Solver answer
A♥ 9♥ 4♥: how often should the cutoff c-bet?
6-max cash, 100 big blinds · Cutoff opens, big blind calls · Flop A♥ 9♥ 4♥ · Big blind checks · Cutoff to act
Updated
The solver's answer
The cutoff's whole range
Check 66% Bet 34%
The cutoff checks most of its range and bets the rest for a third of the pot, the only size this solution offers.
A♥9♥4♥
- Pot
- 5.5 bb
- Behind
- 97.5 bb
- Big blind
- Checks
In a 6-max cash game at 100 big blinds, after the cutoff opens to 2.5 bb and the big blind calls, then checks an A♥ 9♥ 4♥ flop, the cutoff checks 66% of its range and bets a third of the pot (1.8 bb) with 34%, according to a solver answer published free by Poker Skill.
Why the cutoff checks 66% on an all-heart flop
- An all-heart flop is a dynamic one: a heart on the turn or river can change who holds the best hand. On flops like this, bluff c-bets should come less often.
- Top pair checks 71% of the time. The groups that bet most are the nut flush draws (60% of the time) and two pair (55%).
- Even made flushes bet only 51% of the time and sets 49%. The solution keeps strong hands among its checks, so a check doesn't tell the big blind the cutoff is weak.
- The nut flush draw, the K♥ with a card of another suit, bets as a semi-bluff: it can take the pot now or make a flush later.
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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 X 53 % | AKs B 54 % | AQs B 54 % | AJs X 64 % | ATs X 81 % | A9s X 56 % | A8s X 83 % | A7s X 88 % | A6s X 87 % | A5s X 86 % | A4s B 58 % | A3s X 99 % | A2s X 99 % |
| K | AKo B 66 % | KK X 77 % | KQs X 77 % | KJs X 63 % | KTs X 68 % | K9s X 81 % | K8s X 80 % | K7s X 77 % | K6s X 59 % | K5s X 54 % | K4s B 55 % | K3s B 70 % | K2s B 51 % |
| Q | AQo X 52 % | KQo X 69 % | QQ X 89 % | QJs B 69 % | QTs X 52 % | Q9s X 73 % | Q8s X 79 % | Q7s Not in this range here | Q6s X 79 % | Q5s Not in this range here | Q4s Not in this range here | Q3s Not in this range here | Q2s Not in this range here |
| J | AJo X 66 % | KJo X 60 % | QJo B 57 % | JJ X 78 % | JTs B 59 % | J9s X 81 % | J8s X 75 % | J7s X 85 % | 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 X 76 % | KTo X 52 % | QTo X 50 % | JTo X 58 % | TT X 82 % | T9s X 90 % | T8s X 89 % | T7s Not in this range here | T6s Not in this range here | 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 57 % | K9o X 78 % | Q9o Not in this range here | J9o Not in this range here | T9o Not in this range here | 99 X 60 % | 98s X 57 % | 97s Not in this range here | 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 79 % | 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 X 93 % | 87s X 76 % | 86s Not in this range here | 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 84 % | 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 X 82 % | 76s X 80 % | 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 88 % | 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 84 % | 65s B 52 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o X 85 % | 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 66 % | 54s B 92 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o B 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 B 66 % | 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 X 57 % | 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 X 57 % |
- Check: 65.70% of the range (206.69 combos)
- Bet ⅓ pot (1.8 bb): 34.30% of the range (107.91 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 | 52.8% | 47.2% |
| AKs | 3 | 45.8% | 54.2% |
| AQs | 3 | 46.2% | 53.8% |
| AJs | 3 | 63.7% | 36.3% |
| ATs | 3 | 80.9% | 19.1% |
| A9s | 3 | 55.5% | 44.5% |
| A8s | 3 | 82.9% | 17.1% |
| A7s | 3 | 88.3% | 11.7% |
| A6s | 3 | 87.0% | 13.0% |
| A5s | 3 | 85.9% | 14.1% |
| A4s | 3 | 41.8% | 58.2% |
| A3s | 3 | 99.1% | 0.9% |
| A2s | 3 | 99.4% | 0.6% |
| AKo | 9 | 34.5% | 65.5% |
| KK | 5.999 | 77.2% | 22.8% |
| KQs | 4 | 77.2% | 22.8% |
| KJs | 4 | 62.9% | 37.1% |
| KTs | 4 | 68.0% | 32.0% |
| K9s | 3 | 81.1% | 18.9% |
| K8s | 4 | 79.5% | 20.5% |
| K7s | 4 | 76.7% | 23.3% |
| K6s | 4 | 58.6% | 41.4% |
| K5s | 4 | 54.2% | 45.8% |
| K4s | 3 | 45.0% | 55.0% |
| K3s | 4 | 30.2% | 69.8% |
| K2s | 2.692 | 48.6% | 51.4% |
| AQo | 9 | 52.4% | 47.6% |
| KQo | 12 | 69.2% | 30.8% |
| 6 | 88.7% | 11.3% | |
| QJs | 4 | 31.2% | 68.8% |
| QTs | 4 | 52.4% | 47.6% |
| Q9s | 3 | 73.1% | 26.9% |
| Q8s | 3.99 | 79.4% | 20.6% |
| Q6s | 0.827 | 78.9% | 21.1% |
| AJo | 9 | 66.0% | 34.0% |
| KJo | 12 | 60.3% | 39.7% |
| QJo | 12 | 43.4% | 56.6% |
| JJ | 6 | 77.6% | 22.4% |
| JTs | 4 | 41.1% | 58.9% |
| J9s | 3 | 81.3% | 18.7% |
| J8s | 4 | 74.7% | 25.3% |
| J7s | 1.206 | 84.5% | 15.5% |
| ATo | 9 | 76.0% | 24.0% |
| KTo | 12 | 52.1% | 47.9% |
| QTo | 11.994 | 50.2% | 49.8% |
| JTo | 11.999 | 57.6% | 42.4% |
| TT | 6 | 82.2% | 17.8% |
| T9s | 3 | 89.5% | 10.5% |
| T8s | 0.676 | 88.6% | 11.4% |
| A9o | 6 | 42.7% | 57.3% |
| K9o | 4.811 | 78.2% | 21.8% |
| 99 | 3 | 60.1% | 39.9% |
| 98s | 1.879 | 56.9% | 43.1% |
| A8o | 8.998 | 78.9% | 21.1% |
| 88 | 6 | 93.0% | 7.0% |
| 87s | 0.001 | 75.7% | 24.3% |
| A7o | 7.55 | 84.2% | 15.8% |
| 77 | 6 | 82.0% | 18.0% |
| 76s | 0.376 | 79.7% | 20.3% |
| A6o | 1.043 | 87.9% | 12.1% |
| 66 | 6 | 84.2% | 15.8% |
| 65s | 0.952 | 48.2% | 51.8% |
| A5o | 9 | 84.9% | 15.1% |
| 55 | 6 | 66.0% | 34.0% |
| 54s | 0.645 | 8.4% | 91.6% |
| A4o | 0.612 | 29.2% | 70.8% |
| 44 | 1.943 | 34.4% | 65.6% |
| 33 | 0.402 | 56.9% | 43.1% |
| 22 | 0.002 | 57.0% | 43.0% |
Ranges, pot and stacks
- The hand so far: 6-max cash, 100 big blinds · Cutoff opens to 2.5 bb, big blind calls · Flop A♥ 9♥ 4♥: big blind checks · Pot 5.5 bb · Cutoff to act, 97.5 bb behind
- Pot at this decision, including the bets in front: 5.5 bb
- The cutoff: 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 67 % |
| Q | AQo 100 % | KQo 100 % | QQ 100 % | QJs 100 % | QTs 100 % | Q9s 100 % | Q8s 100 % | Q7s Not in this range here | Q6s 21 % | Q5s Not in this range here | Q4s Not in this range here | Q3s Not in this range here | Q2s Not in this range here |
| J | AJo 100 % | KJo 100 % | QJo 100 % | JJ 100 % | JTs 100 % | J9s 100 % | J8s 100 % | J7s 30 % | 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 100 % | KTo 100 % | QTo 100 % | JTo 100 % | TT 100 % | T9s 100 % | T8s 17 % | T7s Not in this range here | T6s Not in this range here | 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 54 % | Q9o Not in this range here | J9o Not in this range here | T9o Not in this range here | 99 100 % | 98s 63 % | 97s Not in this range here | 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 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 | 88 100 % | 87s <1 % | 86s Not in this range here | 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 84 % | 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 | 77 100 % | 76s 9 % | 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 12 % | 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 24 % | 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 22 % | 53s Not in this range here | 52s Not in this range here |
| 4 | A4o 10 % | 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 65 % | 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 7 % | 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 <1 % |
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 91 % | AJs 100 % | ATs 100 % | A9s 97 % | A8s 100 % | A7s 100 % | A6s 100 % | A5s 90 % | A4s 56 % | A3s 99 % | A2s 93 % |
| K | AKo Not in this range here | KK Not in this range here | KQs 98 % | KJs 98 % | KTs 99 % | K9s 100 % | K8s 98 % | K7s 97 % | K6s 80 % | K5s 61 % | K4s 65 % | K3s 2 % | K2s <1 % |
| Q | AQo 100 % | KQo 64 % | QQ Not in this range here | QJs 99 % | QTs 99 % | Q9s 100 % | Q8s 79 % | Q7s 34 % | Q6s 6 % | Q5s Not in this range here | Q4s <1 % | Q3s Not in this range here | Q2s Not in this range here |
| J | AJo 90 % | KJo 49 % | QJo 28 % | JJ <1 % | JTs 99 % | J9s 100 % | J8s 99 % | J7s 2 % | 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 100 % | KTo 90 % | QTo 62 % | JTo 55 % | TT 99 % | T9s 100 % | T8s 99 % | T7s 84 % | T6s Not in this range here | 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 77 % | K9o Not in this range here | Q9o Not in this range here | J9o Not in this range here | T9o Not in this range here | 99 97 % | 98s 97 % | 97s 93 % | 96s 90 % | 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 Not in this range here | 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 | 88 100 % | 87s 99 % | 86s 100 % | 85s 41 % | 84s Not in this range here | 83s Not in this range here | 82s Not in this range here |
| 7 | A7o Not in this range here | 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 93 % | 76s 99 % | 75s 100 % | 74s 5 % | 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 76 % | 65s 100 % | 64s 97 % | 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 75 % | 54s 91 % | 53s 88 % | 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 85 % | 43s 84 % | 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 88 % | 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 99 % |
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-R2.5-F-F-C·flop X - Solver notation
-
Ah9h4h. 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.