is still played (not alot but you can find a game if you look) while hi draw is virtually extinct. Bad players would go broke here as surely as anywhere else but it often took awhile and they usually enjoyed some nice runs while awaiting the inevitable; hi-draw was both cruel and decisive to weak players - they lost and they lost fast.

As for High-only limit Omaha, you'd have a hard time finding any game and a near impossible time finding a game where you could win at this rate; the game just doesn't much reward good play but it does provide a wild ride. Place this game near the top in terms of volatility.

Omaha 8 - same stakes, same win rate - is far less volatile than the hi-only version; this is among the least volatile games - 2nd only to high-draw.

Razz is virtually never spread anymore; if you do stumble across a game don't expect to win much if the ante is low unless your competition is clueless but while you won't win much you won't see many swings and those you do see will be small.

*

The term you'll want to look up or run a search for is "Coefficient of Variation (or "of Varience). This will show why varience alone does not provide enough data to allow you to make an informed choice of where to sit down.




Look at it this way.

Bonds are typically less volatile than blue-chips and blue-chips less volatile than lesser known holdings yet the typical portfolio contains some of all three.

*

It's worth noting that increasing your win rate will seldom if ever decrease your varience; in fact it usually tends to INCREASE it. The changes in your game that allow you to win more typically include thin value bets and tough folds.

(This is similar to what happens at blackjack when you replace a simple-count with an advanced point-count; the new system finds more advantageous situations but the extra ones it finds are the least advantageous and therefore add pennies to the win rate while adding hugely to the swings).

It's also important to note that in and of themselves varience and win rate are unrelated. (The relationship that does exist is the "coefficient of varience").

Changing the win rate translates into changing the break even point but does not change the size of the swings above and below that break even point. The best way to prove this is to look at the effect of the rake (or time charge).

If you play 10-20, win $40 per hour (pre-rake) and pay $10/hour to play (btw, this is the current fee in A.C.) your actual win rate is $30/hour. If the charge is raised to $20/hour your win rate drops to $20/hour but your varience stays the same. What does change is the break-even point, a/k/a/ your win rate.

- Imagine a society where all adult females are between 5'2" and 5'8" in height. If they all took to wearing 4" heels [img]/images/graemlins/smile.gif[/img] the average height would rise by 4 inches and but the range and the varience would remain the same. (If this increase in heel height were accompanied by increase in the average breast size, the varience would still remain the same however there would be an increase in the happiness level for this society's male members [img]/images/graemlins/grin.gif[/img] [img]/images/graemlins/smile.gif[/img] [img]/images/graemlins/cool.gif[/img] [img]/images/graemlins/wink.gif[/img]).
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  #10  
Old 12-09-2005, 06:38 PM
gergery gergery is offline
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Default Re: Variance in different forms of poker


It seems like what you really want to measure is the ratio of your winrate to your “swinginess”. Or winrate/100 hands divided by standard deviation (or maybe variance).
And NL is almost certainly less variance for the winrate than limit.
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