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4 different kinds of royal flushes, 5 cards each.

***NOTE this takes into account that no one has any hole cards.. Im doing the math with a full 52 card deck****

The first flop card has to be one of those 20 royal flush cards in the deck of 52 so the probability of that hitting is 20/52

Once that first card hits, The suit of the royal flush is now set and there is only 4 remaining cards in the deck to complete the hand.

Therefore the 2nd and 3rd flop cards probabilities are 4/51 and 3/50

The turn then has to be 2/49 cards and the river the last 1/48

Multiplying these: 20/52 * 4/51 * 3/50 * 2/49 * 1/48 = 480/311,875,200

Or simply just under 1 in 650,000 times :)

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16y ago

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