Originally Posted by Stu_Ungar
It definitely favours big draws but has no effect on made hand vs made hand.
It turns the draw from an underdog overall closer to a coinflip.
For one thing the second card to be dealt (assuming the first didnt hit the draw) is now dealt from a deck that contains one less non-flush card than before. Its going to alter the probabilities slightly and if you are behind its altering them slightly in your favour.
So the guy on the draw is fractionally less likely to loose twice with a FD when running it twice than he would be to loose 2 all-ins with 2 FDs that were run once.
Assuming the FD misses the first time the ratio of flush to non flush cards has increased slightly.
Are you suggesting that the second run doesn't include the cards that were dealt from the first run? Surely that isn't true?
I was under the impression that the two runs were completely independent trials, each with the exact same probabilities. For example, if we're 60/40 favored to win a $1000 pot, our expected payout is 60% x $1000 = $600 (assuming no splits are possible here) without running it twice.
Now if we run it twice, the probability of winning both trials is 60% x 60% = 36%, and the probability of losing both trials is 40% x 40% = 16%. This leaves 48% that we each win one trial and split the pot. Therefore, our expected payout is 36% x $1000 + 48% x $500 = $600 again.
The only difference is that our variance is reduced, since almost half the time we don't lose any money, instead of the all or nothing nature of the standard deal. I'm too lazy to compute the variance, which is simply the square root of the sum of the squared deviations of the possible outcomes from the expected outcome.
Or am I missing something, either subtle or obvious?