Solver answer
Top pair, weak kicker on the river: bet for thin value?
6-max cash, 100 big blinds · Button opens, big blind calls · River K♦ 9♦ 4♣ 2♠ 7♥ · Big blind checks · Button to act
Updated
The solver's answer
K♠8♠ and K♥8♦, standing in for K♣5♣.
K♠8♠
Bet 71% Check 29%
¾ pot · 13.7 bb
K♥8♦
Check 88% Bet 12%
Kings with a weak kicker split here: one bets most of the time, the other mostly checks.
K♣5♣ almost never reaches this river in this solution: its only flop c-bet is an overbet, and the button rarely makes it with king-five and then checks the turn. Two kings with an eight that do reach it stand in: K♠8♠ and K♥8♦. In the solver's multi-size solution, where king-five gets here more often, it bets too.
K♦9♦4♣2♠7♥
K♠8♠ Stand-in
K♥8♦ Stand-in
- Pot
- 18.3 bb
- Behind
- 91.1 bb
- Big blind
- Checks
In a 6-max cash game at 100 big blinds, after the big blind calls the button's 6.4 bb flop c-bet on K♦ 9♦ 4♣, the 2♠ turn is checked through and the big blind checks the 7♥ river, the button bets 13.7 bb into 18.3 bb with K♠8♠ 71% of the time and with K♥8♦ 12%, according to a solver answer published free by Poker Skill.
When top pair with a weak kicker bets
- A thin value bet is made with a hand that is probably best but not strong enough to expect calls only from worse hands. It pays when worse hands call often enough.
- Both kings have about 88% equity against the big blind's checking range, and for each, betting and checking are worth almost the same: K♠8♠ 15.34 bb against 15.29 bb, K♥8♦ 15.07 bb against 15.20 bb.
- The button's top pairs as a group bet 54% of the time: king-queen suited 92%, king-jack offsuit 45%.
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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 X 100 % | AKs X 95 % | AQs X 100 % | AJs X 100 % | ATs X 100 % | A9s X 100 % | A8s X 100 % | A7s X 100 % | A6s X 100 % | A5s X 99 % | A4s X 91 % | A3s X 93 % | A2s X 100 % |
| K | AKo X 96 % | KK Not in this range here | KQs B 92 % | KJs B 63 % | KTs B 93 % | K9s B 100 % | K8s B 70 % | K7s B 100 % | K6s B 88 % | K5s B 81 % | K4s B 100 % | K3s B 74 % | K2s B 100 % |
| Q | AQo X 100 % | KQo B 70 % | QQ X 72 % | QJs X 84 % | QTs X 88 % | Q9s X 100 % | Q8s X 86 % | Q7s X 100 % | Q6s X 94 % | Q5s B 53 % | Q4s X 100 % | Q3s X 51 % | Q2s Not in this range here |
| J | AJo X 100 % | KJo X 55 % | QJo X 89 % | JJ X 100 % | JTs X 92 % | J9s X 100 % | J8s X 86 % | J7s X 100 % | J6s X 95 % | J5s X 53 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo X 100 % | KTo X 52 % | QTo X 91 % | JTo X 96 % | TT X 99 % | T9s X 100 % | T8s X 76 % | T7s X 100 % | T6s X 96 % | 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 X 98 % | K9o B 100 % | Q9o X 100 % | J9o X 100 % | T9o X 100 % | 99 Not in this range here | 98s X 100 % | 97s B 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 X 100 % | K8o B 54 % | Q8o Not in this range here | J8o Not in this range here | T8o X 77 % | 98o Not in this range here | 88 X 100 % | 87s X 100 % | 86s X 76 % | 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 X 100 % | K7o B 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 B 100 % | 76s X 100 % | 75s X 100 % | 74s Not in this range here | 73s Not in this range here | 72s Not in this range here |
| 6 | A6o X 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 X 100 % | 65s B 78 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o X 100 % | 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 X 100 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o X 99 % | 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 X 94 % | 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 X 100 % | 32s Not in this range here |
| 2 | A2o X 100 % | 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 |
- Check: 82.82% of the range (71.97 combos)
- Bet ¾ pot (13.7 bb): 17.18% of the range (14.93 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 | Check | Bet ¾ pot (13.7 bb) |
|---|---|---|---|
| AA | 1.004 | 99.6% | 0.4% |
| AKs | 0.611 | 94.8% | 5.2% |
| AQs | 0.002 | 100.0% | 0.0% |
| AJs | 0.109 | 99.9% | 0.1% |
| ATs | 1.169 | 100.0% | 0.0% |
| A9s | 0.389 | 99.7% | 0.3% |
| A8s | 0.981 | 100.0% | 0.0% |
| A7s | 0.946 | 99.9% | 0.1% |
| A6s | 0.47 | 99.9% | 0.1% |
| A5s | 1.137 | 99.0% | 1.0% |
| A4s | 0.001 | 91.3% | 8.7% |
| A3s | 2.059 | 93.2% | 6.8% |
| A2s | 0.438 | 100.0% | 0.0% |
| AKo | 1.484 | 96.2% | 3.8% |
| KQs | 1.088 | 7.6% | 92.4% |
| KJs | 1.334 | 36.7% | 63.3% |
| KTs | 0.88 | 6.9% | 93.1% |
| K9s | 0.027 | 0.0% | 100.0% |
| K8s | 0.597 | 30.4% | 69.6% |
| K7s | 0.006 | 0.0% | 100.0% |
| K6s | 0.003 | 12.5% | 87.5% |
| K5s | 0.003 | 19.3% | 80.7% |
| K4s | 0.12 | 0.0% | 100.0% |
| K3s | 0.003 | 25.6% | 74.4% |
| K2s | 0.001 | 0.0% | 100.0% |
| AQo | 0.001 | 100.0% | 0.0% |
| KQo | 3.92 | 30.5% | 69.5% |
| 0.003 | 72.3% | 27.7% | |
| QJs | 1.79 | 84.1% | 15.9% |
| QTs | 1.909 | 88.3% | 11.7% |
| Q9s | 0.118 | 100.0% | 0.0% |
| Q8s | 0.554 | 86.4% | 13.6% |
| Q7s | 0.743 | 99.9% | 0.1% |
| Q6s | 1.051 | 93.6% | 6.4% |
| Q5s | 0.676 | 46.7% | 53.3% |
| Q4s | 0.002 | 99.8% | 0.2% |
| Q3s | 0.169 | 50.9% | 49.1% |
| AJo | 0.192 | 100.0% | 0.0% |
| KJo | 4.508 | 54.7% | 45.3% |
| QJo | 5.427 | 89.3% | 10.7% |
| JJ | 0.004 | 99.5% | 0.5% |
| JTs | 1.646 | 92.0% | 8.0% |
| J9s | 0.033 | 100.0% | 0.0% |
| J8s | 1.028 | 86.0% | 14.0% |
| J7s | 1.243 | 100.0% | 0.0% |
| J6s | 1.447 | 95.0% | 5.0% |
| J5s | 0.389 | 53.3% | 46.7% |
| ATo | 2.719 | 100.0% | 0.0% |
| KTo | 2.779 | 52.4% | 47.6% |
| QTo | 4.891 | 91.2% | 8.8% |
| JTo | 6.629 | 95.7% | 4.3% |
| TT | 0.21 | 98.9% | 1.1% |
| T9s | 0.028 | 100.0% | 0.0% |
| T8s | 1.04 | 75.5% | 24.5% |
| T7s | 1.317 | 100.0% | 0.0% |
| T6s | 0.976 | 96.1% | 3.9% |
| A9o | 2.552 | 98.3% | 1.7% |
| K9o | 0.002 | 0.0% | 100.0% |
| Q9o | 0.845 | 100.0% | 0.0% |
| J9o | 0.132 | 100.0% | 0.0% |
| T9o | 0.249 | 100.0% | 0.0% |
| 98s | 0.035 | 100.0% | 0.0% |
| 97s | 0.021 | 0.0% | 100.0% |
| A8o | 2.319 | 99.5% | 0.5% |
| K8o | 1.215 | 45.9% | 54.1% |
| T8o | 0.483 | 77.0% | 23.0% |
| 88 | 0.001 | 100.0% | 0.0% |
| 87s | 0.401 | 100.0% | 0.0% |
| 86s | 0.886 | 76.2% | 23.8% |
| A7o | 3.107 | 99.8% | 0.2% |
| K7o | 0.004 | 0.0% | 100.0% |
| 77 | 0.001 | 0.0% | 100.0% |
| 76s | 0.172 | 100.0% | 0.0% |
| 75s | 0.001 | 99.8% | 0.2% |
| A6o | 4.809 | 99.9% | 0.1% |
| 66 | 0.003 | 100.0% | 0.0% |
| 65s | 1.026 | 22.3% | 77.7% |
| A5o | 1.49 | 99.5% | 0.5% |
| 54s | 0.003 | 99.8% | 0.2% |
| A4o | 0.178 | 98.5% | 1.5% |
| A3o | 4.432 | 94.4% | 5.6% |
| 33 | 0.008 | 100.0% | 0.0% |
| A2o | 0.219 | 99.9% | 0.1% |
What each action is worth with K♠8♠
| Action | How often | Expected value |
|---|---|---|
| Check | 29.23% | 15.289 bb |
| Bet ¾ pot (13.7 bb) | 70.77% | 15.339 bb |
What each action is worth with K♥8♦
| Action | How often | Expected value |
|---|---|---|
| Check | 88.41% | 15.203 bb |
| Bet ¾ pot (13.7 bb) | 11.59% | 15.073 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 K♦ 9♦ 4♣: big blind checks, button bets 6.4 bb, big blind calls · Turn 2♠: big blind checks, button checks · River 7♥: big blind checks · Pot 18.3 bb · Button to act, 91.1 bb behind
- Pot at this decision, including the bets in front: 18.3 bb
- The button: 91.1 bb behind
- The big blind: 91.1 bb behind
| A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | AA 17 % | AKs 20 % | AQs <1 % | AJs 3 % | ATs 29 % | A9s 13 % | A8s 25 % | A7s 32 % | A6s 12 % | A5s 28 % | A4s <1 % | A3s 52 % | A2s 15 % |
| K | AKo 17 % | KK Not in this range here | KQs 36 % | KJs 45 % | KTs 29 % | K9s 1 % | K8s 20 % | K7s <1 % | K6s <1 % | K5s <1 % | K4s 6 % | K3s <1 % | K2s <1 % |
| Q | AQo <1 % | KQo 44 % | QQ <1 % | QJs 45 % | QTs 48 % | Q9s 4 % | Q8s 14 % | Q7s 25 % | Q6s 26 % | Q5s 17 % | Q4s <1 % | Q3s 4 % | Q2s Not in this range here |
| J | AJo 2 % | KJo 50 % | QJo 45 % | JJ <1 % | JTs 41 % | J9s 1 % | J8s 26 % | J7s 41 % | J6s 36 % | J5s 10 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo 23 % | KTo 31 % | QTo 41 % | JTo 55 % | TT 4 % | T9s 1 % | T8s 26 % | T7s 44 % | T6s 24 % | 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 28 % | K9o <1 % | Q9o 9 % | J9o 2 % | T9o 3 % | 99 Not in this range here | 98s 1 % | 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 19 % | K8o 14 % | Q8o Not in this range here | J8o Not in this range here | T8o 4 % | 98o Not in this range here | 88 <1 % | 87s 13 % | 86s 22 % | 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 35 % | 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 6 % | 75s <1 % | 74s Not in this range here | 73s Not in this range here | 72s Not in this range here |
| 6 | A6o 40 % | 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 26 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o 12 % | 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 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 37 % | 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 2 % | 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 25 % | ATs 21 % | A9s 100 % | A8s 22 % | A7s 23 % | A6s 17 % | A5s 18 % | A4s 86 % | A3s 16 % | A2s 23 % |
| K | AKo Not in this range here | KK Not in this range here | KQs Not in this range here | KJs <1 % | KTs <1 % | K9s 3 % | K8s <1 % | K7s 2 % | K6s 3 % | K5s 1 % | K4s <1 % | K3s 1 % | K2s Not in this range here |
| Q | AQo 9 % | KQo 2 % | QQ Not in this range here | QJs 7 % | QTs <1 % | Q9s 83 % | Q8s Not in this range here | Q7s 19 % | Q6s Not in this range here | Q5s Not in this range here | Q4s 33 % | Q3s Not in this range here | Q2s 1 % |
| J | AJo 9 % | KJo <1 % | QJo <1 % | JJ Not in this range here | JTs Not in this range here | J9s 82 % | J8s Not in this range here | J7s 25 % | J6s Not in this range here | J5s Not in this range here | J4s 4 % | J3s Not in this range here | J2s Not in this range here |
| T | ATo 1 % | KTo <1 % | QTo <1 % | JTo Not in this range here | TT Not in this range here | T9s 66 % | T8s Not in this range here | T7s 27 % | 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 100 % | K9o 2 % | Q9o 18 % | J9o 7 % | T9o 16 % | 99 82 % | 98s 61 % | 97s 41 % | 96s 31 % | 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 13 % | 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 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 11 % | 76s 23 % | 75s 28 % | 74s 18 % | 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 1 % | 65s Not in this range here | 64s 18 % | 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 5 % | 53s Not in this range here | 52s 3 % |
| 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 58 % | 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 Not in this range here |
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 button's only flop c-bet is an overbet, 6.4 bb, and its river bet is three-quarters of the pot. K♣5♣ reaches this river so rarely in this solution that two kings with an eight 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
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F-F-F-R2.5-F-C·flop X-R6.4-C, turn X-X, river X - Solver notation
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Kd9d4c2s7h·Ks8s·Kh8d·Kc5c. 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.