Solver answer
The 5♥ is a third heart: should the button bet again?
6-max cash, 100 big blinds · Button opens, big blind calls · Turn K♥ 8♥ 3♣ 5♥ · Big blind checks · Button to act
Updated
The solver's answer
The button's whole range
Check 67% Bet 33%
The button checks most of its range; its made flushes, sets and aces keep betting.
K♥8♥3♣5♥
- Pot
- 9.1 bb
- Behind
- 95.7 bb
- Big blind
- Checks
In a 6-max cash game at 100 big blinds, after the button c-bets 1.8 bb on a K♥ 8♥ 3♣ flop and the big blind calls, then checks the 5♥ turn, the button bets 6.1 bb into 9.1 bb with 33% of its range and checks 67%, according to a solver answer published free by Poker Skill.
Who keeps betting when the flush card comes
- The 5♥ puts a third heart on the board, so any hand with two hearts now has a flush. The button checks 67% of its range.
- Its strongest hands bet: made flushes 73% of the time, sets 69% and aces 86%. Aces holding the A♥ also have a draw to the best flush.
- Top pair mostly checks: it bets 32% of the time. Second pair almost never bets.
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 86 % | AKs X 68 % | AQs X 84 % | AJs X 67 % | ATs B 64 % | A9s B 70 % | A8s X 100 % | A7s B 57 % | A6s X 70 % | A5s X 100 % | A4s X 65 % | A3s X 75 % | A2s X 66 % |
| K | AKo X 72 % | KK X 71 % | KQs B 93 % | KJs B 61 % | KTs X 95 % | K9s X 100 % | K8s X 63 % | K7s X 100 % | K6s X 100 % | K5s X 53 % | K4s X 100 % | K3s X 100 % | K2s X 100 % |
| Q | AQo X 70 % | KQo B 81 % | QQ X 100 % | QJs X 66 % | QTs X 52 % | Q9s X 69 % | Q8s X 100 % | Q7s B 51 % | Q6s B 63 % | Q5s X 83 % | Q4s B 71 % | Q3s X 73 % | Q2s Not in this range here |
| J | AJo X 88 % | KJo X 58 % | QJo X 67 % | JJ X 100 % | JTs X 85 % | J9s X 82 % | J8s X 100 % | J7s X 68 % | J6s X 57 % | J5s X 97 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo X 73 % | KTo X 96 % | QTo X 50 % | JTo X 84 % | TT X 100 % | T9s X 71 % | T8s X 100 % | T7s X 52 % | T6s B 55 % | 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 64 % | K9o X 100 % | Q9o B 51 % | J9o X 78 % | T9o X 62 % | 99 X 100 % | 98s X 100 % | 97s B 51 % | 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 X 61 % | Q8o Not in this range here | J8o Not in this range here | T8o X 100 % | 98o Not in this range here | 88 B 90 % | 87s X 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 B 81 % | K7o X 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 X 100 % | 76s B 63 % | 75s X 63 % | 74s Not in this range here | 73s Not in this range here | 72s Not in this range here |
| 6 | A6o B 66 % | 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 X 61 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o X 79 % | 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 B 58 % | 54s X 64 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o B 54 % | 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 90 % | 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 B 92 % | 32s Not in this range here |
| 2 | A2o X 64 % | 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 85 % |
- Check: 66.76% of the range (170.64 combos)
- Bet ⅔ pot (6.1 bb): 33.24% of the range (84.95 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 ⅔ pot (6.1 bb) |
|---|---|---|---|
| AA | 4.47 | 14.2% | 85.8% |
| AKs | 2.246 | 67.8% | 32.2% |
| AQs | 1.907 | 84.2% | 15.8% |
| AJs | 1.532 | 66.5% | 33.5% |
| ATs | 0.891 | 36.0% | 64.0% |
| A9s | 0.816 | 30.1% | 69.9% |
| A8s | 2.668 | 99.9% | 0.1% |
| A7s | 1.175 | 43.2% | 56.8% |
| A6s | 1.651 | 69.6% | 30.4% |
| A5s | 1.847 | 99.8% | 0.2% |
| A4s | 2.285 | 64.5% | 35.5% |
| A3s | 2.184 | 74.8% | 25.2% |
| A2s | 3.156 | 65.7% | 34.3% |
| AKo | 5.736 | 72.0% | 28.0% |
| KK | 2.92 | 70.9% | 29.1% |
| KQs | 2.572 | 7.3% | 92.7% |
| KJs | 2.054 | 39.0% | 61.0% |
| KTs | 2.121 | 94.9% | 5.1% |
| K9s | 1.946 | 99.9% | 0.1% |
| K8s | 1.653 | 62.5% | 37.5% |
| K7s | 1.598 | 99.9% | 0.1% |
| K6s | 1.165 | 99.9% | 0.1% |
| K5s | 1.248 | 53.2% | 46.8% |
| K4s | 0.416 | 99.9% | 0.1% |
| K3s | 1.368 | 99.6% | 0.4% |
| K2s | 0.93 | 99.9% | 0.1% |
| AQo | 6.525 | 70.0% | 30.0% |
| KQo | 6.747 | 19.2% | 80.8% |
| 1.947 | 99.9% | 0.1% | |
| QJs | 1.744 | 65.9% | 34.1% |
| QTs | 2.092 | 51.5% | 48.5% |
| Q9s | 2.453 | 68.6% | 31.4% |
| Q8s | 1.855 | 100.0% | 0.0% |
| Q7s | 1.781 | 49.0% | 51.0% |
| Q6s | 2.07 | 37.0% | 63.0% |
| Q5s | 1.161 | 83.0% | 17.0% |
| Q4s | 1.869 | 29.2% | 70.8% |
| Q3s | 1.68 | 72.6% | 27.4% |
| AJo | 5.153 | 87.9% | 12.1% |
| KJo | 5.84 | 58.0% | 42.0% |
| QJo | 7.51 | 66.5% | 33.5% |
| JJ | 2.158 | 99.9% | 0.1% |
| JTs | 2.599 | 85.0% | 15.0% |
| J9s | 2.723 | 81.5% | 18.5% |
| J8s | 1.553 | 100.0% | 0.0% |
| J7s | 2.247 | 68.4% | 31.6% |
| J6s | 1.859 | 57.4% | 42.6% |
| J5s | 0.76 | 97.0% | 3.0% |
| ATo | 3.397 | 72.7% | 27.3% |
| KTo | 5.617 | 96.2% | 3.8% |
| QTo | 8.294 | 50.3% | 49.7% |
| JTo | 8.546 | 84.3% | 15.7% |
| TT | 2.571 | 99.9% | 0.1% |
| T9s | 3.003 | 70.5% | 29.5% |
| T8s | 1.555 | 100.0% | 0.0% |
| T7s | 2.306 | 51.8% | 48.2% |
| T6s | 2.066 | 44.9% | 55.1% |
| A9o | 1.876 | 35.9% | 64.1% |
| K9o | 4.972 | 99.9% | 0.1% |
| Q9o | 7.429 | 48.8% | 51.2% |
| J9o | 7.259 | 77.7% | 22.3% |
| T9o | 7.665 | 62.4% | 37.6% |
| 99 | 2.739 | 99.9% | 0.1% |
| 98s | 0.775 | 100.0% | 0.0% |
| 97s | 2.338 | 48.6% | 51.4% |
| A8o | 6.146 | 99.9% | 0.1% |
| K8o | 3.404 | 60.5% | 39.5% |
| T8o | 0.355 | 99.9% | 0.1% |
| 88 | 2.994 | 10.5% | 89.5% |
| 87s | 1.632 | 100.0% | 0.0% |
| 86s | 1.203 | 100.0% | 0.0% |
| A7o | 5.044 | 19.0% | 81.0% |
| K7o | 0.848 | 99.9% | 0.1% |
| 77 | 1.739 | 99.7% | 0.3% |
| 76s | 2.183 | 36.9% | 63.1% |
| 75s | 0.012 | 63.1% | 36.9% |
| A6o | 6.155 | 34.2% | 65.8% |
| 66 | 2.273 | 99.8% | 0.2% |
| 65s | 1.839 | 61.3% | 38.7% |
| A5o | 7.059 | 78.8% | 21.2% |
| 55 | 1.059 | 41.8% | 58.2% |
| 54s | 0.761 | 64.0% | 36.0% |
| A4o | 8.528 | 46.2% | 53.8% |
| 44 | 2.699 | 99.9% | 0.1% |
| A3o | 5.91 | 90.0% | 10.0% |
| 33 | 2.996 | 7.9% | 92.1% |
| A2o | 0.659 | 63.6% | 36.4% |
| 22 | 0.807 | 85.4% | 14.6% |
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♥ 8♥ 3♣: big blind checks, button bets 1.8 bb, big blind calls · Turn 5♥: big blind checks · Pot 9.1 bb · Button to act, 95.7 bb behind
- Pot at this decision, including the bets in front: 9.1 bb
- The button: 95.7 bb behind
- The big blind: 95.7 bb behind
| A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | AA 75 % | AKs 75 % | AQs 48 % | AJs 38 % | ATs 22 % | A9s 20 % | A8s 89 % | A7s 29 % | A6s 41 % | A5s 62 % | A4s 57 % | A3s 73 % | A2s 79 % |
| K | AKo 64 % | KK 97 % | KQs 86 % | KJs 69 % | KTs 71 % | K9s 65 % | K8s 55 % | K7s 53 % | K6s 39 % | K5s 42 % | K4s 14 % | K3s 68 % | K2s 31 % |
| Q | AQo 54 % | KQo 75 % | QQ 32 % | QJs 44 % | QTs 52 % | Q9s 61 % | Q8s 62 % | Q7s 45 % | Q6s 52 % | Q5s 39 % | Q4s 47 % | Q3s 56 % | Q2s Not in this range here |
| J | AJo 43 % | KJo 65 % | QJo 63 % | JJ 36 % | JTs 65 % | J9s 68 % | J8s 52 % | J7s 56 % | J6s 47 % | J5s 25 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo 28 % | KTo 62 % | QTo 69 % | JTo 71 % | TT 43 % | T9s 75 % | T8s 52 % | T7s 58 % | T6s 52 % | 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 16 % | K9o 55 % | Q9o 62 % | J9o 61 % | T9o 64 % | 99 46 % | 98s 26 % | 97s 58 % | 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 68 % | K8o 57 % | Q8o Not in this range here | J8o Not in this range here | T8o 4 % | 98o Not in this range here | 88 100 % | 87s 54 % | 86s 40 % | 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 42 % | K7o 9 % | 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 29 % | 76s 55 % | 75s <1 % | 74s Not in this range here | 73s Not in this range here | 72s Not in this range here |
| 6 | A6o 51 % | 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 38 % | 65s 61 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o 78 % | 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 35 % | 54s 25 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o 71 % | 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 45 % | 43s Not in this range here | 42s Not in this range here |
| 3 | A3o 66 % | 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 | 33 100 % | 32s Not in this range here |
| 2 | A2o 6 % | 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 13 % |
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 99 % | ATs 98 % | A9s 41 % | A8s 100 % | A7s 43 % | A6s 21 % | A5s 33 % | A4s 27 % | A3s 95 % | A2s 21 % |
| K | AKo Not in this range here | KK Not in this range here | KQs Not in this range here | KJs 86 % | KTs 100 % | K9s 97 % | K8s 41 % | K7s 100 % | K6s 99 % | K5s 87 % | K4s 84 % | K3s 56 % | K2s <1 % |
| Q | AQo 30 % | KQo 88 % | QQ Not in this range here | QJs 48 % | QTs 30 % | Q9s 23 % | Q8s 74 % | Q7s 8 % | Q6s 6 % | Q5s Not in this range here | Q4s 10 % | Q3s 48 % | Q2s <1 % |
| J | AJo 100 % | KJo 33 % | QJo 21 % | JJ Not in this range here | JTs 26 % | J9s 16 % | J8s 100 % | J7s 14 % | J6s 6 % | J5s Not in this range here | J4s 2 % | J3s Not in this range here | J2s Not in this range here |
| T | ATo 79 % | KTo 40 % | QTo 17 % | JTo 22 % | TT Not in this range here | T9s 12 % | T8s 100 % | T7s 21 % | T6s 10 % | 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 51 % | K9o 76 % | Q9o 3 % | J9o 2 % | T9o 13 % | 99 90 % | 98s 100 % | 97s 34 % | 96s 19 % | 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 75 % | 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 56 % | 87s 82 % | 86s 82 % | 85s 86 % | 84s Not in this range here | 83s Not in this range here | 82s Not in this range here |
| 7 | A7o 8 % | 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 97 % | 76s 26 % | 75s <1 % | 74s 8 % | 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 14 % | 64s 23 % | 63s 1 % | 62s Not in this range here |
| 5 | A5o 1 % | 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 6 % | 53s 63 % | 52s Not in this range here |
| 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 94 % | 43s 55 % | 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 2 % | 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 86 % |
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 turn bet is two-thirds of the pot; on the flop it c-bet 1.8 bb. 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 - Solver notation
-
Kh8h3c5h. 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.