Solver answer
Second pair facing a river bet: call or fold?
6-max cash, 100 big blinds · Button opens, big blind calls · River Q♥ T♣ 5♠ 2♦ 7♣ · Button bets 34 bb into 40.9 bb · Big blind to act
Updated
The solver's answer
A♠T♦ and K♥T♠, standing in for T♠9♠.
A♠T♦
Call 100%
K♥T♠
Fold 100%
With second pair, a pair of tens here, the other card decides it: ace-ten calls and king-ten folds.
T♠9♠ never reaches this river in this solution, because the big blind 3-bets it before the flop 100% of the time. Two second pairs that do reach it stand in: A♠T♦ and K♥T♠.
Q♥T♣5♠2♦7♣
A♠T♦ Stand-in
K♥T♠ Stand-in
- Pot
- 40.9 bb
- Behind
- 79.8 bb
- Button
- Bets 34 bb
In a 6-max cash game at 100 big blinds, when the big blind has called the button's flop and turn bets and faces a 34 bb bet into 40.9 bb on a Q♥ T♣ 5♠ 2♦ 7♣ board, it calls with A♠T♦ 100% of the time and folds K♥T♠ 100%, according to a solver answer published free by Poker Skill.
Why ace-ten calls and king-ten folds
- Calling 34 bb to win 74.9 bb needs 31.2% equity. A♠T♦ has 32.3% against the button's bet, and calling is worth 1.00 bb to it on average; K♥T♠ has 30.6%, and calling loses 0.87 bb.
- A pair of tens beats only the button's bluffs: its 34 bb bets are top pair or better or hands with no pair at all.
- Many of those bluffs are king-high. King-four suited bets 34 bb 90% of the time and king-three suited 85%. Holding a king leaves the button fewer of them, while holding an ace takes away some of its value bets, such as aces and ace-queen, so A♠T♦ ends up with more equity than K♥T♠.
- As a group, the big blind's second pairs fold 61%, call 31% and move all in 8%. The big blind's whole range continues 52% of the time, calling 35% and moving all in 17%, a little under the 55% that the minimum defense frequency formula gives for a bet this size.
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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 C 100 % | 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 Not in this range here | A4s Not in this range here | A3s Not in this range here | A2s F 99 % |
| K | AKo Not in this range here | KK Not in this range here | KQs Not in this range here | KJs F 100 % | KTs F 100 % | K9s Not in this range here | K8s Not in this range here | K7s Not in this range here | K6s Not in this range here | K5s F 100 % | K4s Not in this range here | K3s Not in this range here | K2s Not in this range here |
| Q | AQo Not in this range here | KQo C 100 % | QQ Not in this range here | QJs C 65 % | QTs Not in this range here | Q9s F 86 % | Q8s C 79 % | Q7s R 100 % | Q6s C 95 % | Q5s R 100 % | Q4s C 58 % | Q3s C 97 % | Q2s R 98 % |
| J | AJo F 100 % | KJo F 100 % | QJo C 65 % | JJ Not in this range here | 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 F 100 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo C 100 % | KTo F 100 % | QTo R 100 % | JTo F 98 % | TT Not in this range here | T9s Not in this range here | T8s F 96 % | T7s R 100 % | T6s F 63 % | T5s Not in this range here | T4s F 84 % | T3s F 61 % | T2s Not in this range here |
| 9 | A9o Not in this range here | K9o Not in this range here | Q9o F 86 % | J9o Not in this range here | T9o Not in this range here | 99 Not in this range here | 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 F 86 % | 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 F 100 % | 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 C 52 % | 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 F 100 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o F 99 % | 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 100 % | 54s F 100 % | 53s F 100 % | 52s R 100 % |
| 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 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 R 100 % |
- Fold: 47.70% of the range (14.98 combos)
- Call (34 bb): 35.04% of the range (11.01 combos)
- All-in (79.8 bb): 17.26% of the range (5.42 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 (34 bb) | All-in (79.8 bb) |
|---|---|---|---|---|
| ATs | 0.783 | 0.2% | 99.7% | 0.1% |
| A2s | 0.002 | 99.4% | 0.6% | 0.0% |
| KJs | 0.087 | 100.0% | 0.0% | 0.0% |
| KTs | 0.942 | 99.8% | 0.1% | 0.2% |
| K5s | 0.065 | 100.0% | 0.0% | 0.0% |
| KQo | 2.494 | 0.0% | 100.0% | 0.0% |
| QJs | 0.053 | 20.2% | 65.1% | 14.7% |
| Q9s | 0.449 | 86.3% | 10.9% | 2.7% |
| Q8s | 0.567 | 11.0% | 79.3% | 9.6% |
| Q7s | 0.441 | 0.0% | 0.0% | 100.0% |
| Q6s | 1.336 | 3.2% | 94.5% | 2.3% |
| Q5s | 0.011 | 0.0% | 0.0% | 100.0% |
| Q4s | 1.865 | 34.6% | 58.3% | 7.0% |
| Q3s | 1.532 | 0.3% | 97.4% | 2.3% |
| Q2s | 0.597 | 0.0% | 1.7% | 98.3% |
| AJo | 1.43 | 100.0% | 0.0% | 0.0% |
| KJo | 1.364 | 100.0% | 0.0% | 0.0% |
| QJo | 0.092 | 24.6% | 64.6% | 10.8% |
| JTs | 0.026 | 98.5% | 0.0% | 1.5% |
| J5s | 0.001 | 100.0% | 0.0% | 0.0% |
| ATo | 2.819 | 0.1% | 99.7% | 0.1% |
| KTo | 2.846 | 99.6% | 0.1% | 0.3% |
| QTo | 0.006 | 0.0% | 0.0% | 100.0% |
| JTo | 0.26 | 98.1% | 0.0% | 1.9% |
| T8s | 0.513 | 96.4% | 0.0% | 3.6% |
| T7s | 1.276 | 0.0% | 0.0% | 100.0% |
| T6s | 1.048 | 63.3% | 0.0% | 36.7% |
| T4s | 0.651 | 84.1% | 0.0% | 15.9% |
| T3s | 0.558 | 61.2% | 0.0% | 38.8% |
| Q9o | 1.497 | 86.3% | 11.1% | 2.5% |
| T8o | 1.296 | 85.8% | 0.0% | 14.2% |
| 85s | 0.741 | 100.0% | 0.0% | 0.0% |
| 75s | 0.587 | 0.0% | 52.2% | 47.8% |
| 65s | 0.812 | 100.0% | 0.0% | 0.0% |
| A5o | 0.039 | 99.0% | 1.0% | 0.0% |
| 55 | 0.01 | 0.0% | 0.0% | 100.0% |
| 54s | 0.193 | 100.0% | 0.0% | 0.0% |
| 53s | 0.56 | 100.0% | 0.0% | 0.0% |
| 52s | 0.597 | 0.0% | 0.0% | 100.0% |
| 22 | 0.968 | 0.0% | 0.0% | 100.0% |
What each action is worth with A♠T♦
| Action | How often | Expected value |
|---|---|---|
| Fold | 0.00% | 0 bb |
| Call (34 bb) | 99.78% | 0.997 bb |
| All-in (79.8 bb) | 0.22% | 0.092 bb |
What each action is worth with K♥T♠
| Action | How often | Expected value |
|---|---|---|
| Fold | 99.76% | 0 bb |
| Call (34 bb) | 0.07% | -0.867 bb |
| All-in (79.8 bb) | 0.17% | -1.835 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 Q♥ T♣ 5♠: big blind checks, button bets 1.8 bb, big blind calls · Turn 2♦: big blind checks, button bets 15.9 bb, big blind calls · River 7♣: big blind checks, button bets 34 bb into 40.9 bb · Big blind to act, 79.8 bb behind
- Pot at this decision, including the bets in front: 74.9 bb
- The big blind: 79.8 bb behind
- The button: 45.8 bb behind, 34 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 26 % | 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 Not in this range here | A4s Not in this range here | A3s Not in this range here | A2s <1 % |
| K | AKo Not in this range here | KK Not in this range here | KQs Not in this range here | KJs 2 % | KTs 31 % | K9s Not in this range here | K8s Not in this range here | K7s Not in this range here | K6s Not in this range here | K5s 2 % | K4s Not in this range here | K3s Not in this range here | K2s Not in this range here |
| Q | AQo Not in this range here | KQo 28 % | QQ Not in this range here | QJs 2 % | QTs Not in this range here | Q9s 15 % | Q8s 19 % | Q7s 22 % | Q6s 45 % | Q5s 1 % | Q4s 62 % | Q3s 51 % | Q2s 30 % |
| J | AJo 12 % | KJo 11 % | QJo 1 % | JJ Not in this range here | JTs 1 % | 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 <1 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo 31 % | KTo 32 % | QTo <1 % | JTo 3 % | TT Not in this range here | T9s Not in this range here | T8s 17 % | T7s 43 % | T6s 35 % | T5s Not in this range here | T4s 22 % | T3s 19 % | T2s Not in this range here |
| 9 | A9o Not in this range here | K9o Not in this range here | Q9o 17 % | J9o Not in this range here | T9o Not in this range here | 99 Not in this range here | 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 14 % | 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 25 % | 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 29 % | 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 27 % | 64s Not in this range here | 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 <1 % | 54s 6 % | 53s 19 % | 52s 30 % |
| 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 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 32 % |
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 12 % | AKs Not in this range here | AQs 12 % | AJs Not in this range here | 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 <1 % | A5s Not in this range here | A4s <1 % | A3s <1 % | A2s Not in this range here |
| K | AKo Not in this range here | KK 10 % | KQs 10 % | KJs Not in this range here | KTs Not in this range here | K9s 2 % | K8s <1 % | K7s Not in this range here | K6s 3 % | K5s Not in this range here | K4s 7 % | K3s 9 % | K2s Not in this range here |
| Q | AQo 9 % | KQo 10 % | QQ 9 % | QJs Not in this range here | QTs 5 % | 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 7 % | Q4s Not in this range here | Q3s Not in this range here | Q2s 9 % |
| J | AJo Not in this range here | KJo Not in this range here | QJo Not in this range here | JJ Not in this range here | JTs Not in this range here | J9s 2 % | J8s 2 % | J7s Not in this range here | J6s 1 % | J5s Not in this range here | J4s 2 % | J3s 1 % | J2s Not in this range here |
| T | ATo Not in this range here | KTo Not in this range here | QTo 5 % | JTo Not in this range here | TT 21 % | 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 3 % | 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 2 % | T9o Not in this range here | 99 Not in this range here | 98s 3 % | 97s Not in this range here | 96s <1 % | 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 1 % | Q8o Not in this range here | J8o <1 % | T8o Not in this range here | 98o 1 % | 88 Not in this range here | 87s Not in this range here | 86s <1 % | 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 2 % | 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 Not in this range here | 64s <1 % | 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 12 % | 54s Not in this range here | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o 2 % | 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 <1 % | 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 8 % |
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. The flop, turn and river bets follow the button's most-used size on each street: 1.8 bb, 15.9 bb and 34 bb. Facing the river bet, the big blind can fold, call or move all in. T♠9♠ never reaches this river in this solution, so A♠T♦ and K♥T♠ 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-R1.8-C, turn X-R15.9-C, river X-R34 - Solver notation
-
QhTc5s2d7c·AsTd·KhTs·Ts9s. 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.