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Basic Odds and Outs

If you ever wanted to know some of the odds and probabilities of Texas hold'em poker, from the chances of flopping a flush (0.8%) or set (12%) to the odds of an overcard coming on the flop when you hold pocket jacks (57%), the CardPlayer.com Basic Poker Odds and Outs section is a good place to start your search for the answer. This section has plenty of numbers to satisfy your burning poker math questions, and more sections will be added constantly.

 

Odds of being dealt certain starting hands

Hand Probability Odds
 
A-Ks (or any specific suited cards) 0.00302 331-1
A-A (or any specific pair) 0.00453 220-1
A-Ks, K-Qs, Q-Js, or J-10s (suited cards) 0.0121 81.9-1
A-K (or any specific non-pair, incl. suited) 0.0121 81.9-1
A-A, K-K, or Q-Q 0.0136 72.7-1
A-A, K-K, Q-Q, or J-J 0.0181 54.3-1
Suited cards, jack or better 0.0181 54.3-1
A-A, K-K, Q-Q, J-J, or 10-10 0.0226 43.2-1
Suited cards, 10 or better 0.0302 32.2-1
Suited connectors 0.0392 24.5-1
Connected cards, 10 or better 0.0483 19.7-1
Any two cards with rank at least queen 0.0498 19.1-1
Any pocket pair 0.0588 16-1
Any two cards with rank at least jack 0.0905 10.1-1
Any two cards with rank at least 10 0.143 5.98-1
Connected cards (cards of consecutive rank) 0.157 5.38-1
Any two cards with rank at least 9 0.208 3.81-1
Neither connected nor suited, at least one 2-9 0.534 0.873-1

Odds of making a hand with certain number of outs

Example drawing to Outs Make on turn Make on river Make on turn or river
    Prob. Odds Prob. Odds Prob. Odds
 
Inside straight flush;
Four of a kind		 1 0.0213 46.0-1 0.0217 45.0-1 0.0426 22.5-1
Open-ended straight flush;
Three of a kind		 2 0.0426 22.5-1 0.0435 22.0-1 0.0842 10.9-1
High pair 3 0.0638 14.7-1 0.0652 14.3-1 0.1249 7.01-1
Inside straight;
Full house		 4 0.0851 10.8-1 0.0870 10.5-1 0.1647 5.07-1
Three of a kind or two pair 5 0.1064 8.40-1 0.1087 8.20-1 0.2035 3.91-1
Either pair 6 0.1277 6.83-1 0.1304 6.67-1 0.2414 3.14-1
Full house or four of a kind; (see note)
Inside straight or high pair		 7 0.1489 5.71-1 0.1522 5.57-1 0.2784 2.59-1
Open-ended straight 8 0.1702 4.88-1 0.1739 4.75-1 0.3145 2.18-1
Flush 9 0.1915 4.22-1 0.1957 4.11-1 0.3497 1.86-1
Inside straight or pair 10 0.2128 3.70-1 0.2174 3.60-1 0.3839 1.60-1
Open-ended straight or high pair 11 0.2340 3.27-1 0.2391 3.18-1 0.4172 1.40-1
Inside straight or flush;
Flush or high pair		 12 0.2553 2.92-1 0.2609 2.83-1 0.4496 1.22-1
  13 0.2766 2.62-1 0.2826 2.54-1 0.4810 1.08-1
Open-ended straight or pair 14 0.2979 2.36-1 0.3043 2.29-1 0.5116 0.955-1
Open-ended straight or flush;
Flush or pair; Inside straight,
flush or high pair		 15 0.3191 2.13-1 0.3261 2.07-1 0.5412 0.848-1
  16 0.3404 1.94-1 0.3478 1.88-1 0.5698 0.755-1
  17 0.3617 1.76-1 0.3696 1.71-1 0.5976 0.673-1
Inside straight or flush or pair;
Open-ended straight, flush or high pair		 18 0.3830 1.61-1 0.3913 1.56-1 0.6244 0.601-1
  19 0.4043 1.47-1 0.4130 1.42-1 0.6503 0.538-1
  20 0.4255 1.35-1 0.4348 1.30-1 0.6753 0.481-1
Open-ended straight, flush or pair 21 0.4468 1.24-1 0.4565 1.19-1 0.6994 0.430-1

Odds Against Flopping

Hand Odds Percent
 
A flush 118-1 0.8%
A straight when holding any two connecting cards J-10 through 5-4 76-1 1.3%
Three of a kind when holding a pocket pair 7.5-1 11.8%
A pair (matching one of your holecards) 2.45-1 29.0%

Odds of two hands versus each other preflop (approximated)

Situation Hands Odds Percent
 
Higher pair vs. lower pair Js Jc vs. 7h 7d 4.09-1 80.3% vs. 19.7%
Pair vs. two higher cards 7s 7c vs. Ah Jd 1.23-1 55.1% vs. 44.9%
Pair vs. two lower card Qs Qc vs. 9h 7d 4.77-1 82.7% vs. 17.3%
Pair vs. a higher and a lower card Js Jc vs. Ah 7d 2.50-1 71.4% vs. 28.6%
Two higher cards vs. two lower cards Qs Jc vs. 6h 5d 1.70-1 62.9% vs. 37.1%
A higher and a lower card vs.
two middle cards		 As 6c vs. Jh 9d 1.27-1 55.9% vs. 44.1%
Highest and third highest card vs.
second highest and lowest card		 As 6c vs. Jh 2d 1.73-1 63.3% vs. 36.7%
Highest and common card vs. lowest and common card As Jc vs. Jh 9d 2.74-1 73.3% vs. 26.7%

Chance of an overcard hitting the board when holding a pocket pair

Hand Overcard on Flop Overcard on Complete Board
 
2-2 100% 100%
3-3 99.9% 99.9997%
4-4 99.4% 99.988%
5-5 98.1% 99.91%
6-6 95.8% 99.6%
7-7 92.1% 98.8%
8-8 86.7% 96.9%
9-9 79.3% 93.3%
10-10 69.5% 86.9%
J-J 57% 76.3%
Q-Q 41.4% 59.9%
K-K 22.6% 35.3%
A-A 0% 0%

Probability of facing a larger pair when holding...

Hand Against 1 Against 2 Against 3 Against 4 Against 5 Against 6 Against 7 Against 8 Against 9
 
K-K 0.0049 0.0098 0.0147 0.0196 0.0244 0.0293 0.0342 0.0391 0.0439
Q-Q 0.0098 0.0195 0.0292 0.0388 0.0484 0.0579 0.0673 0.0766 0.0859
J-J 0.0147 0.0292 0.0436 0.0577 0.0717 0.0856 0.0992 0.1127 0.1259
10-10 0.0196 0.0389 0.0578 0.0764 0.0946 0.1124 0.1299 0.1470 0.1637
9-9 0.0245 0.0484 0.0718 0.0946 0.1168 0.1384 0.1593 0.1795 0.1990
8-8 0.0294 0.0580 0.0857 0.1125 0.1384 0.1634 0.1873 0.2101 0.2318
7-7 0.0343 0.0674 0.0994 0.1301 0.1595 0.1874 0.2138 0.2387 0.2619
6-6 0.0392 0.0769 0.1130 0.1473 0.1799 0.2104 0.2389 0.2651 0.2890
5-5 0.0441 0.0862 0.1263 0.1642 0.1996 0.2324 0.2623 0.2892 0.3129
4-4 0.0490 0.0956 0.1395 0.1806 0.2186 0.2532 0.2841 0.3109 0.3334
3-3 0.0539 0.1048 0.1526 0.1967 0.2370 0.2729 0.3040 0.3300 0.3503
2-2 0.0588 0.1141 0.1654 0.2124 0.2546 0.2914 0.3222 0.3464 0.3633

Probability of facing multiple larger pairs when holding...

Hand Against 1 Against 2 Against 3 Against 4 Against 5 Against 6 Against 7 Against 9
 
K-K < 0.00001 0.00001 0.00003 0.00004 0.00007 0.00009 0.00012 0.00016
Q-Q 0.00006 0.00018 0.00037 0.00061 0.00091 0.00128 0.00171 0.00220
J-J 0.00017 0.00051 0.00102 0.00171 0.00257 0.00360 0.00482 0.00621
10-10 0.00033 0.00099 0.00200 0.00335 0.00504 0.00709 0.00950 0.01226
9-9 0.00054 0.00164 0.00330 0.00553 0.00836 0.01177 0.01580 0.02045
8-8 0.00081 0.00244 0.00493 0.00828 0.01253 0.01769 0.02378 0.03084
7-7 0.00112 0.00341 0.00689 0.01160 0.01758 0.02487 0.03351 0.04353
6-6 0.00149 0.00454 0.00918 0.01550 0.02353 0.03335 0.04503 0.05861
5-5 0.00191 0.00583 0.01182 0.01998 0.03040 0.04318 0.05840 0.07619
4-4 0.00239 0.00728 0.01480 0.02506 0.03821 0.05438 0.07371 0.09635
3-3 0.00291 0.00890 0.01812 0.03075 0.04698 0.06699 0.09099 0.11919
2-2 0.00349 0.01068 0.02180 0.03706 0.05673 0.08107 0.11034 0.14484

Probability of facing an ace with larger kicker when holding...

Hand Against 1 Against 2 Against 3 Against 4 Against 5 Against 6 Against 7 Against 8 Against 9
 
AK 0.00245 0.00489 0.00733 0.00976 0.01219 0.01460 0.01702 0.01942 0.02183
AQ 0.01224 0.02434 0.03629 0.04809 0.05974 0.07126 0.08263 0.09386 0.10496
AJ 0.02204 0.04360 0.06468 0.08529 0.10545 0.12517 0.14445 0.16331 0.18175
AT 0.03184 0.06266 0.09250 0.12139 0.14937 0.17645 0.20267 0.22805 0.25263
A9 0.04163 0.08153 0.11977 0.15642 0.19154 0.22520 0.25745 0.28837 0.31799
A8 0.05143 0.10021 0.14649 0.19038 0.23202 0.27152 0.30898 0.34452 0.37823
A7 0.06122 0.11870 0.17266 0.22331 0.27086 0.31550 0.35741 0.39675 0.43369
A6 0.07102 0.13700 0.19829 0.25523 0.30812 0.35726 0.40291 0.44531 0.48471
A5 0.08082 0.15510 0.22338 0.28615 0.34384 0.39687 0.44561 0.49041 0.53160
A4 0.09061 0.17301 0.24795 0.31609 0.37806 0.43442 0.48567 0.53227 0.57465
A3 0.10041 0.19073 0.27199 0.34509 0.41085 0.47000 0.52322 0.57109 0.61416
A2 0.11020 0.20826 0.29552 0.37315 0.44223 0.50370 0.55840 0.60706 0.65037

A board being dealt consisting of...

Board Texture Making on flop Making by turn Making by river
  Prob. Odds Prob. Odds Prob. Odds
 
Three or more of same suit 0.05177 18.3-1 0.13522 6.40-1 0.23589 3.24-1
Four or more of same suit     0.01056 93.7-1 0.03394 28.5-1
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 0.11820 7.46-1 0.25068 2.99-1
Four cards to a straight (but not five)     0.03877 24.8-1 0.18991 4.27-1
Three or more cards of
consecutive rank and same suit		 0.00217 459-1 0.00869 114-1 0.02172 45.0-1
Three of a kind
(but not a full house or four of a kind)		 0.00235 424-1 0.00935 106-1 0.02128 46-1
A pair
(but not two pair or three or
four of a kind)		 0.16941 4.90-1 0.30417 2.29-1 0.42450 1.36-1
Two pair (but not a full house)     0.01037 95.4-1 0.04716 20.2-1

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