Probability that one
or more
players will have an Ace dealt to them with 9, 8, 7, 6, 5, 4, 3, 2 players
9: 83%
8: 72%,
7: 67%,
6: 62%,
5: 55%,
4: 47%,
3: 38%,
2: 27%,
8: 47%,
7: 42%,
6: 38%,
5: 32%,
4: 27%,
3: 21%,
2: 15%,
1: 7%,
Probability of facing an ace with larger kicker when holding AX  
AX  Against 1  Against 2  Against 3  Against 4  Against 5  Against 6  Against 7  Against 8  Against 9 
A2  11.0%  20.8%  29.6%  37.3%  44.2%  50.4%  55.8%  60.7%  65.0% 
A3  10.0%  19.1%  27.2%  34.5%  41.1%  47.0%  52.3%  57.1%  61.4% 
A4  9.1%  17.3%  24.8%  31.6%  37.8%  43.4%  48.6%  53.2%  57.5% 
A5  8.1%  15.5%  22.3%  28.6%  34.4%  39.7%  44.6%  49.0%  53.2% 
A6  7.1%  13.7%  19.8%  25.5%  30.8%  35.7%  40.3%  44.5%  48.5% 
A7  6.1%  11.9%  17.3%  22.3%  27.1%  31.6%  35.7%  39.7%  43.4% 
A8  5.1%  10.0%  14.6%  19.0%  23.2%  27.2%  30.9%  34.5%  37.8% 
A9  4.2%  8.2%  12.0%  15.6%  19.2%  22.5%  25.7%  28.8%  31.8% 
AT  3.2%  6.3%  9.3%  12.1%  14.9%  17.6%  20.3%  22.8%  25.3% 
AJ  2.2%  4.4%  6.5%  8.5%  10.5%  12.5%  14.4%  16.3%  18.2% 
AQ  1.2%  2.4%  3.6%  4.8%  6.0%  7.1%  8.3%  9.4%  10.5% 
AK  0.2%  0.5%  0.7%  1.0%  1.2%  1.5%  1.7%  1.9%  2.2% 
Better than 1 in 3 chance no better AX in the hand (3 opponents is the key) 
Type of draw  Hand  The flop  Specific outs  # Outs  Flop to turn  Turn to river  Turn & River 
Pocket pair to set  22  Q49  22  2  4.3%(221)  4.3% (221)  8.4% (111) 
One overcard  A8  952  AAA  3  6.4% (141)  6.5%(141)  12.5% (71) 
Inside straight draw  J9  Q84  10  4  8.5% (111)  8.7% (111)  16.5% (51) 
Two pair to full house  KQ  KQ5  KKQQ  4  8.5% (111)  8.7% (111)  16.5% (51) 
One pair to two pair or trips  AQ  A 103  AAQQQ  5  10.6% (81)  10.9% (81)  20.3% (41) 
No pair to pair  97  23J  999777  6  12.8% (132)  13% (132)  24.1% (31) 
Two overcards to overpair  AJ  10 8 2  AAAJJJ  6  12.8% (132)  13% (132)  24.1% (31) 
Set to full house/ four of a kind  66  67J  6777JJJ  7  14.9% (112)  15.2% (112)  27.8% (52) 
Openended straight draw  98  7103  J6  8  17% (51)  17.4% (51)  31.5% (21) 
Flush draw  KJ  A68  2345789107  9  19.1% (41)  19.6% (41)  35% (21) 
Inside straight draw and two overcards  AK  10 2  JAAAKKK  10  21.3% (41)  21.7% (41)  38.4% (32) 
Inside straight and flush draw  AK  JQ3  102456789Q  12  25.5% (31)  26.1% (31)  45% (54) 
Openended Straight and Flush Draw  KQ  10 J 4  9A235678J  15  31.9% (21)  32.6% (21)  54.1% (56) 
The “ win probavility formula” looks like this:
(OUTS X 2) + 1 = % of getting a card you need
That formula works anytime you have between three and eleven outs.
If you have FEWER than three outs, it doesn’t really matter… since you should fold anyway.
For example, let’s say you pick up an openended straight draw and have eight outs.
(8 outs x 2) + 1 = 17%
"Rule of Four and Two". With two cards to come, the percent chance of hitting x outs is about (Outs X 4 (%); With one car to come its Outs X 2 (%)  
Outs  Make on turn or river  Make on river 
1  4.2%  2.2% 
2  8.4%  4.3% 
3  12.5%  6.5% 
4  16.5%  8.7% 
5  20.3%  10.9% 
6  24.1%  13.0% 
7  27.8%  15.2% 
8  31.4%  17.4% 
9  34.9%  19.5% 
10  38.4%  21.7% 
11  41.7%  23.9% 
12  44.9%  26.1% 
13  48.1%  28.2% 
14  51.1%  30.4% 
15  54.1%  32.6% 
16  56.9%  34.8% 
17  59.8%  36.9% 
18  62.4%  39.1% 
19  65.0%  41.3% 
20  67.5%  43.4% 
21  69.9%  45.6% 
22  72.2%  47.8% 
23  74.5%  50.0% 
Better than 30% 
..  A  K  Q  J  T  9  8  7  6  5  4  3  2 
As  64  40  38  37  36  33  32  31  30  30  29  28  27 
Ks  43  59  36  35  34  31  29  28  27  
Qs  41  39  54  34  33  30  28  
Js  40  38  37  50  32  29  27  
Ts  39  37  36  35  46  29  27  
9s  36  35  33  33  33  42  
8s  35  33  31  31  31  30  38  
7s  34  32  29  29  29  28  28  35  
6s  33  31  29  27  32  
5s  34  30  28  29  
4s  33  29  27  27  
3s  32  29  27  
2s  31  28  27  
>7  
>30%  
Suited  A2  K5  Q8  J8  T8  
Unsuited  A2  K9  Q9  JT  TT 
Common Odds When Holding Three Gapped Connectors From A5 To AT:  
flopping a straight (including the slight chance of a straight flush in some cases)  0.3% 
flopping an 8 out straight draw*  2.6% 
Common Odds When Holding One Gapped Connectors From 53 To QT:  
flopping a straight (including the slight chance of a straight flush in some cases)  1.0% 
flopping an 8 out straight draw*  8.0% 
Common Odds When Holding Connectors From 54 To JT:  
flopping a straight (including the slight chance of a straight flush in some cases)  1.0% 
flopping an 8 out straight draw*  10.0% 
Common Odds When Holding Two Suited Cards:  
flopping a flush (including the slight chance of a straight flush in some cases)  0.8% 
flopping a four flush  10.9% 
Common Odds When Holding Two Unsuited Cards:  
flopping a four flush  2.2% 
Common Odds When Holding Paired Hole Cards:  
flopping EXACTLY two pair by pairing the board  16.1% 
flopping EXACTLY trips by flopping a set for your pocket pair  10.8% 
flopping EXACTLY a full house, a set to your hole pair and pairing the board  0.7% 
flopping EXACTLY a full house, by the board tripping up  0.3% 
flopping EXACTLY four of a kind, two cards to your hole pair  0.3% 
Common Odds When Holding Unpaired Hole Cards:  
flopping EXACTLY one pair by pairing a hole card  26.9% 
flopping EXACTLY two pair by pairing a hole card AND pairing on the board  2.0% 
flopping EXACTLY two pair by pairing EACH of your hole cards  2.0% 
flopping EXACTLY trips by flopping two cards to one hole card  1.3% 
flopping EXACTLY a full house, trips of one hole card and pairing the other  0.1% 
flopping EXACTLY four of a kind, three cards to one of your hole cards  0.1% 
With 4 cards of the same suit after the flop there is a 38.3% chance of completing the flush by the river.
With 3 cards of the same suit after the flop, there is a 32.6% chance of completing the flush by the river.
With 2 cards of the same suit after the flop, there is a 29.8% chance of completing the flush by the river.
With 4 connected cards after the flop, there is a 34.8% chance of completing a 5card straight by the river.
With 2 connected cards after the flop, there is an 8.7% chance of completing a 5card straight by the river.
With 3 connected cards after the flop, there is a 17% chance of completing a 5card straight by the river.
With AKQ after the flop, you have approximately a 17.0% chance of completing a 5card straight by the river.
Probability of Completing Hand  Flop => River  
No. of Outs  Percent  No. of Outs  Percent 
20  68  10  38 
19  65  9  35 
18  62  8  31 
17  60  7  28 
16  57  6  24 
15  54  5  20 
14  51  4  16 
13  48  3  12 
12  45  2  8 
11  42  1  4 
Straight Flush Draw  
Inside Straight Draw => 4  
Flush Draw => 9  
two pair or gunshot draw  
Pair to Set of 3 => 2  
Two pair to Full House => 4  
Open Ended Straight Draw => 8 
Poker Odds Chart  
Odds and outs  
Outs 
Odds: FlopTurn / TurnRiver 
Odds: FlopRiver 
Example 
1  46:1  22.5:1  Backdoor flush draw 
2  22.5:1  11:1  Pocket pair to set 
4  11:1  5:1  Gunshot straight 
5  8:1  4:1  Two pair/trips 
8  5:1  2:1  Openended straight draw 
9  4:1  2:1  Flush draw 
12  3:1  1:1  Flush draw + gutshot 
13  2.5:1  1:1  OESD + pair 
14  2.5:1  1:1  Flush draw + pair 
15  2:1  1:1  Flush draw + OESD 
[6,7,8,9,10,J,Q,K,A]
>5 1:2
>6 2:5 [7,8,9,10,J,Q,K,A] 8 of 13 cards
>7 1:3
>8 1:5
>9 1:6
>10 1:11 [J,Q,K,A]
Odds of connecting with the Flop in Hold’em
Probability of there being a flop with 3 Suited cards
Your first card can be anything. So you have 52 choices out of 52 cards (because no matter what card you draw you can get a full hand of the same suite). Your second card, has to be the same suit as your first card, so probability of that is 1251 because there are 13 of each suite and you have to subtract 1 for the one card you have drawn. Your third card has to be the same suite as the first and the second, notice there are only 11 cards left of that suite, so selecting that specific card will be 11/50
Giving a total probability of:
(52/52)×(12/51)×(11/50) = 0.05 => 1 in 20
Completing the Flush
With 4 suited cards (various combos) => you have 9 outs to make your hand on the turn or river (There are 13 cards per suit and you have 4 of them). So you have 9 outs out of 47 total unknown cards (52 cards in the deck – your 2 cards and – 3 more on the flop) => 9/47 => 1 in 5 chance to hit your flush after the turn or the river. The odds can get better late in the game as fewer cards remain in the pack BUT some of your suited cards may have been buried.
With 3 suited cards after the flop, you have 10 outs to make your hand after the turn and river but you need to score twice (both times) => Your chance of hitting the flush on the turn is 9/47 = 19.15% (about 1 in 5). If you don't hit on the turn, your change of hitting the river is 9/46 = 19.57%. Your overall chances are 19.15% + (19.57% * (10.1915)) = almost exactly 35%.
This is especially where “outs” come into your line of thinking and how all of these Texas Hold’em odds are generated. For example, if you have 4 cards to a flush you have 9 outs to make your hand on the turn. There are 13 cards per suit and you have 4 of them.
There are 9 unknown cards left that could complete your flush so you have 9 outs out of 47 total unknown cards (52 cards in the deck – your 2 cards and – 3 more on the flop). This is how Texas Hold’em odds are calculated. 9/47 = 19.1, or a 19.1% chance to hit your flush on the turn.
Drawing to openended straights and flushes, or fear of your opponents doing so, is one of the most common scenarios in Hold’em.
Note that the figures above also apply on the turn to calculate odds for the river since you have the same 1 card to come.
The following set of odds is the likelihood to complete these hands by the river on the flop, so with 2 cards to come.
Pairs  chance overcard in flop  . 
KK  22% 
41%  
JJ  56% 
TT  69% 
99  80% 
88  86% 
77  92% 
66  96% 
55  98% 
higher pair beats lower pair  82% 
lower pair beats higher pair  18% 
KK same chance as 33 or 22 against AA  18% 
Pair beats 2 higher cards (22 vs AJ)  55% 
Pair beats 2 lower cards (QQ vs T6)  86% 
Pair beats 2 lower cards (suited or connected)  70% 
Pair beats cards 1 higher/1 lower (QQ vs A7)  71% 
Pair flops a set or better  11.8% 
Pair flops a set  11% 
Pair flops a full house  1% 
Pair flops 4 of a kind 1  0.25% 
Matched Pair to trip  8% 
Have 2 pairs after flop => full house  16% 
Odds get an A  15% 
Odds get an A or a pair  21% 
Dealt an A, probability of no one else having one:  . 
2 players  88% 
3 players  77% 
4 players  67% 
5 players  58% 
6 players  50% 
7 players  43% 
8 players  36% 
9 players  30% 
That is if you have an A with 9 other players,  . 
there’s a 70% chance that at least one other player also has an A!  . 
.  . 
Straights  chance to complete  . 
3 card straight after flop the chance of completing  30% 
2 connected cards to complete straight  2% 
J10 is the best of the connectors in one way – because these are the only cards that make 4 straights and each straight is the nuts! nuts.  . 
.  . 
Trips  . 
Trips on the flop chance of full house or better  33% 
.  . 
Flushes  . 
If you start with any 2 suited cards:  . 
to flop a flush  1% 
to flop a four card flush  11% 
to complete a flush with four cards flushed  35% 
with any 2 suited cards get a complet flush  4% 
.  
AK  . 
AK unsuited vs small suited connectors  7:5. 
AK suited vs small unsuited connectors  9:5. 
AK unsuited vs a pair  10:11. 
AK suited vs a pair  1:1 
.  . 
Other odds  . 
Any 2 cards vs any 2 lower cards (e.g. AK vs 72)  63% 
Two higher cards vs a pair (e.g. KQ vs 99)  45% 
Two suited higher cards vs a pair (e.g. KQs vs 99)  50% 
One card higher and one lower than a pair (e.g. K10 vs QQ)  40% 
One card higher and one in between Villain’s 2 cards (e.g. AJ vs K9)  150% 
One card higher and one lower than Villain’s 2 cards (e.g. A2 vs J4)  56% 
One card the same as Villain’s, the other higher (e.g. A10 vs A9)  71% 
No pair in card improving to at least a pair  27% 
.  . 
Other insights  . 
Most flops miss pairing most hands! (Indeed, if you hold AK, you won’t pair either card on the flop 68% of the time).  . 
The probability that your opponent is bluffing is a least 10%  . 
Any time you have an A in your hand and you are getting a little over 2:1 pot odds to call, you pretty much have to call. It’s only against AA that your chances are markedly worse.  . 
Flop to Turn  Turn to River  Turn and River  
Outs  %  Odds  %  Odds  %  Odds 
20  42.6%  1.351  43.5%  1.301  67.5%  0.481 
19  40.4%  1.471  41.3%  1.421  65.0%  0.541 
18  38.3%  1.611  39.1%  1.561  62.4%  0.601 
17  36.2%  1.771  37.0%  1.711  59.8%  0.671 
16  34.0%  1.941  34.8%  1.881  57.0%  0.751 
15  31.9%  2.131  32.6%  2.071  54.1%  0.851 
14  29.8%  2.361  30.4%  2.291  51.2%  0.951 
13  27.7%  2.621  28.3%  2.541  48.1%  1.081 
12  25.5%  2.921  26.1%  2.831  45.0%  1.221 
11  23.4%  3.271  23.9%  3.181  41.7%  1.401 
10  21.3%  3.701  21.7%  3.601  38.4%  1.601 
9  19.1%  4.221  19.6%  4.111  35.0%  1.861 
8  17.0%  4.881  17.4%  4.751  31.5%  2.171 
7  14.9%  5.711  15.2%  5.571  27.8%  2.601 
6  12.8%  6.831  13.0%  6.671  24.1%  3.151 
5  10.6%  8.401  10.9%  8.201  20.3%  3.931 
4  8.5%  10.751  8.7%  10.501  16.5%  5.061 
3  6.4%  14.671  6.5%  14.331  12.5%  7.001 
2  4.3%  22.501  4.3%  22.001  8.4%  10.901 
1  2.1%  46.001  2.2%  45.001  4.3%  22.261 
The Probability that.... 
Odds 
% 

Nonpairs will pair at least one card 
2to1 
32% 

Nonpairs will pair both hold cards 
50to1 
2% 

A pair will flop a set 
8to1 
12% 

A pair will flop four of a kind 
400to1 
0.3% 

Two suited cards will flop a flush 
118to1 
1% 

Two suited cards flop a four flush (flush draw) 
9to1 
11% 

Two suited cards will make a flush by the river 
15to1 
7% 

Probability that .... 

You Hold 
Hope to Make 
Outs 

A Pair 
Three of a Kind 
2 

Two Pair 
Full House 
4 

Inside Straight 
Straight 
4 

Overcards 
Pair 
6 

Openended Straight 
Straight 
8 

Four Flush 
Flush 
9 

Straight & Flush Draw 
Straight / Flush or Better 
15 

Probability of improving on the flop 

Starting hand 
Improvement on flop 
Probability in % 
Odds 
Pocket pair 
Threeofakind or better 
12.7 
7:1 
Pocket pair 
Threeofakind 
11.8 
8:1 
Pocket pair 
Full house 
0.73 
136:1 
Pocket pair 
Fourofakind 
0.24 
415:1 
2 unpaired cards 
Pair 
32.4 
2:1 
2 unpaired cards 
Two pair 
2 
48:1 
Suited cards 
Flush 
0.8 
118:1 
Suited cards 
Flush draw 
10.9 
8:1 
Suited cards 
Backdoor flush draw 
41.6 
2:1 
Connectors 45oJTo 
Open Ended Straight Draw 
9.6 
9.:1 
Connectors 45sJTs 
Straight draw / flush draw 
19.1 
4:1 
Connectors 45oJTo 
Straight 
1.31 
75:1 
Probability of improving on the turn 

Starting hand 
Improvement on flop 
Probability in % 
Odds 
Flush draw 
Flush 
19.1 
4.:1 
OESD 
Straight 
17 
5:1 
Gutshot straight draw 
Straight 
8.5 
11:1 
Threeofakind 
Fourofakind 
2.1 
47:1 
Two pair 
Full house 
8.5 
11:1 
Pair 
Threeofakind 
4.3 
22.:1 
Two unpaired cards 
Pair (with hole card) 
12.8 
7:1 
Probability of improving on the river 

Starting hand 
Improvement on flop 
Probability in % 
Odds 
Flush draw 
Flush 
19.6 
4.1:1 
Open Ended Straight Draw 
Straight 
17.4 
4.74:1 
Gutshot straight draw 
Straight 
8.7 
10.5:1 
Threeofakind 
Fourofakind 
2.2 
45.46:1 
Two pair 
Full house 
8.7 
10.5:1 
Pair 
Threeofakind 
4.3 
22.26:1 
Two unpaired cards 
Pair (with hole card) 
13 
6.7:1 
Probability of improving from flop to river 

Starting hand 
Improvement on flop 
Probability in % 
Odds 
Flush draw 
Flush 
35 
1.86:1 
Backdoor flush draw 
Flush 
4.2 
22.8:1 
OESD 
Straight 
32 
2.13:1 
Gutshot straight draw 
Straight 
17 
4.88:1 
Threeofakind 
Fourofakind 
4.3 
22.26:1 
Two pair 
Full house 
17 
4.88:1 
Pair 
Fourofakind 
0.09 
1100:1 
Pair 
Threeofakind 
8.4 
10.9:1 
Probability of seeing a specific board on the flop 

On the flop 
Probability in % 
Odds 

Threeofakind 
0.24 
415:1 

Pair 
16.9 
5:1 

3 suited cards 
5.17 
18:1 

2 suited cards 
55 
0.8:1 

Rainbow 
39.8 
1.5:1 

3 connected straight cards 
3.45 
28:1 

2 connected straight cards 
40 
1.5:1 

No connected cards 
55.6 
0.81 

Rules for Starting Cards 

Starting Pairs 
Number (suited) 
Odds of getting these Start Cards 

AA to A7 
124 (31) 

KK to K7 
108 (28) 

QQ to Q10 
44 (11) 

JJ and J10 
28 (7) 

Additional Pairs & Adjacent Cards >6 
136 (24) 

Total for all above with 2652 combos 
440 (101) 
about 1 in 6 hands 

Including A6 to A2 suited , K6 to K2 suited and Q9 to Q7 suited 
500 
about 1 in 5 hands 