Solver answer
K♠Q♦ vs a check-raise at 40bb: call or re-raise?
6-max cash, 40 big blinds · Button opens, big blind calls · Flop Q♠ 9♦ 4♥ · Big blind raises to 9.5 bb into 5.5 bb · Button to act
Updated
The solver's answer
Call 78% Raise 22%
K♠Q♦ never folds to the check-raise, and mostly calls.
The solver plays K♠Q♦ along this line to this decision 99.96% of the time; otherwise it acts differently earlier in the hand.
Q♠9♦4♥
K♠Q♦ You
- Pot
- 5.5 bb
- Behind
- 33.5 bb
- Your bet
- 4 bb
- Big blind
- Raises to 9.5 bb
In a 6-max cash game at 40 big blinds, after the button opens to 2.5 bb, the big blind calls, the button c-bets 4 bb on a Q♠ 9♦ 4♥ flop and the big blind check-raises to 9.5 bb, the button calls with K♠Q♦ 78% of the time and re-raises to 15.5 bb 22%, according to a solver answer published free by Poker Skill.
Why K♠Q♦ never folds to the check-raise
- With short stacks the price is low and top pair is strong: calling 5.5 bb to win 19 bb needs 22.4% equity, and K♠Q♦ has 69.5% against the big blind's check-raising range.
- Low stack-to-pot ratios favor made hands like top pair, and calling and re-raising are worth about the same here: 14.13 bb against 14.01 bb.
- The button still folds 41% of its range, mostly its ace-high hands, which fold 90% of the time. Its top pairs never fold.
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 C 71 % | AKs C 88 % | AQs R 97 % | AJs F 77 % | ATs F 55 % | A9s C 100 % | A8s F 56 % | A7s F 55 % | A6s F 77 % | A5s F 49 % | A4s C 100 % | A3s C 48 % | A2s F 48 % |
| K | AKo F 98 % | KK R 94 % | KQs C 66 % | KJs C 77 % | KTs C 99 % | K9s C 85 % | K8s F 100 % | K7s F 100 % | K6s F 100 % | K5s F 100 % | K4s C 64 % | K3s F 100 % | K2s F 100 % |
| Q | AQo R 99 % | KQo C 69 % | QQ C 100 % | QJs C 93 % | QTs C 95 % | Q9s C 74 % | Q8s C 100 % | Q7s C 100 % | Q6s C 100 % | Q5s C 100 % | Q4s C 85 % | Q3s Not in this range here | Q2s Not in this range here |
| J | AJo F 99 % | KJo C 76 % | QJo C 73 % | JJ F 35 % | JTs C 92 % | J9s C 77 % | J8s R 81 % | J7s F 100 % | J6s F 100 % | J5s F 100 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo F 100 % | KTo C 65 % | QTo C 94 % | JTo C 100 % | TT F 90 % | T9s C 100 % | T8s C 83 % | T7s F 100 % | 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 C 100 % | K9o F 40 % | Q9o R 63 % | J9o R 51 % | T9o C 98 % | 99 C 72 % | 98s C 100 % | 97s C 100 % | 96s Not in this range here | 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 F 100 % | K8o F 100 % | Q8o C 100 % | J8o Not in this range here | T8o Not in this range here | 98o Not in this range here | 88 F 77 % | 87s F 100 % | 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 F 99 % | K7o F 100 % | 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 R 90 % | 76s F 96 % | 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 F 100 % | 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 R 80 % | 65s F 95 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o F 96 % | 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 R 82 % | 54s Not in this range here | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o C 88 % | 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 C 94 % | 43s Not in this range here | 42s Not in this range here |
| 3 | A3o F 97 % | 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 F 98 % | 32s Not in this range here |
| 2 | A2o F 95 % | 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: 41.27% of the range (97.99 combos)
- Call (9.5 bb): 40.22% of the range (95.49 combos)
- Raise ¼ pot (to 15.5 bb): 18.50% of the range (43.92 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 (9.5 bb) | Raise ¼ pot (to 15.5 bb) |
|---|---|---|---|---|
| AA | 5.998 | 0.0% | 70.8% | 29.2% |
| AKs | 1.04 | 11.6% | 88.3% | 0.1% |
| AQs | 2.998 | 0.0% | 3.3% | 96.7% |
| AJs | 0.464 | 76.6% | 23.1% | 0.3% |
| ATs | 0.389 | 55.0% | 44.9% | 0.1% |
| A9s | 2.637 | 0.0% | 99.9% | 0.1% |
| A8s | 0.769 | 56.2% | 43.3% | 0.5% |
| A7s | 1.184 | 55.2% | 27.2% | 17.6% |
| A6s | 0.865 | 77.4% | 6.8% | 15.8% |
| A5s | 1.717 | 49.0% | 47.5% | 3.5% |
| A4s | 2.561 | 0.1% | 99.6% | 0.3% |
| A3s | 2.117 | 45.3% | 48.2% | 6.5% |
| A2s | 1.974 | 47.5% | 39.8% | 12.7% |
| AKo | 0.855 | 98.2% | 1.3% | 0.6% |
| KK | 6 | 0.0% | 6.2% | 93.8% |
| KQs | 2.992 | 0.0% | 65.7% | 34.3% |
| KJs | 3.425 | 0.1% | 76.6% | 23.3% |
| KTs | 3.388 | 0.5% | 99.2% | 0.3% |
| K9s | 1.565 | 12.0% | 84.6% | 3.5% |
| K8s | 2.885 | 99.9% | 0.0% | 0.1% |
| K7s | 2.631 | 99.8% | 0.0% | 0.1% |
| K6s | 2.989 | 99.8% | 0.0% | 0.1% |
| K5s | 3.184 | 99.8% | 0.0% | 0.1% |
| K4s | 1.926 | 0.4% | 64.3% | 35.3% |
| K3s | 3.704 | 99.8% | 0.0% | 0.1% |
| K2s | 1.548 | 99.8% | 0.0% | 0.1% |
| AQo | 8.995 | 0.0% | 0.7% | 99.3% |
| KQo | 8.995 | 0.0% | 69.1% | 30.9% |
| 0.714 | 0.0% | 99.6% | 0.4% | |
| QJs | 2.149 | 0.0% | 92.8% | 7.2% |
| QTs | 2.313 | 0.0% | 94.6% | 5.4% |
| Q9s | 1.74 | 0.0% | 73.8% | 26.2% |
| Q8s | 1.999 | 0.0% | 99.8% | 0.2% |
| Q7s | 1.495 | 0.0% | 99.9% | 0.1% |
| Q6s | 1.086 | 0.0% | 99.9% | 0.1% |
| Q5s | 0.834 | 0.0% | 99.9% | 0.1% |
| Q4s | 0.085 | 0.0% | 84.6% | 15.4% |
| AJo | 4.525 | 99.0% | 0.1% | 0.8% |
| KJo | 9.067 | 0.3% | 75.7% | 24.0% |
| QJo | 6.914 | 0.0% | 73.3% | 26.7% |
| JJ | 2.024 | 34.8% | 32.4% | 32.9% |
| JTs | 2.026 | 0.0% | 91.8% | 8.2% |
| J9s | 2.168 | 7.9% | 76.5% | 15.6% |
| J8s | 1.462 | 14.9% | 3.9% | 81.2% |
| J7s | 3.739 | 99.8% | 0.0% | 0.2% |
| J6s | 2.204 | 99.8% | 0.0% | 0.1% |
| J5s | 1.087 | 99.8% | 0.0% | 0.1% |
| ATo | 7.111 | 99.7% | 0.1% | 0.2% |
| KTo | 7.239 | 1.5% | 64.5% | 34.0% |
| QTo | 5.315 | 0.0% | 94.4% | 5.6% |
| JTo | 8.213 | 0.0% | 99.7% | 0.3% |
| TT | 2.26 | 90.0% | 1.7% | 8.3% |
| T9s | 0.514 | 0.2% | 99.7% | 0.1% |
| T8s | 2.091 | 0.6% | 82.5% | 17.0% |
| T7s | 2.148 | 99.8% | 0.0% | 0.1% |
| A9o | 5.187 | 0.1% | 99.7% | 0.1% |
| K9o | 2.2 | 40.2% | 28.2% | 31.6% |
| Q9o | 6.976 | 0.0% | 37.3% | 62.7% |
| J9o | 1.86 | 27.7% | 20.9% | 51.4% |
| T9o | 0.07 | 1.6% | 97.9% | 0.4% |
| 99 | 1.249 | 0.0% | 71.5% | 28.5% |
| 98s | 0.136 | 0.1% | 99.9% | 0.1% |
| 97s | 0.03 | 0.0% | 99.9% | 0.0% |
| A8o | 5.946 | 99.8% | 0.1% | 0.2% |
| K8o | 5.47 | 99.9% | 0.0% | 0.1% |
| Q8o | 0.255 | 0.0% | 99.8% | 0.2% |
| 88 | 0.001 | 77.4% | 0.1% | 22.5% |
| 87s | 1.226 | 99.6% | 0.0% | 0.3% |
| A7o | 6.215 | 99.3% | 0.0% | 0.6% |
| K7o | 0.001 | 99.9% | 0.0% | 0.1% |
| 77 | 0.001 | 10.0% | 0.2% | 89.8% |
| 76s | 0.283 | 95.8% | 0.0% | 4.2% |
| A6o | 6.905 | 99.6% | 0.0% | 0.4% |
| 66 | 0.002 | 20.0% | 0.2% | 79.9% |
| 65s | 0.001 | 95.1% | 0.0% | 4.9% |
| A5o | 8.564 | 96.3% | 0.1% | 3.7% |
| 55 | 0.003 | 17.6% | 0.1% | 82.3% |
| A4o | 3.682 | 0.1% | 87.9% | 11.9% |
| 44 | 2.998 | 0.0% | 94.2% | 5.8% |
| A3o | 11.034 | 96.6% | 0.1% | 3.3% |
| 33 | 0.001 | 98.3% | 0.1% | 1.6% |
| A2o | 4.792 | 95.1% | 0.1% | 4.8% |
What each action is worth with K♠Q♦
| Action | How often | Expected value |
|---|---|---|
| Fold | 0.00% | 0 bb |
| Call (9.5 bb) | 78.22% | 14.133 bb |
| Raise ¼ pot (to 15.5 bb) | 21.78% | 14.005 bb |
Ranges, pot and stacks
- The hand so far: 6-max cash, 40 big blinds · Button opens to 2.5 bb, big blind calls · Flop Q♠ 9♦ 4♥: big blind checks, button bets 4 bb, big blind raises to 9.5 bb into 5.5 bb · Button to act, 33.5 bb behind
- Pot at this decision, including the bets in front: 19 bb
- The button: 33.5 bb behind, 4 bb in front
- The big blind: 28 bb behind, 9.5 bb in front
| A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | AA 100 % | AKs 26 % | AQs 100 % | AJs 12 % | ATs 10 % | A9s 88 % | A8s 19 % | A7s 30 % | A6s 22 % | A5s 43 % | A4s 85 % | A3s 53 % | A2s 49 % |
| K | AKo 7 % | KK 100 % | KQs 100 % | KJs 86 % | KTs 85 % | K9s 52 % | K8s 72 % | K7s 66 % | K6s 75 % | K5s 80 % | K4s 64 % | K3s 93 % | K2s 39 % |
| Q | AQo 100 % | KQo 100 % | QQ 24 % | QJs 72 % | QTs 77 % | Q9s 87 % | Q8s 67 % | Q7s 50 % | Q6s 36 % | Q5s 28 % | Q4s 4 % | Q3s Not in this range here | Q2s Not in this range here |
| J | AJo 38 % | KJo 76 % | QJo 77 % | JJ 34 % | JTs 51 % | J9s 72 % | J8s 37 % | J7s 94 % | J6s 55 % | J5s 27 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo 59 % | KTo 60 % | QTo 59 % | JTo 68 % | TT 38 % | T9s 17 % | T8s 52 % | T7s 54 % | 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 58 % | K9o 24 % | Q9o 100 % | J9o 21 % | T9o 1 % | 99 42 % | 98s 5 % | 97s 1 % | 96s Not in this range here | 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 50 % | K8o 46 % | Q8o 3 % | J8o Not in this range here | T8o Not in this range here | 98o Not in this range here | 88 <1 % | 87s 31 % | 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 52 % | K7o <1 % | 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 <1 % | 76s 7 % | 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 57 % | 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 <1 % | 65s <1 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o 71 % | 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 <1 % | 54s Not in this range here | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o 41 % | 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 | 44 100 % | 43s Not in this range here | 42s Not in this range here |
| 3 | A3o 92 % | 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 <1 % | 32s Not in this range here |
| 2 | A2o 40 % | 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 Not in this range here | AKs Not in this range here | AQs Not in this range here | AJs Not in this range here | ATs <1 % | A9s 5 % | A8s Not in this range here | A7s Not in this range here | A6s Not in this range here | A5s <1 % | A4s 12 % | A3s <1 % | A2s <1 % |
| K | AKo Not in this range here | KK Not in this range here | KQs Not in this range here | KJs 61 % | KTs <1 % | K9s <1 % | K8s <1 % | K7s <1 % | K6s <1 % | K5s <1 % | K4s 3 % | K3s Not in this range here | K2s <1 % |
| Q | AQo Not in this range here | KQo 56 % | QQ Not in this range here | QJs 63 % | QTs <1 % | Q9s 31 % | Q8s 16 % | Q7s <1 % | Q6s <1 % | Q5s <1 % | Q4s Not in this range here | Q3s <1 % | Q2s Not in this range here |
| J | AJo Not in this range here | KJo 32 % | QJo 24 % | JJ Not in this range here | JTs 1 % | J9s Not in this range here | J8s 1 % | J7s <1 % | J6s Not in this range here | J5s Not in this range here | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo Not in this range here | KTo 21 % | QTo 11 % | JTo 18 % | TT Not in this range here | T9s Not in this range here | T8s 20 % | T7s <1 % | 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 <1 % | K9o Not in this range here | Q9o Not in this range here | J9o Not in this range here | T9o Not in this range here | 99 Not in this range here | 98s 15 % | 97s <1 % | 96s 6 % | 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 Not in this range here | K8o Not in this range here | Q8o Not in this range here | J8o Not in this range here | T8o Not in this range here | 98o Not in this range here | 88 Not in this range here | 87s Not in this range here | 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 Not in this range here | 77 Not in this range here | 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 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 Not in this range here | 66 Not in this range here | 65s <1 % | 64s 4 % | 63s Not in this range here | 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 <1 % | 54s 7 % | 53s <1 % | 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 46 % | 43s 5 % | 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 <1 % |
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 40 big blinds, with a 5% rake capped at 15 bb and 2.5 bb opens. It allows one bet size at each decision. Here the button's c-bet is 4 bb, the big blind's check-raise goes to 9.5 bb and the button's re-raise to 15.5 bb, which leaves chips behind rather than putting the button all 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-R9.5 - Solver notation
-
Qs9d4h·KsQd. 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.