Originally Posted by RoyalFish
But they have an equal probability of running good or bad over any finite set of future hands. :-)
Of course. However if you and I agree to flip coins 1000 times or whatever (that is, each of us flipping our own coin), it is expected that we will end up with a different number of heads, one of us will have more.
In fact I was curious so I just wrote a little program that simulates this. I did 1000 series of 1000 flips each. The 2 players had a different number of heads 982/1000 of these times. The average difference was +.39 flip for player 1 (which is just noise) but the average absolute deviation was 17.5 flips.
A surprising result to some people, I think, is that if you increase the number of flips, the disparity gets greater. For example, 1000 runs of 10k flips has 992/1000 results where one player got more heads than the other and the average absolute deviation was 60.
However we can see that deviation/N decreases, since we went from
17.5/1000 = 0.0175
60/10000 = 0.006
But yes, by no means, do we expect 2 people to have "equal luck"