Solver answer
T♥9♥ missed its draws: bluff the river or give up?
6-max cash, 100 big blinds · Button opens, big blind calls · River 8♥ 7♥ 2♣ K♠ Q♣ · Big blind checks · Button to act
Updated
The solver's answer
Bet 90% Check 10%
¾ pot · 16 bb
T♥9♥ bluffs most of the time: betting is worth a little more than checking.
The solver plays T♥9♥ along this line to this decision 98.53% of the time; otherwise it acts differently earlier in the hand.
8♥7♥2♣K♠Q♣
T♥9♥ You
- Pot
- 21.3 bb
- Behind
- 89.6 bb
- Big blind
- Checks
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 8♥ 7♥ 2♣ and 6.1 bb turn bet on the K♠, then checks the Q♣ river, the button bets T♥9♥ for 16 bb into 21.3 bb 90% of the time and checks 10%, according to a solver answer published free by Poker Skill.
Why T♥9♥ bluffs
- T♥9♥ missed both its flush draw and its open-ended straight draw. Against the big blind's checking range it has 4.5% equity, so checking almost never wins.
- Betting is worth 0.98 bb and checking 0.90 bb. The bet wins when the big blind folds, and the big blind folds 50% of its range to it.
- The button bluffs first with hands that can't win at showdown: hands with no pair bet 64% of the time, while ace-high, which sometimes wins when checked, bets 32%.
- Its top pairs and better bet almost every time, so the bet holds both value and bluffs.
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 B 100 % | AKs B 100 % | AQs X 100 % | AJs X 100 % | ATs X 100 % | A9s X 100 % | A8s X 100 % | A7s X 100 % | A6s B 57 % | A5s B 57 % | A4s X 93 % | A3s X 80 % | A2s X 100 % |
| K | AKo B 100 % | KK B 100 % | KQs B 100 % | KJs B 100 % | KTs B 100 % | K9s B 100 % | K8s B 100 % | K7s B 100 % | K6s B 100 % | K5s B 100 % | K4s B 100 % | K3s B 99 % | K2s B 100 % |
| Q | AQo X 100 % | KQo B 100 % | QQ B 100 % | QJs X 97 % | QTs X 95 % | Q9s X 97 % | Q8s B 100 % | Q7s B 100 % | Q6s X 94 % | Q5s X 96 % | Q4s X 99 % | Q3s X 100 % | Q2s Not in this range here |
| J | AJo X 100 % | KJo B 100 % | QJo X 77 % | JJ X 100 % | JTs B 72 % | J9s B 69 % | J8s X 100 % | J7s X 100 % | J6s B 99 % | J5s B 99 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo X 100 % | KTo B 100 % | QTo X 82 % | JTo B 63 % | TT X 100 % | T9s B 62 % | 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 X 98 % | K9o B 100 % | Q9o X 78 % | J9o B 54 % | T9o X 56 % | 99 X 100 % | 98s X 100 % | 97s X 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 100 % | Q8o Not in this range here | J8o Not in this range here | T8o X 100 % | 98o Not in this range here | 88 B 100 % | 87s B 100 % | 86s X 100 % | 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 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 X 57 % | 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 Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o B 58 % | 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 B 100 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o B 65 % | 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 X 100 % | 43s Not in this range here | 42s Not in this range here |
| 3 | A3o X 95 % | 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 B 100 % |
- Check: 46.56% of the range (68.02 combos)
- Bet ¾ pot (16 bb): 53.44% of the range (78.08 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 (16 bb) |
|---|---|---|---|
| AA | 2.272 | 0.1% | 99.9% |
| AKs | 1.735 | 0.0% | 100.0% |
| AQs | 0.001 | 99.9% | 0.1% |
| AJs | 0.009 | 99.7% | 0.3% |
| ATs | 0.898 | 99.6% | 0.4% |
| A9s | 1.122 | 99.7% | 0.3% |
| A8s | 1.907 | 100.0% | 0.0% |
| A7s | 0.09 | 100.0% | 0.0% |
| A6s | 0.864 | 42.8% | 57.2% |
| A5s | 0.985 | 43.3% | 56.7% |
| A4s | 0.333 | 92.5% | 7.5% |
| A3s | 0.624 | 79.6% | 20.4% |
| A2s | 0.002 | 99.9% | 0.1% |
| AKo | 4.035 | 0.0% | 100.0% |
| KK | 1.786 | 0.0% | 100.0% |
| KQs | 0.437 | 0.0% | 100.0% |
| KJs | 1.004 | 0.1% | 99.9% |
| KTs | 1.056 | 0.1% | 99.9% |
| K9s | 1.334 | 0.2% | 99.8% |
| K8s | 1.487 | 0.0% | 100.0% |
| K7s | 1.224 | 0.0% | 100.0% |
| K6s | 1.418 | 0.5% | 99.5% |
| K5s | 0.93 | 0.5% | 99.5% |
| K4s | 0.972 | 0.4% | 99.6% |
| K3s | 0.707 | 0.6% | 99.4% |
| K2s | 1.149 | 0.0% | 100.0% |
| AQo | 0.003 | 99.5% | 0.5% |
| KQo | 1.507 | 0.0% | 100.0% |
| 0.217 | 0.0% | 100.0% | |
| QJs | 0.711 | 97.1% | 2.9% |
| QTs | 1.353 | 95.2% | 4.8% |
| Q9s | 1.632 | 97.0% | 3.0% |
| Q8s | 0.823 | 0.0% | 100.0% |
| Q7s | 0.001 | 0.0% | 100.0% |
| Q6s | 1.302 | 94.4% | 5.6% |
| Q5s | 1.243 | 96.3% | 3.7% |
| Q4s | 0.678 | 99.4% | 0.6% |
| Q3s | 0.627 | 99.6% | 0.4% |
| AJo | 0.005 | 99.8% | 0.2% |
| KJo | 2.84 | 0.0% | 100.0% |
| QJo | 3.85 | 77.2% | 22.8% |
| JJ | 3.008 | 100.0% | 0.0% |
| JTs | 2.538 | 28.5% | 71.5% |
| J9s | 1.918 | 31.3% | 68.7% |
| J8s | 0.399 | 100.0% | 0.0% |
| J7s | 0.001 | 100.0% | 0.0% |
| J6s | 0.189 | 0.6% | 99.4% |
| J5s | 0.344 | 0.7% | 99.3% |
| ATo | 0.007 | 99.5% | 0.5% |
| KTo | 4.42 | 0.1% | 99.9% |
| QTo | 5.774 | 81.6% | 18.4% |
| JTo | 4.893 | 36.6% | 63.4% |
| TT | 4.64 | 100.0% | 0.0% |
| T9s | 2.847 | 38.3% | 61.7% |
| T8s | 0.443 | 100.0% | 0.0% |
| T7s | 0.001 | 100.0% | 0.0% |
| T6s | 1.596 | 0.2% | 99.8% |
| A9o | 3.318 | 98.0% | 2.0% |
| K9o | 6.071 | 0.2% | 99.8% |
| Q9o | 6.179 | 77.6% | 22.4% |
| J9o | 5.146 | 46.3% | 53.7% |
| T9o | 5.607 | 55.5% | 44.5% |
| 99 | 4.776 | 100.0% | 0.0% |
| 98s | 0.439 | 100.0% | 0.0% |
| 97s | 0.001 | 100.0% | 0.0% |
| A8o | 5.654 | 100.0% | 0.0% |
| K8o | 3.614 | 0.0% | 100.0% |
| T8o | 0.201 | 100.0% | 0.0% |
| 88 | 2.94 | 0.0% | 100.0% |
| 87s | 1.711 | 0.0% | 100.0% |
| 86s | 0.358 | 100.0% | 0.0% |
| A7o | 1.599 | 100.0% | 0.0% |
| K7o | 0.995 | 0.0% | 100.0% |
| 77 | 2.858 | 0.0% | 100.0% |
| 76s | 0.001 | 100.0% | 0.0% |
| A6o | 3.717 | 56.6% | 43.4% |
| 66 | 0.001 | 99.9% | 0.1% |
| 65s | 1.74 | 0.1% | 99.9% |
| A5o | 3.088 | 42.0% | 58.0% |
| 55 | 0.001 | 99.9% | 0.1% |
| 54s | 0.001 | 0.1% | 99.9% |
| A4o | 3.326 | 35.5% | 64.5% |
| 44 | 0.001 | 99.9% | 0.1% |
| A3o | 3.678 | 95.4% | 4.6% |
| 33 | 0.001 | 99.9% | 0.1% |
| 22 | 0.882 | 0.0% | 100.0% |
What each action is worth with T♥9♥
| Action | How often | Expected value |
|---|---|---|
| Check | 9.75% | 0.902 bb |
| Bet ¾ pot (16 bb) | 90.25% | 0.981 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 8♥ 7♥ 2♣: big blind checks, button bets 1.8 bb, big blind calls · Turn K♠: big blind checks, button bets 6.1 bb, big blind calls · River Q♣: big blind checks · Pot 21.3 bb · Button to act, 89.6 bb behind
- Pot at this decision, including the bets in front: 21.3 bb
- The button: 89.6 bb behind
- The big blind: 89.6 bb behind
| A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | AA 38 % | AKs 58 % | AQs <1 % | AJs <1 % | ATs 22 % | A9s 28 % | A8s 64 % | A7s 3 % | A6s 22 % | A5s 25 % | A4s 8 % | A3s 16 % | A2s <1 % |
| K | AKo 45 % | KK 60 % | KQs 22 % | KJs 34 % | KTs 35 % | K9s 45 % | K8s 74 % | K7s 61 % | K6s 47 % | K5s 31 % | K4s 32 % | K3s 24 % | K2s 57 % |
| Q | AQo <1 % | KQo 22 % | QQ 7 % | QJs 24 % | QTs 45 % | Q9s 54 % | Q8s 41 % | Q7s <1 % | Q6s 43 % | Q5s 41 % | Q4s 23 % | Q3s 21 % | Q2s Not in this range here |
| J | AJo <1 % | KJo 32 % | QJo 43 % | JJ 50 % | JTs 64 % | J9s 48 % | J8s 13 % | J7s <1 % | J6s 5 % | J5s 9 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo <1 % | KTo 49 % | QTo 64 % | JTo 41 % | TT 77 % | T9s 71 % | T8s 15 % | T7s <1 % | T6s 40 % | 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 68 % | Q9o 69 % | J9o 43 % | T9o 47 % | 99 80 % | 98s 15 % | 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 63 % | K8o 52 % | Q8o Not in this range here | J8o Not in this range here | T8o 2 % | 98o Not in this range here | 88 98 % | 87s 57 % | 86s 12 % | 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 18 % | K7o 14 % | 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 95 % | 76s <1 % | 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 31 % | 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 44 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o 26 % | 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 <1 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o 28 % | 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 Not in this range here | 42s Not in this range here |
| 3 | A3o 31 % | 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 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 29 % |
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 33 % | ATs 31 % | A9s 21 % | A8s 52 % | A7s 69 % | A6s 13 % | A5s 10 % | A4s 10 % | A3s 6 % | A2s 92 % |
| K | AKo Not in this range here | KK Not in this range here | KQs Not in this range here | KJs 50 % | KTs 44 % | K9s 33 % | K8s 71 % | K7s 99 % | K6s 18 % | K5s 3 % | K4s 15 % | K3s 9 % | K2s <1 % |
| Q | AQo 10 % | KQo 94 % | QQ Not in this range here | QJs 32 % | QTs 22 % | Q9s 7 % | Q8s 74 % | Q7s 76 % | Q6s <1 % | Q5s Not in this range here | Q4s <1 % | Q3s Not in this range here | Q2s 4 % |
| J | AJo 8 % | KJo 10 % | QJo Not in this range here | JJ Not in this range here | JTs <1 % | J9s 8 % | J8s 100 % | J7s 83 % | J6s Not in this range here | J5s Not in this range here | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo 10 % | KTo 5 % | QTo Not in this range here | JTo Not in this range here | TT Not in this range here | T9s 51 % | T8s 100 % | 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 Not in this range here | K9o 14 % | Q9o Not in this range here | J9o Not in this range here | T9o 16 % | 99 72 % | 98s 100 % | 97s 100 % | 96s 29 % | 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 51 % | 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 7 % | 87s 15 % | 86s 96 % | 85s 92 % | 84s Not in this range here | 83s Not in this range here | 82s Not in this range here |
| 7 | A7o 42 % | 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 84 % | 75s 88 % | 74s 60 % | 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 20 % | 65s 30 % | 64s 3 % | 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 17 % | 54s 7 % | 53s Not in this range here | 52s 10 % |
| 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 15 % | 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 49 % | 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 flop and turn bets are 1.8 bb and 6.1 bb, and its river bet is three-quarters of the pot. 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-R6.1-C, river X - Solver notation
-
8h7h2cKsQc·Th9h. 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.