[MikeL05]

Sigh... the AA vs. KK thing has nothing to do with my original point... it was just to show why Tom's comment ("So your odds of winning the first run are equal to the odds of winning the second run. Therefore, EV is the same.") just makes no sense.

My original point, which no one has really approached yet, was regarding how a player could use two of his outs in the first run in order to gain the same effect that would be gained by only hitting one of the outs.

I have no interest in listening to people just blindly tell me that this doesn't matter because of burning 3 cards vs. 1, or whatever else. I understand how that works, and bringing it up makes me think you're missing my point.

I'd like to see some math here. I'll try to do this myself if I ever get un-lazy enough to take the time to do it. Basically, you should be able to draw some kind of branching probability thing, in which you take the possibilities of the first run (neither player improving, one player improving, the other player improving, both improving, and the diamond flush player improving by using TWO diamonds instead of one to win), multiply them by their probabilities, and figure out the odds of the second run concurrent upon the results of the first run.

Let's go back to what I was saying before, but trying a different example. Let's say instead we run this 12 times. The A/ [img]/images/graemlins/diamond.gif[/img] player uses up 2 of his outs to win in the first 6 trials; he now has a 0% chance of winning the last 6 trials. Conversely, if he uses just one of his A/ [img]/images/graemlins/diamond.gif[/img] outs to win the first 6 trials in a row, he still has some chance of winning trials 7 through 12.

Now running it once, as normal, none of this matters. But when running it 2+ times, it DOES seem to matter to me how many outs someone uses up to win each individual trial. So it would appear to me that the player who is ahead going into the trials, and thus does not rely on outs, has an advantage in trials in which two outs can be used up.