Something I've been thinking about

[Rainclouds]

Ringmaster is spot on and he has answered all questions which can be asked about this situation, imo.

To summarize once again:
1) our equity vs villains range is 50% in all situations (we all agreed on that)
2) therefore, our chance of winning the pot is 50% (ORLY)
3) if you lose the pot, you lose all, if you win the pot, you win the whole pot (ORLY)
4) therefore, no matter what the distribution of villains range is, we have 50% chance of winning the whole pot, and 50% chance of losing the whole pot (YA RLY).
5) variance is the mean square deviation of values from their arithmetic mean
6) the arithmetic mean is 0.5
7) if we win, we win 1. The deviation from the arithmetic mean is 0.5. The square deviation is 0.5*0.5=0.25
8) if we lose, we win 0. The deviation from the arithmetic mean is -0.5. The square deviation is -0.5*-0.5=0.25
9) The variance is the mean of 0.25 and 0.25, which is 0.25 (ORLY)
10) From (1) to (9) follows that the variance is the same for all situations.

It's mathematically proven so there's not really anything to argue about. And now I must go to sleep.