Solver answer
Does the button range bet a dry ace-high flop?
6-max cash, 100 big blinds · Button opens, big blind calls · Flop A♠ 8♦ 3♣ · Big blind checks · Button to act
Updated
The solver's answer
The button's whole range
Bet 56% Check 44%
⅓ pot · 1.8 bb
The button bets 258 of its 462 hand combinations, all for a third of the pot, the only size this solution offers.
A♠8♦3♣
- Pot
- 5.5 bb
- Behind
- 97.5 bb
- Big blind
- Checks
In a 6-max cash game at 100 big blinds, after the button opens to 2.5 bb and the big blind calls, then checks an A♠ 8♦ 3♣ flop, the button bets a third of the pot (1.8 bb) with 56% of its range and checks 44%, according to a solver answer published free by Poker Skill.
Why the button checks 44% of its range
- Its range is only a little ahead: 53% equity against the big blind's 47%. A range bet goes with a much bigger edge, so the button keeps some hands back.
- The hands it keeps back can win at showdown without a bet. King-queen offsuit checks 93% of the time and pocket kings 81%, and its king-high hands as a group check 71%. King-high wins a checked-down pot more often than queen-high.
- Its weakest hands bet instead: queen-jack offsuit 71% of the time and jack-ten offsuit 72%. A bet gives them a way to win the pot, and a pure bluff of 1.8 bb into 5.5 bb breaks even when the big blind folds 25% of the time.
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 95 % | AKs B 83 % | AQs B 89 % | AJs B 74 % | ATs B 78 % | A9s B 81 % | A8s B 69 % | A7s B 51 % | A6s B 54 % | A5s X 54 % | A4s B 67 % | A3s X 53 % | A2s X 82 % |
| K | AKo B 76 % | KK X 81 % | KQs X 99 % | KJs X 96 % | KTs X 95 % | K9s X 95 % | K8s B 74 % | K7s B 54 % | K6s B 52 % | K5s B 85 % | K4s B 59 % | K3s B 96 % | K2s B 76 % |
| Q | AQo B 68 % | KQo X 93 % | QQ X 81 % | QJs X 62 % | QTs X 55 % | Q9s B 61 % | Q8s B 81 % | Q7s B 52 % | Q6s X 56 % | Q5s B 72 % | Q4s B 71 % | Q3s B 97 % | Q2s B 81 % |
| J | AJo B 64 % | KJo X 81 % | QJo B 71 % | JJ X 61 % | JTs B 83 % | J9s B 70 % | J8s B 80 % | J7s B 67 % | J6s B 54 % | J5s B 80 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo B 60 % | KTo X 71 % | QTo B 71 % | JTo B 72 % | TT B 53 % | T9s B 83 % | T8s B 55 % | T7s B 62 % | T6s B 70 % | 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 56 % | K9o X 70 % | Q9o B 73 % | J9o B 74 % | T9o B 68 % | 99 B 57 % | 98s X 60 % | 97s B 54 % | 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 B 76 % | K8o B 66 % | Q8o Not in this range here | J8o Not in this range here | T8o X 84 % | 98o Not in this range here | 88 B 98 % | 87s B 77 % | 86s B 89 % | 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 51 % | K7o X 52 % | 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 59 % | 76s B 57 % | 75s X 66 % | 74s Not in this range here | 73s Not in this range here | 72s Not in this range here |
| 6 | A6o B 62 % | 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 70 % | 65s X 52 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o X 56 % | 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 64 % | 54s B 93 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o X 53 % | 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 55 % | 43s Not in this range here | 42s Not in this range here |
| 3 | A3o B 61 % | 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 90 % | 32s Not in this range here |
| 2 | A2o X 78 % | 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 77 % |
- Check: 44.12% of the range (203.88 combos)
- Bet ⅓ pot (1.8 bb): 55.88% of the range (258.27 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 ⅓ pot (1.8 bb) |
|---|---|---|---|
| AA | 2.999 | 5.5% | 94.5% |
| AKs | 3 | 17.4% | 82.6% |
| AQs | 3 | 10.8% | 89.2% |
| AJs | 3 | 25.8% | 74.2% |
| ATs | 3 | 21.7% | 78.3% |
| A9s | 3 | 18.9% | 81.1% |
| A8s | 2 | 31.4% | 68.6% |
| A7s | 3 | 49.0% | 51.0% |
| A6s | 3 | 46.0% | 54.0% |
| A5s | 3 | 53.7% | 46.3% |
| A4s | 3 | 33.0% | 67.0% |
| A3s | 2 | 52.7% | 47.3% |
| A2s | 3 | 82.4% | 17.6% |
| AKo | 9 | 24.3% | 75.7% |
| KK | 6 | 81.1% | 18.9% |
| KQs | 4 | 99.2% | 0.8% |
| KJs | 4 | 96.1% | 3.9% |
| KTs | 4 | 95.0% | 5.0% |
| K9s | 4 | 94.9% | 5.1% |
| K8s | 3 | 26.3% | 73.7% |
| K7s | 4 | 45.9% | 54.1% |
| K6s | 4 | 48.1% | 51.9% |
| K5s | 4 | 15.4% | 84.6% |
| K4s | 4 | 41.1% | 58.9% |
| K3s | 3 | 4.4% | 95.6% |
| K2s | 4 | 24.2% | 75.8% |
| AQo | 9 | 32.0% | 68.0% |
| KQo | 12 | 93.4% | 6.6% |
| 6 | 80.6% | 19.4% | |
| QJs | 4 | 62.0% | 38.0% |
| QTs | 4 | 55.1% | 44.9% |
| Q9s | 4 | 39.4% | 60.6% |
| Q8s | 3 | 18.8% | 81.2% |
| Q7s | 4 | 47.7% | 52.3% |
| Q6s | 4 | 55.9% | 44.1% |
| Q5s | 4 | 27.7% | 72.3% |
| Q4s | 4 | 28.9% | 71.1% |
| Q3s | 2.105 | 2.8% | 97.2% |
| Q2s | 0.001 | 18.7% | 81.3% |
| AJo | 9 | 36.0% | 64.0% |
| KJo | 12 | 81.1% | 18.9% |
| QJo | 12 | 28.9% | 71.1% |
| JJ | 6 | 60.6% | 39.4% |
| JTs | 4 | 17.1% | 82.9% |
| J9s | 4 | 30.3% | 69.7% |
| J8s | 3 | 20.1% | 79.9% |
| J7s | 4 | 33.0% | 67.0% |
| J6s | 3.985 | 45.8% | 54.2% |
| J5s | 4 | 20.2% | 79.8% |
| ATo | 9 | 40.2% | 59.8% |
| KTo | 12 | 70.7% | 29.3% |
| QTo | 12 | 29.4% | 70.6% |
| JTo | 12 | 27.8% | 72.2% |
| TT | 6 | 47.1% | 52.9% |
| T9s | 4 | 16.6% | 83.4% |
| T8s | 3 | 45.3% | 54.7% |
| T7s | 4 | 37.6% | 62.4% |
| T6s | 3.891 | 30.3% | 69.7% |
| A9o | 9 | 55.9% | 44.1% |
| K9o | 12 | 70.1% | 29.9% |
| Q9o | 12 | 26.7% | 73.3% |
| J9o | 11.999 | 26.1% | 73.9% |
| T9o | 12 | 32.2% | 67.8% |
| 99 | 6 | 42.5% | 57.5% |
| 98s | 3 | 60.0% | 40.0% |
| 97s | 4 | 45.6% | 54.4% |
| A8o | 7 | 23.7% | 76.3% |
| K8o | 8.608 | 34.1% | 65.9% |
| T8o | 0.707 | 83.6% | 16.4% |
| 88 | 3 | 2.5% | 97.5% |
| 87s | 3 | 22.6% | 77.4% |
| 86s | 2.848 | 11.3% | 88.7% |
| A7o | 9 | 51.1% | 48.9% |
| K7o | 2.663 | 52.4% | 47.6% |
| 77 | 6 | 58.5% | 41.5% |
| 76s | 4 | 43.2% | 56.8% |
| 75s | 0.033 | 66.4% | 33.6% |
| A6o | 9 | 38.4% | 61.6% |
| 66 | 6 | 69.5% | 30.5% |
| 65s | 3.997 | 52.4% | 47.6% |
| A5o | 9 | 55.7% | 44.3% |
| 55 | 6 | 35.6% | 64.4% |
| 54s | 1.956 | 7.5% | 92.5% |
| A4o | 9 | 52.7% | 47.3% |
| 44 | 6 | 44.6% | 55.4% |
| A3o | 7 | 39.0% | 61.0% |
| 33 | 3 | 9.7% | 90.3% |
| A2o | 0.588 | 77.6% | 22.4% |
| 22 | 1.763 | 23.2% | 76.8% |
Ranges, pot and stacks
- The hand so far: 6-max cash, 100 big blinds · Button opens to 2.5 bb, big blind calls · Flop A♠ 8♦ 3♣: big blind checks · Pot 5.5 bb · Button to act, 97.5 bb behind
- Pot at this decision, including the bets in front: 5.5 bb
- The button: 97.5 bb behind
- The big blind: 97.5 bb behind
| A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | AA 100 % | AKs 100 % | AQs 100 % | AJs 100 % | ATs 100 % | A9s 100 % | A8s 100 % | A7s 100 % | A6s 100 % | A5s 100 % | A4s 100 % | A3s 100 % | A2s 100 % |
| K | AKo 100 % | KK 100 % | KQs 100 % | KJs 100 % | KTs 100 % | K9s 100 % | K8s 100 % | K7s 100 % | K6s 100 % | K5s 100 % | K4s 100 % | K3s 100 % | K2s 100 % |
| Q | AQo 100 % | KQo 100 % | QQ 100 % | QJs 100 % | QTs 100 % | Q9s 100 % | Q8s 100 % | Q7s 100 % | Q6s 100 % | Q5s 100 % | Q4s 100 % | Q3s 70 % | Q2s <1 % |
| J | AJo 100 % | KJo 100 % | QJo 100 % | JJ 100 % | JTs 100 % | J9s 100 % | J8s 100 % | J7s 100 % | J6s 100 % | J5s 100 % | J4s Not in this range here | J3s Not in this range here | J2s Not in this range here |
| T | ATo 100 % | KTo 100 % | QTo 100 % | JTo 100 % | TT 100 % | T9s 100 % | T8s 100 % | T7s 100 % | T6s 97 % | 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 100 % | K9o 100 % | Q9o 100 % | J9o 100 % | T9o 100 % | 99 100 % | 98s 100 % | 97s 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 100 % | K8o 96 % | Q8o Not in this range here | J8o Not in this range here | T8o 8 % | 98o Not in this range here | 88 100 % | 87s 100 % | 86s 95 % | 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 100 % | K7o 22 % | 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 | 77 100 % | 76s 100 % | 75s 1 % | 74s Not in this range here | 73s Not in this range here | 72s Not in this range here |
| 6 | A6o 100 % | 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 | 66 100 % | 65s 100 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o 100 % | 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 | 55 100 % | 54s 49 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o 100 % | 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 | 44 100 % | 43s Not in this range here | 42s Not in this range here |
| 3 | A3o 100 % | 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 7 % | 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 97 % | ATs 99 % | A9s 98 % | A8s 64 % | A7s 100 % | A6s 100 % | A5s 99 % | A4s 100 % | A3s 98 % | A2s 100 % |
| K | AKo Not in this range here | KK Not in this range here | KQs <1 % | KJs 88 % | KTs 100 % | K9s 100 % | K8s 100 % | K7s 100 % | K6s 99 % | K5s 79 % | K4s 78 % | K3s 57 % | K2s <1 % |
| Q | AQo 30 % | KQo 100 % | QQ Not in this range here | QJs 97 % | QTs 96 % | Q9s 100 % | Q8s 74 % | Q7s 76 % | Q6s 75 % | Q5s 16 % | Q4s 75 % | Q3s 48 % | Q2s 1 % |
| J | AJo 98 % | KJo 33 % | QJo 53 % | JJ Not in this range here | JTs 81 % | J9s 87 % | J8s 100 % | J7s 83 % | J6s 39 % | J5s 43 % | J4s 11 % | J3s Not in this range here | J2s Not in this range here |
| T | ATo 92 % | KTo 40 % | QTo 46 % | JTo 65 % | TT Not in this range here | T9s 84 % | T8s 100 % | T7s 98 % | T6s 41 % | 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 99 % | K9o 77 % | Q9o 30 % | J9o 11 % | T9o 37 % | 99 90 % | 98s 100 % | 97s 84 % | 96s 99 % | 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 74 % | 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 75 % | 87s 86 % | 86s 96 % | 85s 93 % | 84s Not in this range here | 83s Not in this range here | 82s Not in this range here |
| 7 | A7o 54 % | 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 83 % | 75s 84 % | 74s 68 % | 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 78 % | 64s 83 % | 63s 1 % | 62s Not in this range here |
| 5 | A5o 27 % | 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 65 % | 53s 78 % | 52s 2 % |
| 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 94 % | 43s 77 % | 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 58 % | 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.
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, and here that size is a third 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 - Solver notation
-
As8d3c. 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.