Key points
- Draw probability, hand frequency and equity are different figures.
- If one card completes two different draws, count it only once as an out.
- With many outs, the Rule of 4 overestimates the actual probability.
01First, Separate These 3 Types of Probability
- Draw odds: The chance of completing a draw on the next board card or by the river.
- Hand frequency: How often a hand is made from seven cards. See the poker hand rankings.
- Win odds: The chance of beating your opponent's hand. Hitting the card you need does not necessarily mean you win.
This article covers draw odds and win odds when two players play the hand to the end.
02Odds of Being Dealt Your Hole Cards
| Two Cards Dealt | Probability |
|---|---|
| Any pocket pair | 5.9% (about 1 in 17) |
| A specific pocket pair (such as AA) | 0.45% (1 in 221) |
| Two cards of the same suit (suited) | 23.5% |
| AK (suited or offsuit) | 1.2% (about 1 in 83) |
03Odds of Improving by the Flop or River
| Hole Cards | Improvement and Probability |
|---|---|
| Pocket pair | At least one card matching your pocket pair appears on the flop: 11.8%. By the river: 19.2%. If one appears, you make a set or better |
| Two cards of the same suit | Make a flush on the flop using your hole cards' suit: 0.8%. Flop a flush draw: 10.9%. Make a flush by the river: 6.4% |
| Two unpaired cards | At least one card matching either hole card appears on the flop: 32.4% |
“By the river” means after seeing all five board cards. The flush figures include straight flushes.
04How to Count Outs
Outs are unseen cards that improve your hand if drawn. After the flop, count them among the 47 cards left after excluding your two hole cards and the three board cards.
Cards that make only a straight
K♥︎♥︎K♦︎♦︎K♣︎♣︎8♥︎♥︎8♦︎♦︎8♣︎♣︎Cards that make a flush (K♠ and 8♠ make a straight flush)
A♠︎♠︎K♠︎♠︎8♠︎♠︎7♠︎♠︎6♠︎♠︎5♠︎♠︎4♠︎♠︎3♠︎♠︎2♠︎♠︎6 + 9 = 15 outs
Here, we are counting cards that complete a made hand. How many of these 15 cards actually give you the winning hand depends on what your opponent holds.
- Count a card that completes two different hands only once.
- If you include cards that may not give you the winning hand, you cannot use the table below as your chance of winning. For example, a flush card can still leave you behind when the board allows your opponent to make a higher flush.
05Outs and Draw Odds
Once you know your number of outs, this is the chance of hitting at least one of them. These figures are not win odds.
- On the turn: Hitting on the next card after the flop.
- On the river: Hitting on the next card after the turn. Recount your outs based on the situation after the turn.
- By the river: Seeing both the turn and river after the flop and hitting on either card.
| Outs | On the Turn | On the River | By the River |
|---|---|---|---|
| 1 | 2.1% | 2.2% | 4.3% |
| 2pocket pair to a set | 4.3% | 4.3% | 8.4% |
| 3 | 6.4% | 6.5% | 12.5% |
| 4gutshot straight draw | 8.5% | 8.7% | 16.5% |
| 5 | 10.6% | 10.9% | 20.4% |
| 6 | 12.8% | 13.0% | 24.1% |
| 7 | 14.9% | 15.2% | 27.8% |
| 8open-ended straight draw | 17.0% | 17.4% | 31.5% |
| 9flush draw | 19.1% | 19.6% | 35.0% |
| 10 | 21.3% | 21.7% | 38.4% |
| 11 | 23.4% | 23.9% | 41.7% |
| 12 | 25.5% | 26.1% | 45.0% |
| 13 | 27.7% | 28.3% | 48.1% |
| 14 | 29.8% | 30.4% | 51.2% |
| 15flush and open-ended straight draw | 31.9% | 32.6% | 54.1% |
If your current call only lets you see the next card, do not use the “By the River” column as-is. See pot odds and expected value for details.
How Far the Rule of 4 and 2 Can Be Off
Multiply your outs by 4 for a rough estimate of your chance of hitting by the river when you will see both cards, or by 2 for a rough estimate of hitting on the next card.
With more outs, multiplying by 4 gives a figure higher than the actual probability. With 8 outs, 32% and 31.5% are almost equal. With 15 outs, however, 60% is 5.9 percentage points higher than 54.1%.
06Win Odds When Two Players Are All-in
These figures assume that two players go all-in preflop and all five board cards are dealt. Ties are not included in the win percentages.
- A♠︎♠︎A♥︎♥︎vsK♦︎♦︎K♣︎♣︎81.1％0.4％18.6％
- Q♠︎♠︎Q♥︎♥︎vsA♦︎♦︎K♣︎♣︎57.0％0.3％42.7％
- 2♠︎♠︎2♥︎♥︎vsA♦︎♦︎K♣︎♣︎52.7％0.6％46.7％
- A♠︎♠︎K♥︎♥︎vsQ♦︎♦︎J♣︎♣︎64.1％0.4％35.5％
- A♠︎♠︎K♥︎♥︎vsA♦︎♦︎Q♣︎♣︎71.7％4.6％23.7％
WinTieLose
- A higher pocket pair is about a 4-to-1 favorite over a lower pocket pair.
- In the matchups shown here against offsuit AK, the pocket pair is a slight favorite. When AK is suited, the matchup against 22 is nearly even, and AK becomes the slight favorite.
- In the AK versus AQ matchup shown here, AQ has the lower kicker and wins only about 1 time in 4.
07Check Your Understanding with 3 Questions
Question 1Your hole cards are Q♠ J♠, and the flop is 10♠ 9♠ 2♦. How many cards complete a straight or flush on the next card?
View answer
There are 6 cards that make only a straight and 9 cards that make a flush, for 15 outs. K♠ and 8♠ can complete both a straight and a flush, so count each of them only once.
Question 2You have 8 outs after the flop. Which figure is closest to your chance of hitting by the river?
View answer
The probability is 31.5%. The 17% figure is your chance of hitting on the next card only.
Question 3You have a flush draw, with a 35% chance of hitting by the river. What can your final chance of winning be?
View answer
You can hit your draw and still lose, or miss it and still win. Draw odds and win odds are different figures.
08Try It in BlackPoker
From the flop onward, the game shows your number of outs and your win odds based on your opponent's actions. At the table, you can see how your number of outs and your chance of winning are different figures.
Frequently asked questions
You are one card short of a flush. What is the chance of hitting by the river?
After the flop, it is 35.0% if you see both the turn and river. For the next card only, it is 19.1%.
What is the chance that a pocket pair makes a set?
The chance of at least one matching rank appearing on the board is 11.8% on the flop and 19.2% by the river. If it appears, you make a set or a stronger hand.
Produced and edited by Predy GamesPublished:Updated:Report an error:Contact
Compare outs and equity in BlackPokerBlackPoker is a single-player Texas Hold'em game played without real-money wagering. From the flop onward, it separately shows your number of outs and your equity against the range suggested by the opponent's actions.
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