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.