[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% * (1-0.1915)) = 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 open-ended 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% |
J-10 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 7-2) | 63% |
Two higher cards vs a pair (e.g. KQ vs 9-9) | 45% |
Two suited higher cards vs a pair (e.g. KQs vs 9-9) | 50% |
One card higher and one lower than a pair (e.g. K-10 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. A-2 vs J-4) | 56% |
One card the same as Villain’s, the other higher (e.g. A-10 vs A-9) | 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% | 1.35-1 | 43.5% | 1.30-1 | 67.5% | 0.48-1 |
19 | 40.4% | 1.47-1 | 41.3% | 1.42-1 | 65.0% | 0.54-1 |
18 | 38.3% | 1.61-1 | 39.1% | 1.56-1 | 62.4% | 0.60-1 |
17 | 36.2% | 1.77-1 | 37.0% | 1.71-1 | 59.8% | 0.67-1 |
16 | 34.0% | 1.94-1 | 34.8% | 1.88-1 | 57.0% | 0.75-1 |
15 | 31.9% | 2.13-1 | 32.6% | 2.07-1 | 54.1% | 0.85-1 |
14 | 29.8% | 2.36-1 | 30.4% | 2.29-1 | 51.2% | 0.95-1 |
13 | 27.7% | 2.62-1 | 28.3% | 2.54-1 | 48.1% | 1.08-1 |
12 | 25.5% | 2.92-1 | 26.1% | 2.83-1 | 45.0% | 1.22-1 |
11 | 23.4% | 3.27-1 | 23.9% | 3.18-1 | 41.7% | 1.40-1 |
10 | 21.3% | 3.70-1 | 21.7% | 3.60-1 | 38.4% | 1.60-1 |
9 | 19.1% | 4.22-1 | 19.6% | 4.11-1 | 35.0% | 1.86-1 |
8 | 17.0% | 4.88-1 | 17.4% | 4.75-1 | 31.5% | 2.17-1 |
7 | 14.9% | 5.71-1 | 15.2% | 5.57-1 | 27.8% | 2.60-1 |
6 | 12.8% | 6.83-1 | 13.0% | 6.67-1 | 24.1% | 3.15-1 |
5 | 10.6% | 8.40-1 | 10.9% | 8.20-1 | 20.3% | 3.93-1 |
4 | 8.5% | 10.75-1 | 8.7% | 10.50-1 | 16.5% | 5.06-1 |
3 | 6.4% | 14.67-1 | 6.5% | 14.33-1 | 12.5% | 7.00-1 |
2 | 4.3% | 22.50-1 | 4.3% | 22.00-1 | 8.4% | 10.90-1 |
1 | 2.1% | 46.00-1 | 2.2% | 45.00-1 | 4.3% | 22.26-1 |
The Probability that.... |
Odds |
% |
|
Non-pairs will pair at least one card |
2-to-1 |
32% |
|
Non-pairs will pair both hold cards |
50-to-1 |
2% |
|
A pair will flop a set |
8-to-1 |
12% |
|
A pair will flop four of a kind |
400-to-1 |
0.3% |
|
Two suited cards will flop a flush |
118-to-1 |
1% |
|
Two suited cards flop a four flush (flush draw) |
9-to-1 |
11% |
|
Two suited cards will make a flush by the river |
15-to-1 |
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 |
|
Open-ended 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 |
Three-of-a-kind or better |
12.7 |
7:1 |
Pocket pair |
Three-of-a-kind |
11.8 |
8:1 |
Pocket pair |
Full house |
0.73 |
136:1 |
Pocket pair |
Four-of-a-kind |
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 45o-JTo |
Open Ended Straight Draw |
9.6 |
9.:1 |
Connectors 45s-JTs |
Straight draw / flush draw |
19.1 |
4:1 |
Connectors 45o-JTo |
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 |
Three-of-a-kind |
Four-of-a-kind |
2.1 |
47:1 |
Two pair |
Full house |
8.5 |
11:1 |
Pair |
Three-of-a-kind |
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 |
Three-of-a-kind |
Four-of-a-kind |
2.2 |
45.46:1 |
Two pair |
Full house |
8.7 |
10.5:1 |
Pair |
Three-of-a-kind |
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 |
Three-of-a-kind |
Four-of-a-kind |
4.3 |
22.26:1 |
Two pair |
Full house |
17 |
4.88:1 |
Pair |
Four-of-a-kind |
0.09 |
1100:1 |
Pair |
Three-of-a-kind |
8.4 |
10.9:1 |
Probability of seeing a specific board on the flop |
|||
On the flop |
Probability in % |
Odds |
|
Three-of-a-kind |
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 |