Odds of Flopping Overcards

• 	No overcard on flop		No overcard by turn		No overcard by river
  	Prob.	Odds	Prob.	Odds	Prob.	Odds
  KK	0.7745	0.29 : 1	0.7086	0.41 : 1	0.6470	0.55 : 1
  QQ	0.5857	0.71 : 1	0.4860	1.06 : 1	0.4015	1.49 : 1
  JJ	0.4304	1.32 : 1	0.3205	2.12 : 1	0.2369	3.22 : 1
  TT	0.3053	2.28 : 1	0.2014	3.97 : 1	0.1313	6.61 : 1
  99	0.2071	3.83 : 1	0.1190	7.40 : 1	0.0673	13.87 : 1
  88	0.1327	6.54 : 1	0.0649	14.40 : 1	0.0310	31.21 : 1
  77	0.0786	11.73 : 1	0.0318	30.48 : 1	0.0124	79.46 : 1
  66	0.0416	23.02 : 1	0.0133	74.26 : 1	0.0040	246.29 : 1
  55	0.0186	52.85 : 1	0.0043	229.07 : 1	0.0009	1,057.32 : 1
  44	0.0061	162.33 : 1	0.0009	1,095.67 : 1	0.0001	8,406.78 : 1
  33	0.0010	979.00 : 1	0.0001	15,352.33 : 1	0.0000	353,125.67 : 1

  Flopping Overcards When Holding a Pocket Pair

  The above table gives the probability that no overcards will come on the flop, turn, and river, for each of the pocket pairs from 3 to K. Notice that there is a better than 35% probability that an ace will come by the river if holding pocket kings, and with pocket queens, the odds are slightly in favor of an ace or a king coming by the turn, and a full 60% in favor of an overcard to the queen by the river. With pocket jacks, there's only a 43% chance that an overcard will not come on the flop and it is better than 3 : 1 that an overcard will come by the river. Notice, though, that those probabilities would be lower if we consider that at least one opponent happens to hold one of those overcards.

  This chart is provided courtesy of Wikipedia and is available under the Creative Commons Attribution-ShareAlike License.

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