[jay_shark]

Lets start with some definitions of what variance means .

It is defined as Var(x) = E(x^2)-E(x) , where x is a random variable denoting the number of buy-ins .

Say you're a consistent 60% winner . In other words , you win 60% of the time independent of tilt or any other psychological factors that may come into play .
Your variance is :


Var(x) = 1^2*0.6 +(-1.05)^2*0.4 - (1*0.6 - 1.05*0.4) = 0.861

Your standard deviation would be sqrt(0.861)=0.9279... .

If you're a 70% winner , your variance is going to be lower .

Var(x) = E(x^2)-E(x)
Var(x) = 1^2*0.7 + (-1.05)^2*0.3 - (1*0.7 - 1.05*0.3)=0.64575

It should be clear that the better player you are , the less variance you will experience playing heads up .

For tournaments it's a bit tricker to quantify since the probability you win a second round match is not the same as the probability you win a first round match . For simplicity , if we assume that the probability you win each match is 60% , independent of each round , then the probability you win a 4 player tourney is 0.6*0.6=0.36

Var(x) = E(x^2)-E(x)= 3^2*0.36 +(-1.05)^2*0.64 - (3*0.36-1.05*0.64) = 3.5376

It should be clear now that your variance increases as you increase the number of players in the heads up tourney .

Ask if you're not clear about something .