Running It Twice (or More)

[Chaser8]

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One thing I've actually wondered about this, though. When you run it twice, you remove cards from the deck so the two runs aren't really identical. The side that lost the first run should typically have a better chance of winning the second one. I imagine the effect on EV is small, but I don't think it's identically zero.

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That might be true, but the Hero isn't going to win it the first time everytime. If the Hero has 70% equity, he's going to lose the first run 30% of the time. In those 30% of times, the Hero is ALSO going to have "a better chance of winning the second one." It all balances out. The point is not to have [for example] 70% equity every time you run it. You will win 70% in the longrun, however, you will fluctuate more on your way to approaching that 70% if you run it only once as opposed to more than once.

Just think of running the exact same hole cards on the exact same board millions of times. Each time, the equity is going to be exactly the same.