[jcm4ccc]

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I wanted logarithmic decay for below-average stacks as well as logarithmic growth for above-average . . . I wanted to model the need for exponential growth centered around the average stack, not your stack. Thus the Q denominator.


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It seems to me that you created a formula to correspond with how you think that the probability of winning should be. There seems to be no theoretical basis for your formula.

As to your formula, you say that doubling up exactly doubles your chances of winning. So let's take a theoretical tournament with 100 players. It's the first hand. At this point, everybody has a 1% chance of winning.

You double up on the first hand. So now, according to your formula, your chances of winning have doubled to 2%. One player is out of the tournament. There are 98 other players left. These 98 players have a 98% chance total of winning the tournament (since you have a 2% chance of winning), which is exactly what they had before you busted that guy. In other words, the fact that you busted out one player does not in any way help the other 98 players. You accrued all the benefits of busting that guy. That does not seem right to me.

Actually, I believe if you used your formula at this point to calculate the chances of all 99 players (yourself included), you will see that the total adds up to something greater than 100%, I believe.

Now let's assume that you busted out 2 players. Your chances of winning the tournament are about 2.69%. There are 97 players left. They have a 97.31% chance of winning the tournament, which is a little bit better than what they had before you busted those two guys. So busting one guy didn't help them, but busting two guys did. Doesn't seem logical to me.