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.
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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.