Re: Poker math problem, not strategically relevant.
It's not because there is some chance that everyone has a royal, ie. if the board comes up royal. Your way would incorrectly count that 10 times, when we only need to count it once. I suppose we could just adjust for that difference and go with your calculation, or:
Focus on the board and divide it into 3 cases:
1) 3 parts on board
2) 4 parts on board
3) 5 parts on board
Find the probability of each and multiply it by the pr. that someone has it, given a board like that. That gives 3 numbers that you just add up.
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