This is a discussion on Variance within the online poker forums, in the Cash Games section; Variance is a word that is bandied around poker circles, especially cash game players, with a sense of 'things go up and down but average 


#1




Variance
Variance is a word that is bandied around poker circles, especially cash game players, with a sense of 'things go up and down but average out in the long run'. This is a fairly good working definition but only scratches the surface, so I thought I might expand on the topic. No doubt someone has done the same here before (and probably made a better job of it) so forgive this relative newcomer to CC if I am raking over old ground.
Let's suppose we are a decent poker player at our chosen level. A session of say 100 hands will have its own ups and downs but our ability is such that we can regard each session as being like a coin flip in which we win $12 on heads and lose $10 on tails. Now that is a profitable game, our expected profit is $1 every time we sit down to play  we are $1 per 100 hands more skilled than our opponents. Now we have a simpler game of coin flipping where we get $12 on heads and pay $10 on tails. We can take this new game and play it 100 times  this represents 10,000 hands of poker. Our expected return on these 100 flips is $100 since we expect to win $12 50 times and lose $10 50 times. Whilst 50 heads and 50 tails is the average result of tossing a coin 100 times we would not be surprised at 49/51 or 48/52  this is where variance comes in. In order for our game to remain profitable we need to score more than 45 heads, less than that and our losses outweigh our wins. It turns out that about five sixths of the time we can expect to throw 45 or more heads  the more heads the more profit, throw 60 and we are on a great run, 70 and we are poker gods. But of course throw less than 45 and we are losing money and that will happen one sixth of the time. What this means is that you might have a winning strategy and be $1 per 100 better than your opponents but don't be too surprised when you lose money over a period of 10,000 hands. And if you do it is quite possible you won't get your losses back on the next 10,000 or the next. Of course once in a while some poor sod throws 95 tails and goes on a horrible bad streak whilst someone else throws 95 heads, and calls himself 'durrrr'. 
#2




Great thread. Makes me feel better, now I can just keep blaming variance for my losses. "Yeah I've lost money over my last 100,000 hands, but thats probably within a couple standard deviations of normal anyway, right?" Just kidding, yeah good post and something I think people should be more aware of.

#4




I'm not so sure that poker outcomes follow the normal distribution upon which your theory appears to be based. However, I agree that variance is being used by poker players to "explain" that their shortterm ups and, more often, their downs, are more a reflection of probability distribution effects than skill level.

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re: Poker & Variance
Thanks for the positive comments and for spotting we are talking about the normal distribution and standard deviation  I was unsure how technical to get with the maths.
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I think that the thing these numbers show is that as a skilled player who is one dollar better than the tables we sit at we should not be in the least bit surprised if we find ourselves on an extended losing run  indeed we should be surprised if it doesn't happen. All it takes is for five 100 hand sessions to go bad. 
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Using my model of coin flipping with a skill advantage of $1 we are in profit if we get 45 or more heads. Equally, there are some players out there who have a skill disadvantage of $1. Because of their lower skill level they need to get a much higher number of heads over the 100 flips. It is nothing that remarkable if they get 60 heads and turn in a profit. We can imagine a poor player who starts playing online and soon racks up 10,000 hands and returns a profit  because of variance. There will be a feedback circuit that will tell them they are a good player so they crack on playing the same style of game. The next 10,000 hands sees them getting 50 heads and so they lose. These loses they blame on variance, having a bad run of luck. Since most people believe they are better than most other people at any given task it is easy to slip into the trap of not analysing one's own game but put losses down to variance  'after all, I did make a profit in the first 10,000 hands.' I can talk about this with great authority as this was what happened to me when I started online! 
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I think your second point is true; though whether you are a 'winning' or 'losing' player is hard to tell from looking at results over 10k or 20k hands. The potential danger for a poor player is to believe their profit is down to skill where they have just got the good end of variance  their bad play is ingrained as 'good play' because they won with it once. As for me, I'm good enough to know I'm not as good as I think I am. 
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#15




re: Poker & Variance
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Out of interest I did a trial of 100 coin flips several times over (using a virtual flipper  I have got a life). Though the expectation is to get 50 heads and 50 tails, in reality I got 44/56, 48/52, 60/40, 53/47 and 42/58. By my reckoning, this series of flips has two losing runs, one just better than breaking even and two highly profitable. 