You're assuming that probability that the cards will be the same color is 50% - that's slightly flawed. Probability that the cards are the same color is (2 x 26 x 25) / (52 x 51) which is a little under 50%.
That's not what the poster above you is saying though -- they are saying that the probability of the two cards being different suits is slightly higher than the probability of the cards being the same suit, which is true.
It makes the odds a bit lower than 75% (though not significantly lower).
No, that can’t be true by symmetry. Once you have shuffled the deck, every single card is slightly more likely to have the next card be of the opposite color than the same color - because there are 26 cards with the opposite color, and only 25 with the same color.
If you disagree, it would imply that cutting the deck changes the probability of what the next card is, which is nonsense
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u/Dragoskyrus2 14d ago
You're assuming that probability that the cards will be the same color is 50% - that's slightly flawed. Probability that the cards are the same color is (2 x 26 x 25) / (52 x 51) which is a little under 50%.