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.