T
The_Pup
Rock Star
Silver Level
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'.
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'.