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.