Re: Running it twice...
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it doesnt change the EV of the hand at all, it just reduces variance.
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Lets say youre playing with a lot of money and have As Ac and get it all in on board of Th 6s 7s against Ts Js. You might offer to run it more than once--and generally you'd do it three times here, for one third of the pot each time, since its a near-coinflip situation. This way the fact that you both made the decision to gamble doesnt get lost, someone will win money, but probably not the whole pot.
Incidentally, in this situation, you burn, turn, burn, river, muck the cards, then do the same twice more. You do not shuffle cards back into deck.
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