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What's the proper way to calculate probability for a card game?
It's not the shuffling it's how they're dealt. If you are handing out the cards one at a time then each card has a 50/50 chance of going to each player; but if you have three cards and you pick (with equal probability) either to split before the first card (all three to P2), before the second (one to P1, two to P2) before the third (two to P1, one to P2) or after the third (all to P1), then there are 4 possible outcomes with 6 combinations each that each have a 25% chance of happening. Essentially you're cutting out all the possibilities of the single card being dealt between the other two.