Solver answer
How much should the button defend against UTG's c-bet?
6-max cash, 100 big blinds · UTG opens, button calls · Flop 8♣ 4♥ 2♠ · UTG bets 2.1 bb into 6.5 bb · Button to act
Updated
The solver's answer
The button's whole range
Call 91% Fold 8% Raise 1%
The button defends far more than the minimum: it folds only 8% of its range.
8♣4♥2♠
- Pot
- 6.5 bb
- Behind
- 97.5 bb
- UTG
- Bets 2.1 bb
In a 6-max cash game at 100 big blinds, after UTG opens to 2.5 bb, the button calls and UTG c-bets 2.1 bb into 6.5 bb on an 8♣ 4♥ 2♠ flop, the button calls with 91% of its range, raises 1% and folds 8%, according to a solver answer published free by Poker Skill.
Why the button defends more than the minimum
- The minimum defense frequency for a 2.1 bb bet into 6.5 bb is 76%: the least the button can continue with before UTG profits by betting any two cards. It is a floor, not a target.
- The button continues with 92.2% of its range, and the price is low: calling 2.1 bb to win 8.6 bb needs 19.6% equity.
- Its folds are almost all ace-high and king-high hands, and even those fold only 14% and 17% of the time. Its pairs never fold.
- UTG c-bets only 18% of its range here, and more than half of those bets are hands with no pair.
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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 Not in this range here | AKs Not in this range here | AQs C 100 % | AJs C 83 % | ATs C 61 % | A9s C 75 % | A8s C 99 % | A7s Not in this range here | A6s Not in this range here | A5s C 99 % | A4s C 100 % | A3s Not in this range here | A2s Not in this range here |
| K | AKo C 100 % | KK Not in this range here | KQs C 84 % | KJs C 88 % | KTs C 68 % | K9s Not in this range here | K8s Not in this range here | K7s Not in this range here | K6s Not in this range here | K5s Not in this range here | K4s Not in this range here | K3s Not in this range here | K2s Not in this range here |
| Q | AQo C 99 % | KQo F 72 % | QQ C 99 % | QJs C 99 % | QTs C 99 % | Q9s Not in this range here | Q8s Not in this range here | Q7s Not in this range here | Q6s Not in this range here | 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 Not in this range here | KJo Not in this range here | QJo Not in this range here | JJ C 100 % | JTs C 99 % | J9s Not in this range here | J8s Not in this range here | J7s Not in this range here | 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 Not in this range here | KTo Not in this range here | QTo Not in this range here | JTo Not in this range here | TT C 100 % | T9s Not in this range here | T8s Not in this range here | 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 Not in this range here | 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 C 100 % | 98s Not in this range here | 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 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 C 96 % | 87s Not in this range here | 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 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 C 100 % | 76s C 99 % | 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 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 C 100 % | 65s C 98 % | 64s Not in this range here | 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 C 100 % | 54s C 100 % | 53s Not in this range here | 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 C 94 % | 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 C 100 % | 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 C 93 % |
- Fold: 7.77% of the range (3 combos)
- Call (2.1 bb): 91.46% of the range (35.26 combos)
- Raise 0.83 pot (to 11 bb): 0.77% of the range (0.3 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 | Fold | Call (2.1 bb) | Raise 0.83 pot (to 11 bb) |
|---|---|---|---|---|
| AQs | 1.934 | 0.1% | 99.5% | 0.4% |
| AJs | 3.771 | 16.5% | 82.7% | 0.8% |
| ATs | 2.971 | 38.5% | 60.7% | 0.8% |
| A9s | 0.68 | 24.3% | 74.6% | 1.1% |
| A8s | 0.077 | 0.0% | 99.2% | 0.8% |
| A5s | 1.048 | 0.0% | 98.8% | 1.2% |
| A4s | 0.209 | 0.0% | 100.0% | 0.0% |
| AKo | 0.264 | 0.0% | 100.0% | 0.0% |
| KQs | 3.295 | 14.9% | 83.6% | 1.5% |
| KJs | 1.812 | 11.1% | 88.1% | 0.8% |
| KTs | 1.069 | 31.5% | 68.0% | 0.5% |
| AQo | 2.914 | 0.9% | 98.5% | 0.7% |
| KQo | 0.007 | 71.6% | 28.2% | 0.2% |
| 0.71 | 0.0% | 98.9% | 1.1% | |
| QJs | 0.354 | 0.2% | 98.8% | 1.1% |
| QTs | 0.022 | 0.7% | 99.1% | 0.2% |
| JJ | 4.631 | 0.0% | 99.5% | 0.5% |
| JTs | 0.807 | 0.2% | 99.1% | 0.7% |
| TT | 3.629 | 0.0% | 99.7% | 0.3% |
| 99 | 2.582 | 0.0% | 99.8% | 0.2% |
| 88 | 1.048 | 0.0% | 96.4% | 3.6% |
| 77 | 1.262 | 0.0% | 100.0% | 0.0% |
| 76s | 0.36 | 0.0% | 99.3% | 0.7% |
| 66 | 0.812 | 0.0% | 100.0% | 0.0% |
| 65s | 0.854 | 0.0% | 98.4% | 1.6% |
| 55 | 0.517 | 0.0% | 99.5% | 0.4% |
| 54s | 0.65 | 0.0% | 99.7% | 0.3% |
| 44 | 0.177 | 0.0% | 94.3% | 5.7% |
| 33 | 0.085 | 0.0% | 100.0% | 0.0% |
| 22 | 0.002 | 0.0% | 93.4% | 6.6% |
Ranges, pot and stacks
- The hand so far: 6-max cash, 100 big blinds · UTG opens to 2.5 bb, button calls · Flop 8♣ 4♥ 2♠: UTG bets 2.1 bb into 6.5 bb · Button to act, 97.5 bb behind
- Pot at this decision, including the bets in front: 8.6 bb
- The button: 97.5 bb behind
- UTG: 95.4 bb behind, 2.1 bb in front
| 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 48 % | AJs 94 % | ATs 74 % | A9s 17 % | A8s 3 % | A7s Not in this range here | A6s Not in this range here | A5s 26 % | A4s 7 % | A3s Not in this range here | A2s Not in this range here |
| K | AKo 2 % | KK Not in this range here | KQs 82 % | KJs 45 % | KTs 27 % | K9s Not in this range here | K8s Not in this range here | K7s Not in this range here | K6s Not in this range here | K5s Not in this range here | K4s Not in this range here | K3s Not in this range here | K2s Not in this range here |
| Q | AQo 24 % | KQo <1 % | QQ 12 % | QJs 9 % | QTs 1 % | Q9s Not in this range here | Q8s Not in this range here | Q7s Not in this range here | Q6s Not in this range here | 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 Not in this range here | KJo Not in this range here | QJo Not in this range here | JJ 77 % | JTs 20 % | J9s Not in this range here | J8s Not in this range here | J7s Not in this range here | 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 Not in this range here | KTo Not in this range here | QTo Not in this range here | JTo Not in this range here | TT 61 % | T9s Not in this range here | T8s Not in this range here | 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 Not in this range here | 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 43 % | 98s Not in this range here | 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 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 35 % | 87s Not in this range here | 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 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 21 % | 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 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 14 % | 65s 21 % | 64s Not in this range here | 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 9 % | 54s 22 % | 53s Not in this range here | 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 6 % | 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 1 % | 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 29 % | AKs 43 % | AQs 25 % | AJs 21 % | ATs 18 % | A9s 2 % | A8s 21 % | A7s 4 % | A6s 15 % | A5s 23 % | A4s 25 % | A3s 23 % | A2s 31 % |
| K | AKo 35 % | KK 30 % | KQs 20 % | KJs 29 % | KTs <1 % | K9s <1 % | K8s 31 % | K7s 1 % | K6s 11 % | K5s 18 % | K4s <1 % | K3s Not in this range here | K2s Not in this range here |
| Q | AQo 22 % | KQo 2 % | QQ 37 % | QJs 31 % | QTs 14 % | Q9s 13 % | Q8s Not in this range here | Q7s Not in this range here | Q6s Not in this range here | 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 5 % | KJo <1 % | QJo 2 % | JJ 36 % | JTs 30 % | J9s Not in this range here | J8s Not in this range here | J7s Not in this range here | 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 <1 % | KTo <1 % | QTo Not in this range here | JTo Not in this range here | TT 28 % | T9s 5 % | T8s Not in this range here | 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 <1 % | 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 24 % | 98s Not in this range here | 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 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 28 % | 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 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 18 % | 76s 4 % | 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 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 4 % | 65s 5 % | 64s Not in this range here | 63s Not in this range here | 62s Not in this range here |
| 5 | A5o 7 % | 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 4 % | 54s 4 % | 53s Not in this range here | 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 4 % | 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 Not in this range here | 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 Not in this range here |
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 UTG's c-bet is 2.1 bb into 6.5 bb and the button's raise goes to 11 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
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R2.5-F-F-C-F-F·flop R2.1 - Solver notation
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8c4h2s. 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.