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?

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.

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

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.

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.

Re: Variance in different forms of poker
 

nicely put

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?

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.

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.

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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]).

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.

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 ]

Then a game like O8 would have ridiculous variance, when in fact it actually has far less than hold em. You only need 1/2 the bankroll for the same stakes (according to the man who posted above me).

Re: Variance in different forms of poker
 

[ 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]

I resemble that remark
 

RESENT - I meant RESENT [img]/images/graemlins/frown.gif[/img]


[ QUOTE ]





[And] NL is almost certainly less variance for the winrate than limit.

[/ QUOTE ]



This is not correct. [img]/images/graemlins/shocked.gif[/img]

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N-L almost certainly has a smaller C.V. than limit for games with equal blinds but this is due to the huge win rates a good player is capable of attaining.

The greatest 10-20 limit holdem player of all time will have a WR that will be dwarfed by that of the greatest (or even a good) 5-10 blind N-L player.

The [much] higher WR of the N-L player will serve to [over]compensate for the higher varience this same player faces.

However (nonetheless and notwithstanding [img]/images/graemlins/smile.gif[/img]) if two players have equal WRs - one at 10-20 limit, the other at 5-10 blind N-L - the varience of the limit player will be much smaller than that of the N-L player.

- The limit player's varience will be much lower REGARDLESS of their win rates, however the N-L player can lower his varience by a significant amount (while only lowering his WR slightly) by avoiding "coin-flips" (AK vs QQ, etc.); the limit player can also stay out of marginally favorable situations but he pays a higher price for doing so (in terms of lowering his WR) than does the N-L player.

Re: I resemble that remark
 

[ QUOTE ]
N-L almost certainly has a smaller C.V. than limit for games with equal blinds but this is due to the huge win rates a good player is capable of attaining.

[/ QUOTE ]

See, this assumption is the problem. If comparing limit to NL is like comparing apples to oranges, then comparing them at the same blind structure makes it even more ridiculous. The stakes of a 2-5 NL game are huge compared to the stakes of a 3-6 limit game. Blind structure isn't a good way to "match" the two.

Re: Variance in different forms of poker
 

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

[/ QUOTE ]

Naaaah. Usually two players are lobbying, and one guy is waiting for the deal to pass so he can get a hand.

Re: Variance in different forms of poker
 

[ QUOTE ]

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.


[/ QUOTE ]
Bad comparison.

Many players maintain a win rate of 10 PTBB/100 through about NL $200. That's $40/100 hands. The standard deviation associated with NL depends a lot on playing style, but $200/100 hands is reasonable.

The player winning the same $40/100 in the $10-$20 limit game should have a SD of about $300/100 hands.

Re: I resemble that remark
 

I agree, but how else can we compare limit to NL ?

If you have a suggestion I'd love to hear it ?

*

When I play 2-5 N-L in A.C. the average stack size is often bigger than the average number of chips on an entire table of 3-6 limit.

Re: I resemble that remark
 

[ QUOTE ]
I agree, but how else can we compare limit to NL ?

If you have a suggestion I'd love to hear it ?

[/ QUOTE ]

By renormalizing results by win rate.

Re: I resemble that remark
 

No, your post is flat out wrong. The blind size has nothing to do with this.

You need to compare the winrates and equivalize them. Then compare the variance you’ll get in achieving that winrate. See pzhon’s post.

-g

Re: I resemble that remark
 

The four forms of poker widely discused on 2+2 in order from highest varience to least
1.MTT
2.Limit Holdem
3.NL Holdem
4.STT

And nobody in the STT forum will say that STT have the most varience. It has varience just like all forms of poker but by far it has the least.

Thank you
 

Now would someone tell gergery.

Re: Variance in different forms of poker
 

I might be mistaken, but doesn't your win rate have a big influence on your variance? More so that the particular game you play? A big absolute win rate gives less variance if my intuition is correct.

Re: Variance in different forms of poker
 

[ QUOTE ]
I might be mistaken, but doesn't your win rate have a big influence on your variance? More so that the particular game you play? A big absolute win rate gives less variance if my intuition is correct.

[/ QUOTE ]

Your intuition is wrong. A big winrate will cushion you psychologically when it comes to variance. It's a lot easier to deal with a $200/hr standard deviation when you are winning $200/hr than if you are winning $20/hr. The reason is that with the bigger winrate you will lose money only 1 out of every 6 hours on average, while if your winrate is $20/hr you will average losing money almost 1 out of every 2 hours ( a little less).

The swings, however, are the same. Both players will average being $100 under their winrate the same number of times over a given sample of similar sessions, for example.

edit- added 2nd para.

Re: I resemble that remark
 

I'd estimate that a $1-$2 NLHE game is about the same as a $4-$8 or $6-$12 limit game (i.e. one with a $2 or $3 SB). I have no proof other than Eyeballing It, but it seems to be realistic to me.

Re: I resemble that remark
 

Are we talking about the win rate for similarly skilled players (similar as in both excellent for this game/limit, both very good for this G/L) ?

If so, I more or less agree. A VERY good (8 on a scale of 1-10) 5-10 limit player should be able to earn $20+/100 hands; I don't play alot of NL but this sounds about right for an "8" at NL with blinds of 1 and 2.

As for varience . . . hard for me to say but I'm guessing these two hypothetical players should have similar S-Ds.

Re: I resemble that remark
 

[ QUOTE ]

If so, I more or less agree. A VERY good (8 on a scale of 1-10) 5-10 limit player should be able to earn $20+/100 hands; I don't play alot of NL but this sounds about right for an "8" at NL with blinds of 1 and 2.

[/ QUOTE ]
No, that's about the right win rate for a good NL $100 player, with a big blind of $1.

Re: Variance in different forms of poker
 

My reason for thinking this is not psychological. Lets go to the extreme, if you suck and lose every hand you play in poker you will have a low variance (and a bad winrate). If you are winning all hands played you will also have a low variance. If you win half your hands and lose the other half, your variance will be high.
So being far away from the rest of the table in terms of skill will decrease your variance.
Is that reasoning correct? (I am not sure)

Huh ?
 

A very good NL player in a game with blinds of .50 and $1 should win $20 per hundred hands ?

If this is true I find it amazing that anyone would play limit.

Are you saying that the best of the 10-20 limit bunch is earning no more than the best of the 1-2 blind N-L players ?

I respectfully disagree; it cannot be so. You are saying that there are a significant number of people out there who are 3-tabling 100 NL and earning $30+ per hour ? (This assumes 50 hands per hour which is about average).

It would then follow that the internet is awash with players 4-tabling 200 NL and earning in excess of double this. (The extra table compensating for the lesser win rate)

I'm aware that the competition at small NL is atrocious; the 1-2 live in A.C. is a joke and the 2-5 is only a little better but this just cannot be.

If you stand by your claim that this is run of the mill money for small NL, where does it end ?

I'm aware that the competition gets tougher as we move up but this seems to suggest that there are more than a few people out there who have a legitimate shot for mid-six figures in 2006 and that the really good (as in REALLY good) ones just might make 1,000,000.

As insane as that sounds when you first hear it, remember - a million per year is only 500/hour for a 40-hr-week worker and 250 for someone with no outside life.

I have heard claims from people whose word is gold of having long-term win rates for LIVE 5-10 blind NL that would shock the avarage person but therein lies the key.

Few people would describe online limit as being harder to play than live but NL - it's just made for live play. I would think the disparity between the good and the excellent, live vs online, would be much smaller on a computer.

Please respond - if I'm wrong I REALLY want to know and you'll be doing me a HUGE favor by telling me.

Best wishes for the holiday,

- Chris

Re: Huh ?
 

um, 10ptbb/100 at 100 nl = 10x2 = $20.

Yes.

Re: Huh ?
 

[ QUOTE ]
A very good NL player in a game with blinds of .50 and $1 should win $20 per hundred hands ?

If this is true I find it amazing that anyone would play limit.

[/ QUOTE ]
It's true.

There are reasons to play limit. It may be easier to multitable to a higher degree in limit and to get in more hands per table-hour. You may be able to find bigger limit games. Some people win at limit and lose at NL. There are many books on limit that can point you in the right direction but no good book I know of for NL cash games (HOH is for tournament play with shorter stacks).

[ QUOTE ]
You are saying that there are a significant number of people out there who are 3-tabling 100 NL and earning $30+ per hour ? (This assumes 50 hands per hour which is about average).

[/ QUOTE ]
Actually, when I 4-table NL $100 6-max, I get over 300 hands per hour, and my average has been just over $70/hour (+- $15/hour).

[ QUOTE ]
If you stand by your claim that this is run of the mill money for small NL, where does it end ?

[/ QUOTE ]
Good question. I'm investigating this myself. Before the Mid-High NL forum split, there was a thread that suggested 5 PTBB/100 is a good rate for NL 600+. The games may have gotten softer since then.

By the way, the SSNL FAQ sugests that 7-8 PTBB/100 is sustained by "fairly good" players. That's very clearly an underestimate for NL 25. It might be more accurate for NL 200 and NL 400, which used to be discussed in SSNL.

[ QUOTE ]
I would think the disparity between the good and the excellent, live vs online, would be much smaller on a computer.

[/ QUOTE ]
I have a lot to learn, but I regularly exploit leaks of winning players. However, the main source of profit is the fish, who exist at all levels.

You'll be interested in several entries in the August 2005 archive of Tillerman's blog.

Re: Variance in different forms of poker
 

Ummmm, no.

Variance shows up not just in differences in kind of outcome (win vs. loss of individual hand) but in quantity: size of pot won vs. amount of money lost.

Here I stand -
 

corrected AND amazed.

- Oh, and grateful

I see '06 as the year I give NL a hard look.

Is the quoted WR of $70/hour for 4 tables of NL 100 before or after rake rebate ?

BTW, what do you find yourself paying in rake per 100 hands at this level ?

*

One of the reasons - perhaps the major reason - I decided that whatever future there was for me playing online lay with mid-high limit was the obscene role the rake played at the lower limits; I get nauseous when I think of the 1/3 of my income that goes to Uncle Sam but the thought of going 50-50 with the a poker site would lead to projectile vomiting. Sadly, most good or even VERY good 2-4, 3-6 players do leave half their winnings on the table due to the rake.

I'm no communist; I do not think the sites should provide a service and not expect to earn a profit but 50-50 is obscene and it is this aversion to working 40 hours and getting paid for 20 that led me away from small NL - a choice I am beginning to question.

I can play 10-20 or 15-30 online and for all intents and purposes ignore the rake - at least in terms of its % impact. "Ignore" is not the best word - unless one is accustomed to ignoring an expense that is often larger than my mortgage payment; what I meant to say was I have never even considered the rake when choosing where, when or if to play 15-30. These three factors are huge when planning a session of 3-6.

I am also speaking of live games - something I played far too little of this year (or last).

East coast rakes/time fees are an atrocity - second only to California - but $12 hour plus tips is still a steal compared to what one must pay to play small stakes whether they play online or live.

Be aware I am not advocating one "cut off one's nose to spite one's face"; I used to play in (and crush) a PL draw game with a 5% rake and NO CAP, and if this group reassembled tomorrow I'd beat a path to the game but in that case my options were limited; here they aren't. I have never sought out the game with the lowest rake but I have always considered it a major factor at the lower limits while attaching virtually no significance to it as I move(d) up.

*

Again, thanks for your detailed response. [img]/images/graemlins/smile.gif[/img]

*

Have a wonderful holiday and a prosperous New Year.



Sincerely,

- Chris

Re: Variance in different forms of poker
 

[ QUOTE ]
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").

[/ QUOTE ]
What is the coefficient of varience?

Re: Here I stand -
 

[ QUOTE ]

Is the quoted WR of $70/hour for 4 tables of NL 100 before or after rake rebate ?

[/ QUOTE ]
The $70 is from the play alone. Rakeback adds a little. Bonuses add a lot.

[ QUOTE ]
BTW, what do you find yourself paying in rake per 100 hands at this level ?

[/ QUOTE ]
The computer where I had PokerTracker installed crashed, and I haven't installed it on another yet. (I don't rely on GT+ or any other outside aid, though perhaps I should.) However, if I recall correctly, it was about $8/100.

Have fun trying online NL.

Coefficient of varience
 

It's the relationship between win rate and varience - more specifically, the WR and SD.

If, for example, you have a win rate at 3-6 holdem of $15 per 100 hands and a S-D of $120/100 hands your coefficient of varience (C.V.) is .8

- Anything above .1 used to be considered great but the xplosion of NL has spoiled us; it's easy these days to find C.V.s of .2 or greater.

Since knowing one is useless without knowing the other, the C.V. provides a ratio you can apply to any game in order to decide whether that game is "good" for you.

A high win rate is of little use if the SD is so high you literally might not live long enough to get into the long run; an overlay on Lotto is a good example. Buying a $1 ticket that has a theoretical value of $3 is not as good as it sounds if your chance of collecting ANYTHING is a million to one.

In poker, a high ante stud game might provide a huge winrate but be so volatile it could take years for you to smooth out the bumps of the short run.

Low draw ("lowball") is also known for having a poor C.V. - unless your opponents are absolutely horrendous it's difficult to find a game with a C.V. better than .05

Some say the reason Holdem took off and left stud and high-draw in its dust was due to the ideal size of its C.V. Poor players almost never won at high-draw while they won too much at stud (assuming a medium to high ante).

If the dummies win too often it's hard for you to make a steady living; if they win too infrequently it's hard to get them to keep coming back.

I'll stop here so as to allow those who have significant experience at all forms of poker to jump in and elaborate on the specifics of how each of the common varieties of poker rate on the list - from highest C.V. to lowest.

Best wishes,

- Chris

Re: Coefficient of varience
 

Hi ohnonotthat:

[ QUOTE ]
If, for example, you have a win rate at 3-6 holdem of $15 per 100 hands and a S-D of $120/100 hands your coefficient of varience (C.V.) is .8

[/ QUOTE ]

Isn't your CV = .125 not .8 in this example?

Best wishes,
Mason

Re: Variance in different forms of poker
 

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

Re: Variance in different forms of poker
 

Hi Cat:

It was always played eight handed in the California cardrooms.

Best wishes,
Mason

Re: I resemble that remark
 

Hi [ QUOTE ]
The limit player's varience will be much lower REGARDLESS of their win rates, however the N-L player can lower his varience by a significant amount (while only lowering his WR slightly) by avoiding "coin-flips" (AK vs QQ, etc.);

[/ QUOTE ]

I don't really agree with this. I suspect you're confusing no limit tournament play with cash game play.

However, one skill in poker that does have the ability to lower your variance (and increase your win rate) is the ability to read hands well. This skill is much more effective at no limit.

Best wishes,
Mason

Too much
 

eggnog - WAY too much eggnog. [img]/images/graemlins/confused.gif[/img]

.125 it is. [img]/images/graemlins/laugh.gif[/img]

Thanks, Mason

Merry Christmas

- Chris

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Wow, could this be a trend ?

A personal response from Mason . . . If this is a trend I know a guy who will be driving around in a new Jag, courtesy of Santa. [img]/images/graemlins/shocked.gif[/img]