Solver answer
K♣T♣ has the nuts on the river: lead or check?
6-max cash, 100 big blinds · Button opens, big blind calls · River Q♦ 7♣ 4♠ 9♥ J♣ · Big blind to act
Updated
The solver's answer
Check 99% Bet 1%
K♣T♣ checks almost every time, then check-raises all in when the button bets.
The solver plays K♣T♣ along this line to this decision 80.43% of the time; otherwise it acts differently earlier in the hand.
Q♦7♣4♠9♥J♣
K♣T♣ You
- Pot
- 9.1 bb
- Behind
- 95.7 bb
- First to act
- You
In a 6-max cash game at 100 big blinds, after the big blind calls the button's 1.8 bb flop c-bet on Q♦ 7♣ 4♠ and the 9♥ turn is checked through, the big blind checks the J♣ river with K♣T♣ 99% of the time and leads 2.3 bb 1%, according to a solver answer published free by Poker Skill.
Why the nuts checks here
- Checking is worth 14.04 bb to K♣T♣ and the lead 13.91 bb. This solution's only lead is a quarter of the pot, a small bet for the nuts.
- When the big blind checks, the button bets 31% of the time. K♣T♣ then check-raises all in every time, worth 26.24 bb against 16.63 bb for a call.
- A check-raise only pays when the opponent is likely to bet; when a check would likely go unpaid, leading is the safer way to get value.
- Many of the big blind's small leads are medium hands making a block bet: second pairs lead 99% of the time and third pairs 82%, while its straights check 94%.
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 Not in this range here | AKs Not in this range here | AQs Not in this range here | AJs B 100 % | ATs X 100 % | A9s B 100 % | A8s X 100 % | A7s X 98 % | A6s X 67 % | A5s X 67 % | A4s X 98 % | A3s B 66 % | A2s B 99 % |
| K | AKo Not in this range here | KK Not in this range here | KQs Not in this range here | KJs B 98 % | KTs X 95 % | K9s B 100 % | K8s B 100 % | K7s X 100 % | K6s B 100 % | K5s B 100 % | K4s X 100 % | K3s B 100 % | K2s Not in this range here |
| Q | AQo X 100 % | KQo X 57 % | QQ Not in this range here | QJs B 100 % | QTs B 100 % | Q9s B 99 % | Q8s B 100 % | Q7s X 67 % | Q6s B 100 % | Q5s B 100 % | Q4s B 53 % | Q3s B 100 % | Q2s B 100 % |
| J | AJo B 100 % | KJo B 98 % | QJo B 100 % | JJ Not in this range here | JTs B 96 % | J9s X 99 % | J8s B 100 % | J7s X 99 % | J6s Not in this range here | J5s Not in this range here | J4s X 91 % | J3s Not in this range here | J2s Not in this range here |
| T | ATo X 100 % | KTo X 90 % | QTo B 100 % | JTo B 99 % | TT Not in this range here | T9s X 72 % | T8s X 100 % | T7s X 100 % | T6s B 100 % | 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 B 100 % | K9o B 100 % | Q9o B 85 % | J9o Not in this range here | T9o X 68 % | 99 B 99 % | 98s B 58 % | 97s X 100 % | 96s B 87 % | 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 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 X 82 % | 87s X 100 % | 86s B 100 % | 85s B 100 % | 84s Not in this range here | 83s Not in this range here | 82s Not in this range here |
| 7 | A7o X 98 % | 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 B 97 % | 76s X 96 % | 75s X 94 % | 74s X 100 % | 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 X 100 % | 65s B 100 % | 64s X 100 % | 63s B 100 % | 62s Not in this range here |
| 5 | A5o X 64 % | 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 X 100 % | 54s X 100 % | 53s B 100 % | 52s Not in this range here |
| 4 | A4o X 97 % | 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 B 99 % | 43s X 100 % | 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 X 100 % | 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 X 98 % |
- Check: 57.60% of the range (101.78 combos)
- Bet ¼ pot (2.3 bb): 42.40% of the range (74.91 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 ¼ pot (2.3 bb) |
|---|---|---|---|
| AJs | 2.98 | 0.0% | 100.0% |
| ATs | 3.989 | 100.0% | 0.0% |
| A9s | 2.996 | 0.1% | 99.9% |
| A8s | 3.409 | 100.0% | 0.0% |
| A7s | 2.115 | 98.0% | 2.0% |
| A6s | 2.249 | 67.0% | 33.0% |
| A5s | 1.91 | 66.7% | 33.3% |
| A4s | 2.998 | 97.5% | 2.5% |
| A3s | 2.453 | 34.3% | 65.7% |
| A2s | 1.592 | 0.9% | 99.1% |
| KJs | 2.404 | 2.2% | 97.8% |
| KTs | 3.31 | 94.8% | 5.2% |
| K9s | 2.564 | 0.2% | 99.8% |
| K8s | 2.272 | 0.0% | 100.0% |
| K7s | 2.998 | 99.9% | 0.1% |
| K6s | 0.89 | 0.0% | 100.0% |
| K5s | 0.533 | 0.0% | 100.0% |
| K4s | 2.533 | 99.9% | 0.1% |
| K3s | 0.005 | 0.0% | 100.0% |
| AQo | 1.988 | 99.5% | 0.5% |
| KQo | 8.153 | 56.6% | 43.4% |
| QJs | 1.527 | 0.1% | 99.9% |
| QTs | 2.744 | 0.5% | 99.5% |
| Q9s | 1.679 | 1.1% | 98.9% |
| Q8s | 2.221 | 0.1% | 99.9% |
| Q7s | 0.019 | 66.8% | 33.2% |
| Q6s | 2.236 | 0.1% | 99.9% |
| Q5s | 0.485 | 0.1% | 99.9% |
| Q4s | 1.307 | 46.6% | 53.4% |
| Q3s | 1.44 | 0.1% | 99.9% |
| Q2s | 0.11 | 0.1% | 99.9% |
| AJo | 8.988 | 0.0% | 100.0% |
| KJo | 2.743 | 2.2% | 97.8% |
| QJo | 3.703 | 0.1% | 99.9% |
| JTs | 1.555 | 4.2% | 95.8% |
| J9s | 0.034 | 99.3% | 0.7% |
| J8s | 0.001 | 0.0% | 100.0% |
| J7s | 2.481 | 99.4% | 0.6% |
| J4s | 0.217 | 91.0% | 9.0% |
| ATo | 10.775 | 99.9% | 0.1% |
| KTo | 1.509 | 90.1% | 9.9% |
| QTo | 4.14 | 0.5% | 99.5% |
| JTo | 0.005 | 1.5% | 98.5% |
| T9s | 1.988 | 71.7% | 28.3% |
| T8s | 0.12 | 99.6% | 0.4% |
| T7s | 2.998 | 99.9% | 0.1% |
| T6s | 0.001 | 0.0% | 100.0% |
| A9o | 2.345 | 0.1% | 99.9% |
| K9o | 0.038 | 0.2% | 99.8% |
| Q9o | 2.127 | 15.5% | 84.5% |
| T9o | 0.001 | 67.5% | 32.5% |
| 99 | 2.701 | 0.6% | 99.4% |
| 98s | 1.515 | 42.1% | 57.9% |
| 97s | 1.992 | 99.8% | 0.2% |
| 96s | 0.666 | 12.9% | 87.1% |
| A8o | 1.351 | 100.0% | 0.0% |
| 88 | 5.961 | 81.5% | 18.5% |
| 87s | 2.98 | 99.9% | 0.1% |
| 86s | 1.133 | 0.0% | 100.0% |
| 85s | 2.023 | 0.0% | 100.0% |
| A7o | 4.534 | 97.6% | 2.4% |
| 77 | 1.122 | 3.2% | 96.8% |
| 76s | 2.728 | 95.6% | 4.4% |
| 75s | 2.513 | 94.1% | 5.9% |
| 74s | 0.507 | 99.8% | 0.2% |
| 66 | 5.23 | 100.0% | 0.0% |
| 65s | 0.829 | 0.0% | 100.0% |
| 64s | 2.059 | 99.8% | 0.2% |
| 63s | 0.007 | 0.0% | 100.0% |
| A5o | 1.546 | 63.5% | 36.5% |
| 55 | 3.505 | 99.9% | 0.1% |
| 54s | 2.394 | 100.0% | 0.0% |
| 53s | 1.473 | 0.0% | 100.0% |
| A4o | 0.129 | 97.3% | 2.7% |
| 44 | 0.007 | 1.5% | 98.5% |
| 43s | 2.136 | 99.7% | 0.3% |
| 33 | 5.964 | 100.0% | 0.0% |
| 22 | 5.807 | 97.9% | 2.1% |
What each action is worth with K♣T♣
| Action | How often | Expected value |
|---|---|---|
| Check | 98.58% | 14.044 bb |
| Bet ¼ pot (2.3 bb) | 1.42% | 13.915 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♦ 7♣ 4♠: big blind checks, button bets 1.8 bb, big blind calls · Turn 9♥: big blind checks, button checks · River J♣ · Pot 9.1 bb · Big blind to act, 95.7 bb behind
- Pot at this decision, including the bets in front: 9.1 bb
- The big blind: 95.7 bb behind
- The button: 95.7 bb behind
| 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 99 % | ATs 100 % | A9s 100 % | A8s 85 % | A7s 71 % | A6s 56 % | A5s 48 % | A4s 100 % | A3s 61 % | A2s 40 % |
| K | AKo Not in this range here | KK Not in this range here | KQs Not in this range here | KJs 80 % | KTs 83 % | K9s 86 % | K8s 57 % | K7s 100 % | K6s 22 % | K5s 13 % | K4s 84 % | K3s <1 % | K2s Not in this range here |
| Q | AQo 22 % | KQo 91 % | QQ Not in this range here | QJs 76 % | QTs 92 % | Q9s 84 % | Q8s 74 % | Q7s 1 % | Q6s 75 % | Q5s 16 % | Q4s 65 % | Q3s 48 % | Q2s 4 % |
| J | AJo 100 % | KJo 31 % | QJo 53 % | JJ Not in this range here | JTs 52 % | J9s 2 % | J8s <1 % | J7s 83 % | J6s Not in this range here | J5s Not in this range here | J4s 11 % | J3s Not in this range here | J2s Not in this range here |
| T | ATo 90 % | KTo 13 % | QTo 46 % | JTo <1 % | TT Not in this range here | T9s 66 % | T8s 3 % | T7s 100 % | T6s <1 % | 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 26 % | K9o <1 % | Q9o 30 % | J9o Not in this range here | T9o <1 % | 99 90 % | 98s 51 % | 97s 100 % | 96s 22 % | 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 11 % | 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 99 % | 87s 99 % | 86s 28 % | 85s 51 % | 84s Not in this range here | 83s Not in this range here | 82s Not in this range here |
| 7 | A7o 50 % | 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 37 % | 76s 91 % | 75s 84 % | 74s 25 % | 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 87 % | 65s 21 % | 64s 69 % | 63s <1 % | 62s Not in this range here |
| 5 | A5o 13 % | 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 58 % | 54s 80 % | 53s 37 % | 52s Not in this range here |
| 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 <1 % | 43s 71 % | 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 99 % | 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 97 % |
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 4 % | AKs 66 % | AQs 16 % | AJs 30 % | ATs 9 % | A9s 3 % | A8s 32 % | A7s 98 % | A6s 39 % | A5s 33 % | A4s 97 % | A3s 14 % | A2s 19 % |
| K | AKo 74 % | KK Not in this range here | KQs 44 % | KJs 1 % | KTs 2 % | K9s 50 % | K8s 15 % | K7s 92 % | K6s 3 % | K5s 20 % | K4s 83 % | K3s 46 % | K2s 16 % |
| Q | AQo 11 % | KQo 27 % | QQ 26 % | QJs 83 % | QTs 90 % | Q9s Not in this range here | Q8s 72 % | Q7s 11 % | Q6s 85 % | Q5s 66 % | Q4s 53 % | Q3s 47 % | Q2s Not in this range here |
| J | AJo 53 % | KJo 2 % | QJo 62 % | JJ 32 % | JTs 14 % | J9s 89 % | J8s 28 % | J7s 67 % | J6s 34 % | J5s 48 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo 30 % | KTo 11 % | QTo 56 % | JTo 17 % | TT 41 % | T9s 52 % | T8s 27 % | T7s 64 % | T6s 18 % | 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 3 % | K9o 73 % | Q9o Not in this range here | J9o 32 % | T9o 65 % | 99 Not in this range here | 98s 46 % | 97s 33 % | 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 38 % | K8o 27 % | Q8o Not in this range here | J8o Not in this range here | T8o 2 % | 98o Not in this range here | 88 54 % | 87s 49 % | 86s 27 % | 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 68 % | K7o 6 % | 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 66 % | 75s 1 % | 74s Not in this range here | 73s Not in this range here | 72s Not in this range here |
| 6 | A6o 61 % | 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 40 % | 65s 41 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o 51 % | 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 40 % | 54s 28 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o 57 % | 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 64 % | 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 41 % | 32s Not in this range here |
| 2 | A2o 3 % | 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 11 % |
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 lead is a quarter of the pot and its only raise is all-in. In the solver's multi-size solution, with bigger leads available, leading K♣T♣ is worth about as much as checking it. 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-X, river (to act) - Solver notation
-
Qd7c4s9hJc·KcTc. 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.