Poker Probability (Texas Hold 'em) - The Flop

The Flop

The value of a starting hand can change dramatically after the flop. Regardless of initial strength, any hand can flop the nuts—for example, if the flop comes with three 2s, any hand holding the fourth 2 has the nuts. Conversely, the flop can undermine the perceived strength of any hand—a player holding A♣ A♥ would not be happy to see 8♠ 9♠ 10♠ on the flop because of the straight and flush possibilities.

There are

possible flops for any given starting hand. By the turn the total number of combinations has increased to

and on the river there are

possible boards to go with the hand.

The following are some general probabilities about what can occur on the board. These assume a "random" starting hand for the player.

Board consisting of Making on flop Making by turn Making by river
Prob. Odds Prob. Odds Prob. Odds
Three or more of same suit (other suit can have two) 0.05177 18.3 : 1 0.17537 4.70 : 1 0.37107 1.69 : 1
Four or more of same suit 0.01056 93.7 : 1 0.04490 21.3 : 1
Rainbow flop (all different suits) 0.39765 1.51 : 1 0.10550 8.48 : 1
Three cards of consecutive rank (but not four consecutive) 0.03475 27.8 : 1 0.10544 8.48 : 1 0.19910 4.02 : 1
Four cards to a straight (but not five) 0.01040 95.1 : 1 0.03763 25.6 : 1
Three or more cards of consecutive rank and same suit 0.00217 459 : 1 0.00675 147 : 1 0.01305 75.6 : 1
Three of a kind (but not a full house or four of a kind) 0.00235 424 : 1 0.00922 107 : 1 0.02113 46.3 : 1
A pair (but not two pair or three or four of a kind) 0.16941 4.90 : 1 0.30425 2.29 : 1 0.42257 1.37 : 1
Two pair (but not a full house) 0.01037 95.4 : 1 0.04754 20.0 : 1

One can see from the table above that more than 60% of the flops will have at least two of the same suit.

Read more about this topic:  Poker Probability (Texas Hold 'em)

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