Why would variance be higher at 6max?

I have read it here repeatedly that your variance will be higher at 6max tables than at full ring. Why would that be? It seems to me that at short handed games, you will win more pots per hour, and that the average pot size will be smaller, so I would think this would lead to lower variance.

My standard deviation based on my pokertracker data is 15/100 hands at 6max, and 21 at full ring. Is this common for everyone else? Doesn't this mean lower variance?

Imagine player at a poker table with 100 people, if this were possible. Would not your variance be much higher? During most hours you wouldn't even win a single hand, but when you won a big hand, it would be enormous. If you were a winning player there at 3BB/100, you might have a standard deviation of 100/100 hands.

Am I missing something here?

[CIncyHR]

Variance is higher becuase, while you win more hands, you play WAAY more hands, and take LOTS more hands to farther streets, and put it quite a few more bets with less stellar hands. Lots more action = lots more variance. You do win more pots though, which is gratifying.

[MrWookie47]

I'm skeptical of all these claims, too, and I'm not the only one. My SD/100 is about the same for the two. I think the reason people complain about the variance is because you play more hands/hr. Thus, if you drop 50 BB, which you do frequently, you'll lose it in much less time, but not necessarily fewer hands.

[lufbradolly]

If your gonna win more hands than in a full ring then your gonna lose more hands as well so when you run good you win more. But when you run bad you lose more therefore you have higher variance.

[deception5]

I don't believe variance is higher at 6-max (my 2/4 variance is actually way lower). The only difference is that you play more hands so the swings come faster, but are not necessarily different. I think the reason a lot of people make the claims that it is higher is because they are used to a comfortable, say 2-4BB/100 winrate at full ring and then they start playing 6-max where they may start off as a 0-2BB/100 player since they have no 6-max experience. With a lower winrate you will have larger and more frequent swings.

[Marquis]

I'm also on the "I'm not so sure this is true" train. I think the fact that you win more pots conteracts the effects of the increased action.

[ellipse_87]

In limit, variance is higher because success depends on exploiting smaller edges than in full ring--you win a lot more pots with middle pair good kicker, for example. This dynamic is created by the increased frequency of paying the blinds (you have to play more hands instead of just waiting for monster hands) and also the uncertainty of the strength the best hand given that there's so few players.

Given that the edges you are pushing are small, it follows that a long string of bad luck is more probable than with the more certain, but less frequent, edges you find ourself exploiting in full games.

Many of these factors are completely different in NL, or absent altogether (i.e., the effect of the increased blind frequency is negligible b/c of the higher implied odds in NL.

A very good NL player will have more opportunities in 6-max to go heads-up with weaker players. So my uneducated hunch is that variance is no greater at NL 6 max.

The conventional wisdom that NL 6-max variance is greater may just be from people misapplying the conditions that obtain in limit hold em.

[@bsolute_luck]

it will be higher for people accustomed to full ring and playing more aggressive with more marginal hands, learning to value bet and 3-bet, and calling down with A-high. i think it is only a higher variance based on a learning/adjustment curve. that and probably more people are cold calling and calling down with hands because there are "less people so i'll win more often" kinda thinking.

as the song goes "you gotta know when to hold 'em..."

As has been discussed before in these forums, playing more hands per hour decreases your variance over time, it doesn't increase it. If you could play a million hands an hour, you would have practically no variance whatsoever.

[Bankuri]

I think you missed all the other 'and' clauses in his post. I think that playing marginal hands on later streets is where the variance will increase from your full-ring games. Also, playing many hands does not lower your variance. This is a game of odds, the variance is always there. I would say that variance is mostly determined by your playing style, not by how much of a winning player you are (there are caveats here having to do with variance of the near break-even players) and certainly not by how many hands you play an hour.

[Aaron W.]

[ QUOTE ]
I have read it here repeatedly that your variance will be higher at 6max tables than at full ring. Why would that be? It seems to me that at short handed games, you will win more pots per hour, and that the average pot size will be smaller, so I would think this would lead to lower variance.

My standard deviation based on my pokertracker data is 15/100 hands at 6max, and 21 at full ring. Is this common for everyone else? Doesn't this mean lower variance?

Imagine player at a poker table with 100 people, if this were possible. Would not your variance be much higher? During most hours you wouldn't even win a single hand, but when you won a big hand, it would be enormous. If you were a winning player there at 3BB/100, you might have a standard deviation of 100/100 hands.

Am I missing something here?

[/ QUOTE ]

Okay, I'm going to bite on the math thing.

Variance is the sum of the squared distance to the mean divided by the number of samples. So let's say you play 100 hands, folding 99 of them (no blinds... since we're playing imaginary poker) and winning 1. To make the numbers match, you need to win 300 BB in the one hand to have a 3 BB/100 winrate.

Then your variance is going to be...

[(0-3)^2 + (0-3)^2 + ... 97 more of these ... + (100-3)^2)/100 = (891+9409)/100 = 103.

Your standard deviation is the square root of variance, which is
10.1 or about .1 BB/100. So unless I'm mistaken in the calculation, your variance and are incredibly *TINY* in this situation.

I don't know how strongly I believe that variance is bigger in 6-max.

There are two factors going into the variance:
1) The size of the pots that you win matter. In a full ring game at these limits, the pot is something around 12 BB on average. So when you win a pot, you're winning about 9 BB over your average. In shorthanded games, the pot is smaller, say 9 BB, which is only 6 BB over your average. This means that the variance for full ring games might tend to be bigger than shorthanded.
2) However, when you play full ring games, you spend a lot more time folding, or investing just 1 SB into the pot to see a flop with a marginal hand, which means you are very consistent in the amount you put in. In shorthanded games, you play more pots, so you don't "hover" around zero as much, and so your pot size statistics are more spread out with wins and losses. This contributes to a larger shorthanded variance and smaller full ring variance.

#2 is what people are usually talking about when they say variance is larger at 6-max. But it's not necessarily a mathematical truth that variance is actually larger. You're not allowed to just sit out most of the hands and wait for a monster pot to collect -- you've got to get involved in hands, and so you see more ups and downs.

The truth is that it just doesn't matter at all. Go play poker and let the statistics do their own thing.

[BatsShadow]

My thought is that while you do have many more marginal decisions, that means that against the truly horrible player, you have that many more chances to make good decisions and your variance should go down while your win rate goes up. -- I guess that means that your decisions aren't really that marginal.

If your opponents are better, then your marginal decisions become more marginal and variance goes up.

[Bankuri]

But variance doesn't have much to do with making good or bad decisions. Variance is the result of random processes in the game itself. If you only play hands that are 60-80% sure to win, your variance will be much smaller than if you are playing hands that win only 30% of the time. You aren't making poor decisions to play the latter if you have 2 or more opponents playing the hands with you, but your variance will be higher.

[Shillx]

In the example you give...

Figures are in BB/hand which would make the mean .03 BB/hand

s = root ((.03*.03*99 + 2.97*2.97)/99) = ~ .3 BB/100

Now let's say that you win 5 pots/100 @ 15 BB each and lose 9 pots/100 @ 8 BB each. The other 85 pots you don't factor into. Again your EV is .03 BB/hand or 3 BB/100.

s = (.03*.03*85 + 14.97*14.97*5 + 7.97*7.97*9)/99) = ~ 4.12 BB/100

Now try it when you win 15 pots/100 @ 15 BB each and lose 20 pots/100 @ 11.1 BB each. Don't factor in the folded hands. Again, our hero's win rate is .03 BB/hand or 3 BB/100.

s = root ((14.97^2*15 + 11.07^2*20)/99) = ~ 7.66 BB/100

The thing is that 6 max pots tend to be about the same size as full ring pots. You just win about twice as many in the same 100 hand peroid (and you lose many more bets in this span as well). This really shoots the SD through the roof. They don't calculate it on a per hand basis though. Say that after 500 hands, your +/- per 100 goes as follows...

+30 BB, -9 BB, +17 BB, -42 BB, +19 BB

mean = + 3 BB/100
s = root 2738/4 = 26.2 BB/100
sigma = root 2738/5 = 23.4 BB/100

This is why you need a biggish sample to get a SD figure from PT. Since you have to divide by (n-1) it takes time to get a somewhat accurate figure.

Brad