[TNixon]

[ QUOTE ]
To make things easier , it is recommended that you reduce the former game to having $10 at 0.5/1 . This is true if we assume that the win rates do not change .

[/ QUOTE ]
omg.

I thought we making progress here, but you are now making the same mistake omg has been making all along.

By trying to make the problem easier, you've completely changed the result. $10 at 0.5/1 *is not the same* as $100 at 5/10. They are both 10BB stacks. But you cannot simply change the value of the big blind and expect to come out with the same result.

[ QUOTE ]

1)You will experience more variance /$ playing with a stack of $100 .

2)You will experience more variance /BB playing with a stack of $10 .


[/ QUOTE ]

And no, I don't agree with those statements. First of all, I'm not sure exactly what you mean when you say variance/$ and variance/BB. The variance is going to be measured in bb/hand or $/hand, depending on whether you use blinds or $ for the calculation. "Variance per dollar", or "Variance per big blind" doesn't really even make sense.

But in any case, after your modification of the stacks, the $10 stack will have a smaller std. deviation measured in bb/hand, so the $10 stack is always lower variance if you match the value of the blinds. In fact, as omg correctly pointed out, in this case, the $100 stack had 100 times the variance of the $10 stack, in all situations, *if the blinds are equal*. The $10 stack has a lower variance whether it's measured in bb/hand or $/hand. (and because the bb happens to = 1, the calculated values for bb/hand and $/hand will be identical, both for the $100 stack and the $10 stack)

But by modifying the stacks and blind levels *you have changed the problem*. The answer is different if you solve the original problem, rather than the "easier" version.

Correction: variance is measured in bb^2/hand^2, std deviance is measured in bb/hand. I do mix these two terms fairly often, which is bad, but it should still be clear what I'm referring to, and they are directly related, so it's not a fatal error.