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.