What You Are Dealt
There are 1,326 distinct two-card starting hands. Every figure in this section counts combinations out of that 1,326.
Starting hand frequencies
| Starting hand | Combinations | Probability | Frequency |
|---|---|---|---|
| Any pocket pair | 78 | 5.88% | 1 in 17 |
| A specific pocket pair, aces for instance | 6 | 0.45% | 1 in 221 |
| Aces, kings or queens | 18 | 1.36% | 1 in 74 |
| A pair of tens or better | 30 | 2.26% | 1 in 44 |
| Any two suited cards | 312 | 23.53% | 1 in 4 |
| Suited connectors, including the ace-to-five wheel | 52 | 3.92% | 1 in 26 |
| A specific suited hand, ace-king suited for instance | 4 | 0.30% | 1 in 332 |
| A specific offsuit hand, ace-king offsuit for instance | 12 | 0.90% | 1 in 110 |
| A specific unpaired hand in any form, ace-king | 16 | 1.21% | 1 in 83 |
| Two cards ten or higher | 190 | 14.33% | 1 in 7 |
| At least one ace | 198 | 14.93% | 1 in 7 |
| Ace-king, ace-queen, or a pair of jacks or better | 56 | 4.22% | 1 in 24 |
| Any two unpaired unsuited cards | 936 | 70.59% |
A pocket pair arrives once every seventeen hands, and aces once every 221.
Specific Starting Hands
A specific pair has six combinations. The same two ranks unpaired and offsuit have twelve, so ace-king offsuit is dealt twice as often as any one pocket pair.
| Hand | Combinations | Probability | Frequency |
|---|---|---|---|
| AA | 6 | 0.4525% | 1 in 221 |
| KK | 6 | 0.4525% | 1 in 221 |
| 6 | 0.4525% | 1 in 221 | |
| JJ | 6 | 0.4525% | 1 in 221 |
| TT | 6 | 0.4525% | 1 in 221 |
| AKs | 4 | 0.3017% | 1 in 332 |
| AKo | 12 | 0.9050% | 1 in 110 |
| AQs | 4 | 0.3017% | 1 in 332 |
| AQo | 12 | 0.9050% | 1 in 110 |
| AJs | 4 | 0.3017% | 1 in 332 |
| KQs | 4 | 0.3017% | 1 in 332 |
Preflop Matchups
Each row enumerates all 1,712,304 five-card boards that can follow the two hands shown, counts wins, losses and ties, and splits the ties. The suits are fixed as printed; changing one moves the figure by about a point.
| Matchup | Favourite | Underdog | Split |
|---|---|---|---|
| A♠ A♣ against K♠ K♣ Aces against kings. Kings are drawing almost entirely to a set. | 82.64% | 17.36% | 0.54% |
| A♠ A♣ against K♠ Q♠ Aces against two lower suited cards. Suitedness is worth three and a half points against a big pair. | 83.56% | 16.44% | 0.46% |
| A♠ A♣ against K♠ Q♦ Aces against two lower offsuit cards | 87.12% | 12.88% | 0.41% |
| A♠ A♣ against A♥ K♦ Aces against ace-king, the case ace. Holding the other ace halves ace-king's outs to pair. | 92.57% | 7.43% | 1.25% |
| K♠ K♣ against A♠ Q♠ Kings against a suited ace | 68.43% | 31.57% | 0.47% |
| J♠ J♣ against A♠ K♠ Jacks against ace-king suited | 54.21% | 45.79% | 0.46% |
| 8♠ 8♣ against A♥ K♦ Eights against ace-king offsuit | 55.57% | 44.43% | 0.30% |
| A♠ K♠ against A♥ Q♦ Ace-king suited against ace-queen. The shared ace leaves ace-queen the three remaining queens to pair. | 75.56% | 24.44% | 4.41% |
| A♠ K♦ against Q♥ J♣ Two overcards against two undercards | 64.30% | 35.70% | 0.39% |
| A♠ K♠ against Q♥ J♥ Ace-king suited against queen-jack suited | 62.72% | 37.28% | 0.50% |
| 7♠ 7♣ against 6♠ 5♠ Sevens against lower suited connectors. The connector holds no overcard, so it has to make a straight or a flush. | 81.84% | 18.16% | 1.34% |
| J♠ J♣ against T♠ 9♠ Jacks against a live suited connector | 82.26% | 17.74% | 0.45% |
| A♠ 2♠ against K♥ Q♦ A weak suited ace against two broadway cards. One overcard against two, plus the flush draw. | 60.36% | 39.64% | 0.49% |
Eights against ace-king is 55.57%, the closest of these to even money.
Running Into a Bigger Pair
The probability that at least one opponent holds a higher pair, by table size. The cards one opponent holds are cards another cannot, so these come from an inclusion-exclusion count rather than a compounded single-opponent figure.
| Your pair | 1 opponent | 2 opponents | 3 opponents | 5 opponents | 8 opponents |
|---|---|---|---|---|---|
| Aces | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% |
| Kings | 0.49% | 0.98% | 1.47% | 2.44% | 3.91% |
| Queens | 0.98% | 1.95% | 2.92% | 4.84% | 7.67% |
| Jacks | 1.47% | 2.92% | 4.36% | 7.18% | 11.29% |
| Tens | 1.96% | 3.89% | 5.78% | 9.47% | 14.77% |
| Nines | 2.45% | 4.84% | 7.19% | 11.71% | 18.13% |
| Eights | 2.94% | 5.80% | 8.58% | 13.91% | 21.36% |
| Sevens | 3.43% | 6.74% | 9.95% | 16.05% | 24.47% |
| Sixes | 3.92% | 7.69% | 11.31% | 18.15% | 27.46% |
Queens against eight opponents meet kings or aces 7.7% of the time.
The Flop
19,600 flops can follow any two hole cards. Each table enumerates all of them for one starting hand type.
Holding a pocket pair
| Outcome | Flops | Probability | Odds against |
|---|---|---|---|
| Flop quads | 48 | 0.24% | 407.3 to 1 |
| Flop a full house | 144 | 0.73% | 135.1 to 1 |
| Flop exactly a set | 2,112 | 10.78% | 8.3 to 1 |
| Flop a set or better | 2,304 | 11.76% | 7.5 to 1 |
| Flop no set, still just a pair | 17,296 | 88.24% |
A set or better lands on 11.76% of flops, one in eight and a half. Set mining has to be priced against the seven that miss.
Holding two suited cards
| Outcome | Flops | Probability | Odds against |
|---|---|---|---|
| Flop a flush | 165 | 0.84% | 117.8 to 1 |
| Flop a four-card flush draw | 2,145 | 10.94% | 8.1 to 1 |
| Flop a backdoor flush draw | 8,151 | 41.59% | 1.4 to 1 |
| Flop no flush help at all | 9,139 | 46.63% | 1.1 to 1 |
A made flush lands on 0.84% of flops; the four-card draw on 10.94%.
Holding two unpaired, unconnected offsuit cards
| Outcome | Flops | Probability | Odds against |
|---|---|---|---|
| Flop trips or better | 284 | 1.45% | 68.0 to 1 |
| Flop two pair using both hole cards | 396 | 2.02% | 48.5 to 1 |
| Flop exactly one pair | 5,676 | 28.96% | 2.5 to 1 |
| Pair at least one hole card | 6,356 | 32.43% | 2.1 to 1 |
| Flop nothing | 13,244 | 67.57% |
Board Texture
Texture is a property of the board alone, so these hold regardless of anyone's hole cards. Counted across all 22,100 three-card flops in a full deck.
| Texture | Flops | Probability |
|---|---|---|
| Rainbow, three different suits | 8,788 | 39.76% |
| Two-tone, a flush draw is live | 12,168 | 55.06% |
| Monotone, all three the same suit | 1,144 | 5.18% |
| Unpaired | 18,304 | 82.82% |
| Paired | 3,744 | 16.94% |
| Three of a kind on board | 52 | 0.24% |
| Three ranks inside a five-card span, a straight is already possible | 4,096 | 18.53% |
| Three consecutive ranks | 768 | 3.48% |
Two-tone is the most common texture at 55.06%. Boards come paired 16.94% of the time.
Drawing Odds
An out is a card that completes your hand. Forty-seven cards are unseen after the flop, forty-six after the turn.
The draws you will hold
| Draw | Outs | Turn only | By the river | Odds against |
|---|---|---|---|---|
| Needing one exact card, a specific pair to make quads | 1 | 2.13% | 4.26% | 22.5 to 1 |
| Pocket pair to a set | 2 | 4.26% | 8.42% | 10.9 to 1 |
| One overcard to pair | 3 | 6.38% | 12.49% | 7.0 to 1 |
| Gutshot straight draw, or two pair to a full house | 4 | 8.51% | 16.47% | 5.1 to 1 |
| One pair to trips or two pair | 5 | 10.64% | 20.35% | 3.9 to 1 |
| Two overcards to a pair | 6 | 12.77% | 24.14% | 3.1 to 1 |
| Open-ended straight draw | 8 | 17.02% | 31.45% | 2.2 to 1 |
| Flush draw | 9 | 19.15% | 34.97% | 1.9 to 1 |
| Flush draw plus a gutshot | 12 | 25.53% | 44.96% | 1.2 to 1 |
| Flush draw plus an open-ended straight draw | 15 | 31.91% | 54.12% |
The "by the river" column only applies when you will see both cards without paying again, which on the flop usually means all-in. If there is a turn bet coming, price the call against the turn column alone.
The Complete Outs Table
| Outs | Flop to turn | Turn to river | Flop to river | Odds against | Rule of 4 | Error |
|---|---|---|---|---|---|---|
| 1 | 2.13% | 2.17% | 4.26% | 22.5 to 1 | 4% | -0.3 |
| 2 | 4.26% | 4.35% | 8.42% | 10.9 to 1 | 8% | -0.4 |
| 3 | 6.38% | 6.52% | 12.49% | 7.0 to 1 | 12% | -0.5 |
| 4 | 8.51% | 8.70% | 16.47% | 5.1 to 1 | 16% | -0.5 |
| 5 | 10.64% | 10.87% | 20.35% | 3.9 to 1 | 20% | -0.4 |
| 6 | 12.77% | 13.04% | 24.14% | 3.1 to 1 | 24% | -0.1 |
| 7 | 14.89% | 15.22% | 27.84% | 2.6 to 1 | 28% | +0.2 |
| 8 | 17.02% | 17.39% | 31.45% | 2.2 to 1 | 32% | +0.5 |
| 9 | 19.15% | 19.57% | 34.97% | 1.9 to 1 | 36% | +1.0 |
| 10 | 21.28% | 21.74% | 38.39% | 1.6 to 1 | 40% | +1.6 |
| 11 | 23.40% | 23.91% | 41.72% | 1.4 to 1 | 44% | +2.3 |
| 12 | 25.53% | 26.09% | 44.96% | 1.2 to 1 | 48% | +3.0 |
| 13 | 27.66% | 28.26% | 48.10% | 1.1 to 1 | 52% | +3.9 |
| 14 | 29.79% | 30.43% | 51.16% | 56% | +4.8 | |
| 15 | 31.91% | 32.61% | 54.12% | 60% | +5.9 | |
| 16 | 34.04% | 34.78% | 56.98% | 64% | +7.0 | |
| 17 | 36.17% | 36.96% | 59.76% | 68% | +8.2 | |
| 18 | 38.30% | 39.13% | 62.44% | 72% | +9.6 | |
| 19 | 40.43% | 41.30% | 65.03% | 76% | +11.0 | |
| 20 | 42.55% | 43.48% | 67.53% | 80% | +12.5 | |
| 21 | 44.68% | 45.65% | 69.94% | 84% | +14.1 |
The Rule of 2 and 4
Multiply outs by two for the next card, or by four for both cards when you are already all-in. The error column above measures the shortcut against the real figure.
Where it works
Below eight outs the rule of 4 lands within a point and a half. That covers a gutshot and a pair drawing to trips.
Where it breaks
It overstates every draw above seven outs, and the error widens as outs go up. At fifteen outs it reads +5.9 points high.
Use the rule of 4 only when no further bet is coming. Discount outs that also complete a better hand for someone else: a non-nut flush draw, or a straight card that puts a third suit on the board. Overcounting outs turns folds into calls.
Pot Odds
Pot odds convert a bet size into the equity you need to call. Calling a bet of B into a pot of P risks B to win P plus B, so the break-even point is B divided by P plus twice B. The table does that arithmetic for common sizes.
| Bet size | Pot lays | Equity needed | Outs, one card | Outs, two cards |
|---|---|---|---|---|
| A quarter of the pot | 1.25 to 0.25 | 16.7% | 8 | 5 |
| A third of the pot | 1.33 to 0.33 | 20.0% | 10 | 5 |
| Half the pot | 1.50 to 0.50 | 25.0% | 12 | 7 |
| Two thirds of the pot | 1.67 to 0.67 | 28.6% | 14 | 8 |
| Three quarters of the pot | 1.75 to 0.75 | 30.0% | 15 | 8 |
| Pot | 2.00 to 1.00 | 33.3% | 16 | 9 |
| One and a half times the pot | 2.50 to 1.50 | 37.5% | 18 | 10 |
| Twice the pot | 3.00 to 2.00 | 40.0% | 19 | 11 |
The outs columns give the smallest count that breaks even. A half-pot bet with one card to come needs twelve outs; a flush draw has nine.
The table assumes the hand ends when you call and that every out is clean. Neither holds often enough to treat the figure as more than a minimum.
Implied and Reverse Implied Odds
Implied odds are the money you expect to win after you hit, added to the pot you are being offered now. A flush draw facing a two-thirds pot bet needs 28.6% to call on direct odds and hits the turn 19.15% of the time. On the table's arithmetic that is a fold. If hitting the flush wins another pot-sized bet on the turn, the same call is clearly profitable.
Implied odds are largest when the draw is hidden, when the opponent holds a strong second-best hand, and when stacks are deep. A set gets paid because nobody sees it coming; a third suited card on the board is visible to everyone. At twenty big blinds there is nothing left behind to win, which is why drawing hands lose value as a tournament progresses.
Reverse implied odds are the money lost on the occasions you hit and are still behind. Drawing to a non-nut flush, or to a straight on a two-tone board, means a fraction of your outs cost a large pot instead of winning one.
The variance calculator models what these edges do over a sample. The rake calculator shows how much of them the house takes back.
Reference Sheets
Seven printable tables, at the URLs they were originally published under. Same ground as the tables above, in a form that fits beside a screen.
- Preflop: odds of being dealt a certain starting hand PDF
- Preflop: common hand matchup probabilities PDF
- Preflop: running into better hands PDF
- Flop: hitting a set, a flush or a straight PDF
- Flop: specific board textures PDF
- Flop: two or more players hitting hard PDF
- Draws and outs on the flop and turn PDF
Figures generated by tools/compute_holdem_odds.py on 2026-08-28. Combinatorial values are exact; each matchup enumerates all 1,712,304 boards.
