Please pardon the elementary question, for some reason I'm not grocking why all possible poker hand combinations are equally probable, as all textbooks and websites say. Just intuitively I would think getting 4 of a number is much more improbably than getting 1 of each number, if I were to draw 4 cards. For example, ignoring order, to get 4 of a single number there are only $4 \choose 4$ distinct possibilities, whereas for 1 of each number I would have ${4 \choose 1}^4$ distinct possibilities.
How are all possible poker hands of equal probability
pokerprobability
Best Answer
Yes, that's true, but they mean that any particular hand of 5 cards has the same probability as any other hand of 5 cards. Once you start talking about the probability of a pair or four of a kind, you're talking about the probability of getting one of a number of hands. To put it another way, the probability of drawing a royal flush in spades is exactly the same as the probability of drawing the 2,3 of diamonds, the 6,8 of clubs, and the Jack of hearts.