Running it Twice.....what are the dis/advantages???

[FBMike]

You can only tell the advantages/disadvantage by running the numbers.

If it gets run once, his expectation is E=.35*$100=$35, which assumes a $100 pot. The real expectation would be E=.35p, where p is the size of the pot. However, you can also just say E=35%, so I'll use those numbers from now on.

If it gets run twice, his expecttion of a win goes way down: E=35%^2=12.25%.

You expectation of a win goes way down too: E=65%^2=42.25%.

The expectation of a tie goes from 0% to 100%-12.25%-42.25%=45.5%.

With these numbers we can compare both expectations.

His comparison is E1=35% and E2=12.25%+(1/2*45.5%)=35%, where 45.5% has to be divided by 2 because it will be a split pot.

As you can see, the expectation stays the same. What changes is that the pot gets split nearly half the time. That's what everybody means by less variance when it gets run twice, because it ends up tied so often, which is impossible if run once. In fact, of the 3 outcomes, a tie is the slight favorite over you winning both runs.

It depends on your philosophy of variance, but I like it when I only lose a hand 12.25% of the time and can still win it 42+% of the time. However, I won't trade my 35% equity as the dog for an almost 60% chance to win or tie, even though the numbers say I should, in order to lower variance. I guess that means I don't like to gamble when ahead, but like to gamble when behind.

HTH.