[jay_shark]

I'm not sure if anyone has written extensively on this topic in regard to heads up games but I'll try to explain things as simple as possible .

Your standard deviation for heads up sng's is a function of your win rate . If you assume that your win rate is ~60% , then your standard deviation will remain fixed for any player who shares the same win rate . A simple calculation proceeds as follows :

Var(x)=E(x^2)-E(x)^2 where E(x) is your win rate(or mean) for a random variable x . For this particular case , we regard the variable x as +1 for when we win 1 unit and -1.05 for when we lose one buyin which also includes the rake .

So assuming you win 60% of the time , your s.d is simply the square root of your variance or var(x) .

E(x^2)=1^2*0.6 +(-1.05)^2*.4
E(x^2)= 1.041

Also E(x)=1*0.6-1*0.4 -0.05
E(x)=0.15

Var(x)=1.041-0.15^2
Var(x)=1.0185

S.D(x)=sqrt(1.0185)~ 1.0092

This means that if your win rate is 60% , then your s.d is approximately equivalent to 1 buyin , no matter what !

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Our standard deviation for cash games may be different for two players who share the same win rate . As I explained earlier , this is not the case for sng's .

To compute our standard deviation for cash games , we need at least 30 cash game sessions to ascertain that our s.d converges to a steady number . We need not even know our win rate which is why the central limit theorem is so very useful in situations like this . Using the numbers that Jakeduke provided , I will calculate the number of hands needed to determine with 95% confidence, our win rate interval .

Lets say after 50k hands , our win rate is (10 bb)/100 hands and bb is not to be mistaken for big bets .

Our standard deviation , using jakeduke's numbers is ~ 11 big blinds/100 hands .

xbar is our sample mean (10 bb/100 hands)
z= our confidence level which is approximately 2 s.d's above and below the mean .
sigma bar is our sample standard deviation .

In this case , sigma bar is 11/sqrt(500)~ 0.4919 per 100 hands .

10 +- 2*0.4919 Which means that we are 95% confident that Jakeduke's win rate lies between 9.0162 to 10.98 BB's per 100 hands .

Using z=3 , we are about 99% confident that Jake's win rate lies between 10 +- 3*0.4919 or between 8.52 to 11.47 BB's per 100 hands .