I always pick Russians, regardless of the number of Axis players. I feel I have the right to choose the underdog even if it unbalances the teams. I admit if Axis is getting thrashed (rarely) I will switch to them.
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Human beings -suck- at probability and odds. It's one of our biggest weaknesses. That's why I said, I don't know if there are any anomalous differences between rolling tons of dice and rolling a single dice. I wouldn't dare tell you if it changes the odds or not, because it's rarely as simple as that.
I think humans are pretty good at statistics In this particular case I suppose at the very least, using many dice would reduce the chances of one of them messing with the odds by being "fixed" or not properly weighted.
No, it's a known problem humans have. Numbers become meaningless when we take them off of a human scale.
Again, very few people can wrap their head around the whole "once an event has happened, the odds become 1:1 for it happening" concept. Trust me, I argue with them all the time.
Why isn't there a "whatever side has the least players" option?
..... Otherwise I just go to which ever team has the fewest players.