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.