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.