Texas Hold'em Poker Probability - Flop (5 cards) cont.

Rather than the previous 5 card combinations, players might also be interested in knowing how often we get open-ended straight or 4 card flush after the flop just shown to us.

4 Card Flush: 111540=C(13,4)*4*(52-13)  pick 4 different numbers from A to K with 4 suits, and pick one from the remaining card without the same suit(52-13).

Open Ended Straight: 60480=9*(13-6)*(4^5-4*3*5-4)  from 2345 to TJQK and pick one from the remaining number without making straight (13-6), the total suit combination 4^5 minus 4-card-flush(4*3*5) minus flush(4).

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After the flop is shown, there is about 1 in 13 players to have something better than one pair.

But if we also include the 4 card flush and open-ended straight, then it's about 1 in 7.

So if there might be 7 players into a game to see the flop, you would better be prepared to fight down through the river.