Solver answer
SPR in a 3-bet pot: does A♠Q♠ call or shove?
6-max cash, 100 big blinds · Button opens, big blind 3-bets, button calls · Flop Q♦ 6♣ 2♥ · Big blind bets 12.9 bb into 27.5 bb · Button to act
Updated
The solver's answer
Call 100%
A♠Q♠ calls almost every time; moving all in is worth less, even with this little behind.
The solver plays A♠Q♠ along this line to this decision 47.19% of the time; otherwise it acts differently earlier in the hand.
Q♦6♣2♥
A♠Q♠ You
- Pot
- 27.5 bb
- Behind
- 86.5 bb
- Big blind
- Bets 12.9 bb
In a 6-max cash game at 100 big blinds, after the button opens to 2.5 bb, the big blind 3-bets and the button calls, then the big blind c-bets 12.9 bb into 27.5 bb on a Q♦ 6♣ 2♥ flop, the button calls with A♠Q♠ 99.9% of the time and moves all in 0.1%, according to a solver answer published free by Poker Skill.
What a low stack-to-pot ratio changes for A♠Q♠
- Stack-to-pot ratio, or SPR, is the effective stack divided by the pot. On this flop 86.5 bb sit behind a 27.5 bb pot, an SPR of 3.1.
- A low SPR favors made hands like top pair: A♠Q♠ has 78.6% equity against the big blind's bet, and a call needs 24.2%.
- It still calls rather than moving all in: calling is worth 36.01 bb and the all-in 32.95 bb.
- The button's range plays the same way. Its top pairs never fold, its second pairs call 89% of the time and it almost never raises.
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 100 % | AKs Not in this range here | AQs C 100 % | AJs C 70 % | ATs F 55 % | A9s F 78 % | A8s F 60 % | A7s C 69 % | A6s Not in this range here | A5s C 57 % | A4s C 85 % | A3s Not in this range here | A2s Not in this range here |
| K | AKo Not in this range here | KK Not in this range here | KQs C 100 % | KJs C 94 % | KTs C 61 % | K9s F 91 % | K8s Not in this range here | K7s Not in this range here | K6s Not in this range here | K5s Not in this range here | K4s Not in this range here | K3s Not in this range here | K2s Not in this range here |
| Q | AQo C 100 % | KQo C 100 % | QQ Not in this range here | QJs C 100 % | QTs C 100 % | Q9s Not in this range here | Q8s Not in this range here | Q7s Not in this range here | Q6s Not in this range here | Q5s Not in this range here | Q4s Not in this range here | Q3s Not in this range here | Q2s Not in this range here |
| J | AJo Not in this range here | KJo Not in this range here | QJo Not in this range here | JJ C 100 % | JTs F 99 % | J9s Not in this range here | J8s Not in this range here | J7s Not in this range here | 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 Not in this range here | QTo Not in this range here | JTo Not in this range here | TT C 100 % | T9s Not in this range here | 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 Not in this range here | Q9o Not in this range here | J9o Not in this range here | T9o Not in this range here | 99 C 84 % | 98s Not in this range here | 97s Not in this range here | 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 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 C 85 % | 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 C 96 % | 76s C 100 % | 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 C 100 % | 65s C 100 % | 64s Not in this range here | 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 C 100 % | 54s C 100 % | 53s Not in this range here | 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 C 100 % | 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 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: 26.25% of the range (17.6 combos)
- Call (12.9 bb): 73.72% of the range (49.43 combos)
- All-in (86.5 bb): 0.03% of the range (0.02 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 (12.9 bb) | All-in (86.5 bb) |
|---|---|---|---|---|
| AA | 0.002 | 0.0% | 100.0% | 0.0% |
| AQs | 1.416 | 0.0% | 99.9% | 0.1% |
| AJs | 4 | 30.2% | 69.8% | 0.0% |
| ATs | 4 | 55.3% | 44.7% | 0.0% |
| A9s | 3.834 | 78.4% | 21.6% | 0.0% |
| A8s | 2.378 | 59.8% | 40.1% | 0.0% |
| A7s | 0.007 | 30.7% | 69.3% | 0.0% |
| A5s | 3.553 | 43.2% | 56.7% | 0.0% |
| A4s | 0.105 | 14.8% | 85.2% | 0.0% |
| KQs | 3 | 0.0% | 99.9% | 0.1% |
| KJs | 4 | 5.6% | 94.4% | 0.0% |
| KTs | 4 | 38.7% | 61.3% | 0.0% |
| K9s | 1.078 | 91.1% | 8.9% | 0.0% |
| AQo | 4.929 | 0.0% | 99.9% | 0.1% |
| KQo | 0.018 | 0.0% | 99.9% | 0.1% |
| QJs | 3 | 0.0% | 99.9% | 0.1% |
| QTs | 2.21 | 0.0% | 99.9% | 0.1% |
| JJ | 0.052 | 0.0% | 100.0% | 0.0% |
| JTs | 3.525 | 99.1% | 0.9% | 0.0% |
| TT | 2.842 | 0.1% | 99.9% | 0.0% |
| 99 | 5.999 | 16.5% | 83.5% | 0.0% |
| 88 | 5.38 | 14.6% | 85.4% | 0.0% |
| 77 | 3.92 | 4.5% | 95.5% | 0.0% |
| 76s | 0.332 | 0.0% | 100.0% | 0.0% |
| 66 | 1.77 | 0.0% | 100.0% | 0.0% |
| 65s | 0.001 | 0.0% | 100.0% | 0.0% |
| 55 | 1.325 | 0.3% | 99.7% | 0.0% |
| 54s | 0.269 | 0.0% | 100.0% | 0.0% |
| 44 | 0.11 | 0.1% | 99.9% | 0.0% |
What each action is worth with A♠Q♠
| Action | How often | Expected value |
|---|---|---|
| Fold | 0.00% | 0 bb |
| Call (12.9 bb) | 99.92% | 36.007 bb |
| All-in (86.5 bb) | 0.08% | 32.953 bb |
Ranges, pot and stacks
- The hand so far: 6-max cash, 100 big blinds · Button opens to 2.5 bb, big blind 3-bets to 13.5 bb, button calls · Flop Q♦ 6♣ 2♥: big blind bets 12.9 bb into 27.5 bb · Button to act, 86.5 bb behind
- Pot at this decision, including the bets in front: 40.4 bb
- The button: 86.5 bb behind
- The big blind: 73.6 bb behind, 12.9 bb in front
| A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | AA <1 % | AKs Not in this range here | AQs 47 % | AJs 100 % | ATs 100 % | A9s 96 % | A8s 60 % | A7s <1 % | A6s Not in this range here | A5s 89 % | A4s 3 % | A3s Not in this range here | A2s Not in this range here |
| K | AKo Not in this range here | KK Not in this range here | KQs 100 % | KJs 100 % | KTs 100 % | K9s 27 % | K8s Not in this range here | K7s Not in this range here | K6s Not in this range here | K5s Not in this range here | K4s Not in this range here | K3s Not in this range here | K2s Not in this range here |
| Q | AQo 55 % | KQo <1 % | QQ Not in this range here | QJs 100 % | QTs 74 % | Q9s Not in this range here | Q8s Not in this range here | Q7s Not in this range here | Q6s Not in this range here | Q5s Not in this range here | Q4s Not in this range here | Q3s Not in this range here | Q2s Not in this range here |
| J | AJo Not in this range here | KJo Not in this range here | QJo Not in this range here | JJ 1 % | JTs 88 % | J9s Not in this range here | J8s Not in this range here | J7s Not in this range here | 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 Not in this range here | QTo Not in this range here | JTo Not in this range here | TT 47 % | T9s Not in this range here | 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 Not in this range here | Q9o Not in this range here | J9o Not in this range here | T9o Not in this range here | 99 100 % | 98s Not in this range here | 97s Not in this range here | 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 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 90 % | 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 65 % | 76s 11 % | 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 59 % | 65s <1 % | 64s Not in this range here | 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 22 % | 54s 7 % | 53s Not in this range here | 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 2 % | 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 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 81 % | AKs 69 % | AQs 81 % | AJs <1 % | ATs Not in this range here | A9s Not in this range here | A8s Not in this range here | A7s Not in this range here | A6s Not in this range here | A5s 1 % | A4s Not in this range here | A3s Not in this range here | A2s <1 % |
| K | AKo 73 % | KK 83 % | KQs 85 % | KJs 11 % | KTs Not in this range here | K9s Not in this range here | K8s Not in this range here | K7s Not in this range here | K6s 1 % | K5s 10 % | K4s 12 % | K3s 30 % | K2s 72 % |
| Q | AQo 56 % | KQo <1 % | QQ 74 % | QJs Not in this range here | QTs Not in this range here | Q9s Not in this range here | Q8s 12 % | Q7s 13 % | Q6s 5 % | Q5s 76 % | Q4s 2 % | Q3s 45 % | Q2s 82 % |
| J | AJo Not in this range here | KJo 57 % | QJo 35 % | JJ 85 % | JTs 1 % | J9s Not in this range here | J8s Not in this range here | J7s 9 % | J6s 51 % | J5s 36 % | J4s <1 % | J3s Not in this range here | J2s 16 % |
| T | ATo 4 % | KTo 50 % | QTo 45 % | JTo 23 % | TT 81 % | T9s 1 % | T8s <1 % | T7s <1 % | T6s 44 % | 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 14 % | Q9o 2 % | J9o <1 % | T9o 9 % | 99 4 % | 98s Not in this range here | 97s Not in this range here | 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 4 % | K8o 5 % | 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 <1 % | 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 13 % | 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 <1 % | 76s <1 % | 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 15 % | 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 9 % | 65s 1 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o 15 % | 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 24 % | 54s 1 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o 35 % | 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 1 % | 43s Not in this range here | 42s Not in this range here |
| 3 | A3o 8 % | 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 44 % | 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 2 % |
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 15 bb and 2.5 bb opens. It allows one bet size at each decision. Here the big blind's c-bet is 12.9 bb into 27.5 bb, and the button's only raise is 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-R13.5-C·flop R12.9 - Solver notation
-
Qd6c2h·AsQs. 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.