Solver answer
K♥Q♥ makes a king-high flush: call or raise the river?
6-max cash, 100 big blinds · Button opens, big blind calls · River T♥ 7♥ 3♣ 9♠ 2♥ · Button bets 29 bb into 34.3 bb · Big blind to act
Updated
The solver's answer
K♥J♥ and K♥9♥, standing in for K♥Q♥.
K♥J♥
Raise 100%
All-in · 83.1 bb
K♥9♥
Raise 100%
All-in · 83.1 bb
The king-high flushes always raise all in: the raise is worth far more than a call.
K♥Q♥ never reaches this river: the big blind 3-bets it before the flop every time. Two king-high flushes that do reach it stand in: K♥J♥ and K♥9♥.
T♥7♥3♣9♠2♥
K♥J♥ Stand-in
K♥9♥ Stand-in
- Pot
- 34.3 bb
- Behind
- 83.1 bb
- Button
- Bets 29 bb
In a 6-max cash game at 100 big blinds, after the big blind calls the button's 4.1 bb flop c-bet on T♥ 7♥ 3♣ and 10.3 bb turn bet on the 9♠, then checks the 2♥ river and faces a 29 bb bet into 34.3 bb, it moves all in with K♥J♥ 100% of the time and with K♥9♥ 100%, according to a solver answer published free by Poker Skill.
Why the king-high flush raises
- A king-high flush is the second-best hand possible on this board: only an ace-high flush beats it.
- Moving all in is worth 73.22 bb to K♥J♥ and calling 57.33 bb; for K♥9♥ it is 72.98 bb against 57.63 bb. Against the bet, K♥J♥ has 94% equity.
- The big blind's flushes as a group raise 69% of the time. The smallest ones, six-three, five-three and four-three suited, just call: six-three suited calls 100% of the time.
Poker Skill's free app has Practice vs AI, where you play full heads-up hands against an AI opponent, with Coach Max grading each decision. Play a heads-up hand vs AI
The full strategy, hand by hand
| A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | AA Not in this range here | AKs Not in this range here | AQs Not in this range here | AJs Not in this range here | ATs F 94 % | A9s R 100 % | A8s R 97 % | A7s Not in this range here | A6s R 100 % | A5s Not in this range here | A4s R 100 % | A3s R 100 % | A2s Not in this range here |
| K | AKo Not in this range here | KK Not in this range here | KQs Not in this range here | KJs F 58 % | KTs F 83 % | K9s R 100 % | K8s R 100 % | K7s Not in this range here | K6s R 100 % | K5s R 100 % | K4s R 100 % | K3s R 100 % | K2s Not in this range here |
| Q | AQo Not in this range here | KQo Not in this range here | QQ Not in this range here | QJs R 100 % | QTs F 75 % | Q9s R 100 % | Q8s R 100 % | Q7s Not in this range here | Q6s R 100 % | Q5s Not in this range here | Q4s Not in this range here | Q3s R 99 % | Q2s Not in this range here |
| J | AJo Not in this range here | KJo F 100 % | QJo Not in this range here | JJ Not in this range here | JTs C 52 % | J9s F 99 % | J8s Not in this range here | J7s F 99 % | J6s Not in this range here | J5s R 99 % | J4s R 99 % | J3s F 80 % | J2s Not in this range here |
| T | ATo F 85 % | KTo F 72 % | QTo F 48 % | JTo C 66 % | TT Not in this range here | T9s Not in this range here | T8s F 68 % | T7s C 100 % | T6s C 99 % | T5s C 97 % | T4s C 88 % | T3s C 99 % | T2s Not in this range here |
| 9 | A9o Not in this range here | K9o Not in this range here | Q9o Not in this range here | J9o F 58 % | T9o C 94 % | 99 R 53 % | 98s F 99 % | 97s C 100 % | 96s R 91 % | 95s C 52 % | 94s Not in this range here | 93s Not in this range here | 92s Not in this range here |
| 8 | A8o F 99 % | K8o Not in this range here | Q8o Not in this range here | J8o Not in this range here | T8o C 55 % | 98o F 54 % | 88 F 79 % | 87s C 66 % | 86s Not in this range here | 85s Not in this range here | 84s Not in this range here | 83s Not in this range here | 82s Not in this range here |
| 7 | A7o Not in this range here | K7o Not in this range here | Q7o Not in this range here | J7o Not in this range here | T7o Not in this range here | 97o Not in this range here | 87o C 75 % | 77 Not in this range here | 76s C 85 % | 75s Not in this range here | 74s F 73 % | 73s Not in this range here | 72s Not in this range here |
| 6 | A6o Not in this range here | K6o Not in this range here | Q6o Not in this range here | J6o Not in this range here | T6o Not in this range here | 96o Not in this range here | 86o Not in this range here | 76o F 56 % | 66 Not in this range here | 65s C 100 % | 64s C 100 % | 63s C 100 % | 62s Not in this range here |
| 5 | A5o Not in this range here | K5o Not in this range here | Q5o Not in this range here | J5o Not in this range here | T5o Not in this range here | 95o Not in this range here | 85o Not in this range here | 75o Not in this range here | 65o Not in this range here | 55 Not in this range here | 54s Not in this range here | 53s C 100 % | 52s Not in this range here |
| 4 | A4o Not in this range here | K4o Not in this range here | Q4o Not in this range here | J4o Not in this range here | T4o Not in this range here | 94o Not in this range here | 84o Not in this range here | 74o Not in this range here | 64o Not in this range here | 54o Not in this range here | 44 Not in this range here | 43s C 100 % | 42s Not in this range here |
| 3 | A3o Not in this range here | K3o Not in this range here | Q3o Not in this range here | J3o Not in this range here | T3o Not in this range here | 93o Not in this range here | 83o Not in this range here | 73o Not in this range here | 63o Not in this range here | 53o Not in this range here | 43o Not in this range here | 33 Not in this range here | 32s Not in this range here |
| 2 | A2o Not in this range here | K2o Not in this range here | Q2o Not in this range here | J2o Not in this range here | T2o Not in this range here | 92o Not in this range here | 82o Not in this range here | 72o Not in this range here | 62o Not in this range here | 52o Not in this range here | 42o Not in this range here | 32o Not in this range here | 22 Not in this range here |
- Fold: 46.65% of the range (26.59 combos)
- Call (29 bb): 37.67% of the range (21.47 combos)
- All-in (83.1 bb): 15.68% of the range (8.94 combos)
Each cell is a hand class. Its letter is the action the class takes most (F fold, X check, C call, B bet, R raise) and its number is how often, in percent. In the labels, s means suited and o means offsuit.
| Hand class | Combos | Fold | Call (29 bb) | All-in (83.1 bb) |
|---|---|---|---|---|
| ATs | 1.403 | 94.4% | 5.1% | 0.5% |
| A9s | 0.762 | 0.1% | 0.0% | 99.9% |
| A8s | 0.492 | 2.9% | 0.0% | 97.1% |
| A6s | 0.576 | 0.0% | 0.0% | 100.0% |
| A4s | 0.328 | 0.0% | 0.0% | 100.0% |
| A3s | 0.283 | 0.0% | 0.0% | 100.0% |
| KJs | 0.576 | 58.2% | 0.0% | 41.8% |
| KTs | 1.36 | 82.8% | 16.7% | 0.4% |
| K9s | 0.369 | 0.0% | 0.0% | 100.0% |
| K8s | 0.002 | 0.0% | 0.0% | 100.0% |
| K6s | 0.093 | 0.0% | 0.0% | 100.0% |
| K5s | 0.134 | 0.0% | 0.0% | 100.0% |
| K4s | 0.103 | 0.0% | 0.0% | 100.0% |
| K3s | 0.588 | 0.0% | 0.0% | 100.0% |
| QJs | 0.628 | 0.0% | 0.0% | 100.0% |
| QTs | 1.466 | 74.7% | 24.8% | 0.5% |
| Q9s | 0.545 | 0.0% | 0.0% | 100.0% |
| Q8s | 0.007 | 0.0% | 0.0% | 100.0% |
| Q6s | 0.184 | 0.0% | 0.0% | 100.0% |
| Q3s | 0.669 | 0.0% | 0.7% | 99.3% |
| KJo | 0.019 | 99.7% | 0.0% | 0.3% |
| JTs | 0.472 | 47.9% | 51.8% | 0.3% |
| J9s | 0.192 | 99.2% | 0.3% | 0.4% |
| J7s | 1.73 | 99.2% | 0.6% | 0.1% |
| J5s | 0.136 | 0.0% | 0.6% | 99.4% |
| J4s | 0.097 | 0.0% | 1.3% | 98.7% |
| J3s | 0.593 | 80.0% | 19.5% | 0.5% |
| ATo | 4.916 | 84.6% | 14.9% | 0.5% |
| KTo | 4.258 | 71.6% | 13.8% | 14.6% |
| QTo | 4.286 | 48.3% | 43.0% | 8.7% |
| JTo | 4.7 | 32.2% | 65.9% | 2.0% |
| T8s | 0.908 | 67.7% | 32.0% | 0.3% |
| T7s | 0.606 | 0.0% | 100.0% | 0.0% |
| T6s | 0.754 | 0.5% | 99.1% | 0.3% |
| T5s | 0.008 | 3.0% | 96.7% | 0.3% |
| T4s | 0.007 | 12.2% | 87.5% | 0.3% |
| T3s | 0.311 | 0.1% | 99.4% | 0.5% |
| J9o | 3.568 | 58.0% | 32.3% | 9.7% |
| T9o | 1.86 | 0.1% | 93.8% | 6.1% |
| 99 | 0.399 | 0.0% | 47.2% | 52.8% |
| 98s | 0.713 | 99.3% | 0.2% | 0.4% |
| 97s | 1.557 | 0.0% | 100.0% | 0.0% |
| 96s | 0.091 | 0.0% | 9.1% | 90.9% |
| 95s | 0.304 | 0.0% | 52.4% | 47.6% |
| A8o | 0.146 | 99.3% | 0.0% | 0.7% |
| T8o | 2.483 | 44.3% | 55.2% | 0.5% |
| 98o | 2.201 | 54.4% | 25.0% | 20.7% |
| 88 | 3.057 | 78.8% | 14.5% | 6.6% |
| 87s | 1.418 | 33.8% | 66.2% | 0.0% |
| 87o | 1.86 | 24.9% | 75.0% | 0.1% |
| 76s | 0.04 | 14.9% | 85.0% | 0.1% |
| 74s | 0.002 | 73.1% | 26.7% | 0.2% |
| 76o | 0.144 | 56.2% | 43.6% | 0.2% |
| 65s | 0.247 | 0.0% | 100.0% | 0.0% |
| 64s | 0.247 | 0.0% | 100.0% | 0.0% |
| 63s | 0.602 | 0.0% | 100.0% | 0.0% |
| 53s | 0.703 | 0.0% | 100.0% | 0.0% |
| 43s | 0.797 | 0.0% | 100.0% | 0.0% |
What each action is worth with K♥J♥
| Action | How often | Expected value |
|---|---|---|
| Fold | 0.00% | 0 bb |
| Call (29 bb) | 0.00% | 57.332 bb |
| All-in (83.1 bb) | 100.00% | 73.216 bb |
What each action is worth with K♥9♥
| Action | How often | Expected value |
|---|---|---|
| Fold | 0.00% | 0 bb |
| Call (29 bb) | 0.00% | 57.631 bb |
| All-in (83.1 bb) | 100.00% | 72.976 bb |
Ranges, pot and stacks
- The hand so far: 6-max cash, 100 big blinds · Button opens to 2.5 bb, big blind calls · Flop T♥ 7♥ 3♣: big blind checks, button bets 4.1 bb, big blind calls · Turn 9♠: big blind checks, button bets 10.3 bb, big blind calls · River 2♥: big blind checks, button bets 29 bb into 34.3 bb · Big blind to act, 83.1 bb behind
- Pot at this decision, including the bets in front: 63.3 bb
- The big blind: 83.1 bb behind
- The button: 54.1 bb behind, 29 bb in front
| A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | AA Not in this range here | AKs Not in this range here | AQs Not in this range here | AJs Not in this range here | ATs 47 % | A9s 25 % | A8s 12 % | A7s Not in this range here | A6s 14 % | A5s Not in this range here | A4s 8 % | A3s 9 % | A2s Not in this range here |
| K | AKo Not in this range here | KK Not in this range here | KQs Not in this range here | KJs 14 % | KTs 45 % | K9s 12 % | K8s <1 % | K7s Not in this range here | K6s 2 % | K5s 3 % | K4s 3 % | K3s 20 % | K2s Not in this range here |
| Q | AQo Not in this range here | KQo Not in this range here | QQ Not in this range here | QJs 16 % | QTs 49 % | Q9s 18 % | Q8s <1 % | Q7s Not in this range here | Q6s 5 % | Q5s Not in this range here | Q4s Not in this range here | Q3s 22 % | Q2s Not in this range here |
| J | AJo Not in this range here | KJo <1 % | QJo Not in this range here | JJ Not in this range here | JTs 16 % | J9s 6 % | J8s Not in this range here | J7s 58 % | J6s Not in this range here | J5s 3 % | J4s 2 % | J3s 20 % | J2s Not in this range here |
| T | ATo 55 % | KTo 47 % | QTo 48 % | JTo 52 % | TT Not in this range here | T9s Not in this range here | T8s 30 % | T7s 20 % | T6s 25 % | T5s <1 % | T4s <1 % | T3s 16 % | T2s Not in this range here |
| 9 | A9o Not in this range here | K9o Not in this range here | Q9o Not in this range here | J9o 40 % | T9o 27 % | 99 13 % | 98s 24 % | 97s 78 % | 96s 3 % | 95s 10 % | 94s Not in this range here | 93s Not in this range here | 92s Not in this range here |
| 8 | A8o 1 % | K8o Not in this range here | Q8o Not in this range here | J8o Not in this range here | T8o 28 % | 98o 25 % | 88 51 % | 87s 47 % | 86s Not in this range here | 85s Not in this range here | 84s Not in this range here | 83s Not in this range here | 82s Not in this range here |
| 7 | A7o Not in this range here | K7o Not in this range here | Q7o Not in this range here | J7o Not in this range here | T7o Not in this range here | 97o Not in this range here | 87o 21 % | 77 Not in this range here | 76s 1 % | 75s Not in this range here | 74s <1 % | 73s Not in this range here | 72s Not in this range here |
| 6 | A6o Not in this range here | K6o Not in this range here | Q6o Not in this range here | J6o Not in this range here | T6o Not in this range here | 96o Not in this range here | 86o Not in this range here | 76o 2 % | 66 Not in this range here | 65s 6 % | 64s 6 % | 63s 20 % | 62s Not in this range here |
| 5 | A5o Not in this range here | K5o Not in this range here | Q5o Not in this range here | J5o Not in this range here | T5o Not in this range here | 95o Not in this range here | 85o Not in this range here | 75o Not in this range here | 65o Not in this range here | 55 Not in this range here | 54s Not in this range here | 53s 23 % | 52s Not in this range here |
| 4 | A4o Not in this range here | K4o Not in this range here | Q4o Not in this range here | J4o Not in this range here | T4o Not in this range here | 94o Not in this range here | 84o Not in this range here | 74o Not in this range here | 64o Not in this range here | 54o Not in this range here | 44 Not in this range here | 43s 27 % | 42s Not in this range here |
| 3 | A3o Not in this range here | K3o Not in this range here | Q3o Not in this range here | J3o Not in this range here | T3o Not in this range here | 93o Not in this range here | 83o Not in this range here | 73o Not in this range here | 63o Not in this range here | 53o Not in this range here | 43o Not in this range here | 33 Not in this range here | 32s Not in this range here |
| 2 | A2o Not in this range here | K2o Not in this range here | Q2o Not in this range here | J2o Not in this range here | T2o Not in this range here | 92o Not in this range here | 82o Not in this range here | 72o Not in this range here | 62o Not in this range here | 52o Not in this range here | 42o Not in this range here | 32o Not in this range here | 22 Not in this range here |
Each cell shows the share of the class's possible combos in the range.
| A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | AA 1 % | AKs Not in this range here | AQs Not in this range here | AJs 1 % | ATs Not in this range here | A9s <1 % | A8s 3 % | A7s Not in this range here | A6s 3 % | A5s 1 % | A4s <1 % | A3s Not in this range here | A2s <1 % |
| K | AKo Not in this range here | KK Not in this range here | KQs <1 % | KJs 4 % | KTs Not in this range here | K9s 4 % | K8s 5 % | K7s Not in this range here | K6s 2 % | K5s 1 % | K4s 1 % | K3s <1 % | K2s Not in this range here |
| Q | AQo Not in this range here | KQo 1 % | QQ <1 % | QJs 3 % | QTs Not in this range here | Q9s 4 % | Q8s 4 % | Q7s Not in this range here | Q6s 2 % | Q5s <1 % | Q4s <1 % | Q3s 2 % | Q2s Not in this range here |
| J | AJo <1 % | KJo 3 % | QJo 4 % | JJ Not in this range here | JTs Not in this range here | J9s 6 % | J8s 14 % | J7s Not in this range here | J6s 1 % | J5s <1 % | J4s 1 % | J3s 1 % | J2s Not in this range here |
| T | ATo Not in this range here | KTo 1 % | QTo <1 % | JTo 1 % | TT Not in this range here | T9s <1 % | T8s Not in this range here | T7s Not in this range here | T6s Not in this range here | T5s Not in this range here | T4s Not in this range here | T3s Not in this range here | T2s Not in this range here |
| 9 | A9o Not in this range here | K9o <1 % | Q9o Not in this range here | J9o 1 % | T9o <1 % | 99 <1 % | 98s 5 % | 97s Not in this range here | 96s 2 % | 95s Not in this range here | 94s Not in this range here | 93s Not in this range here | 92s Not in this range here |
| 8 | A8o 2 % | K8o 3 % | Q8o Not in this range here | J8o 4 % | T8o Not in this range here | 98o 1 % | 88 Not in this range here | 87s Not in this range here | 86s 6 % | 85s <1 % | 84s Not in this range here | 83s Not in this range here | 82s Not in this range here |
| 7 | A7o Not in this range here | K7o Not in this range here | Q7o Not in this range here | J7o Not in this range here | T7o Not in this range here | 97o Not in this range here | 87o Not in this range here | 77 24 % | 76s Not in this range here | 75s Not in this range here | 74s Not in this range here | 73s Not in this range here | 72s Not in this range here |
| 6 | A6o 3 % | K6o Not in this range here | Q6o Not in this range here | J6o Not in this range here | T6o Not in this range here | 96o Not in this range here | 86o Not in this range here | 76o Not in this range here | 66 Not in this range here | 65s <1 % | 64s <1 % | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o <1 % | K5o Not in this range here | Q5o Not in this range here | J5o Not in this range here | T5o Not in this range here | 95o Not in this range here | 85o Not in this range here | 75o Not in this range here | 65o Not in this range here | 55 Not in this range here | 54s <1 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o <1 % | K4o Not in this range here | Q4o Not in this range here | J4o Not in this range here | T4o Not in this range here | 94o Not in this range here | 84o Not in this range here | 74o Not in this range here | 64o Not in this range here | 54o Not in this range here | 44 Not in this range here | 43s Not in this range here | 42s Not in this range here |
| 3 | A3o Not in this range here | K3o Not in this range here | Q3o Not in this range here | J3o Not in this range here | T3o Not in this range here | 93o Not in this range here | 83o Not in this range here | 73o Not in this range here | 63o Not in this range here | 53o Not in this range here | 43o Not in this range here | 33 23 % | 32s Not in this range here |
| 2 | A2o Not in this range here | K2o Not in this range here | Q2o Not in this range here | J2o Not in this range here | T2o Not in this range here | 92o Not in this range here | 82o Not in this range here | 72o Not in this range here | 62o Not in this range here | 52o Not in this range here | 42o Not in this range here | 32o Not in this range here | 22 Not in this range here |
Each cell shows the share of the class's possible combos in the range.
Where the numbers come from
The numbers come from a commercial solver's precomputed solution for a 6-max cash game at 100 big blinds, with a 5% rake capped at 0.6 bb, opens sized by the solver (2.5 bb here) and several bet sizes on each street. Every street follows the button's most-used size: 4.1 bb on the flop, 10.3 bb on the turn and 29 bb on the river. Facing the river bet, the big blind can fold, call or move all in. K♥Q♥ never reaches this river, so K♥J♥ and K♥9♥ stand in. Two players see the flop. Pots with three or more players aren't covered, and neither are bet sizes outside this solution. Poker Skill read the numbers and wrote the explanation.
- Line to this decision
-
F-F-F-R2.5-F-C·flop X-R4.1-C, turn X-R10.3-C, river X-R29 - Solver notation
-
Th7h3c9s2h·KhJh·Kh9h·KhQh. F fold, X check, C call, R2.5 a bet or raise to 2.5 bb, RAI all-in.
Solution read Oct 1, 2026. Each hand-class row is the solver's own total for that class. Ranges are shown by class: how many combos of each class are in the range, and what share that is of the combos the board leaves possible.