Solver answer

A♠Q♠ has the nut straight on the river: how big to bet?

6-max cash, 100 big blinds · Button opens, big blind calls · River K♦ J♠ 6♥ 4♣ T♦ · Big blind checks · Button to act

Updated

The solver's answer

Bet 100%

  • ⅒ pot · 3 bb 0%
  • 0.34 pot · 11 bb 1%
  • 0.6 pot · 19 bb 3%
  • 0.85 pot · 27 bb 9%
  • 1½ pot · 48 bb 9%
  • All-in · 84.3 bb 78%

A♠Q♠ bets big, usually all in; any big size works, and checking gives up the most.

The solver plays A♠Q♠ along this line to this decision 22.36% of the time; otherwise it acts differently earlier in the hand.

K♦J♠6♥4♣T♦
A♠Q♠ You
Pot
31.9 bb
Behind
84.3 bb
Big blind
Checks

In a 6-max cash game at 100 big blinds, after the big blind calls the button's 1.8 bb flop c-bet on K♦ J♠ 6♥ and 11.4 bb turn bet on the 4♣, then checks the T♦ river, the button moves all in with A♠Q♠ for 84.3 bb 78% of the time and uses the smaller sizes the rest of the time, according to a solver answer published free by Poker Skill.

Why the nuts bets big here

  • Every size from 0.6 times the pot to all-in is worth about the same to A♠Q♠, between 52.46 bb and 52.51 bb. Checking is worth 31.20 bb and the smallest bet 47.00 bb.
  • The big blind rarely holds a straight here: its range has far fewer of them than the button's.
  • Against a range that rarely holds the strongest hands, the nuts wants big bets, even overbets, since every call then pays more.
  • The button's straights as a group bet the same way: they move all in 71% 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

The button's strategy by hand class
AKQJT98765432
A AA B 100 % AKs B 100 % AQs B 100 % AJs Not in this range here ATs X 100 % A9s B 100 % A8s B 100 % A7s B 89 % A6s Not in this range here A5s B 87 % A4s B 100 % A3s B 100 % A2s B 100 %
K AKo B 100 % KK B 100 % KQs B 62 % KJs B 100 % KTs B 100 % K9s X 96 % K8s X 100 % K7s Not in this range here K6s B 100 % K5s Not in this range here K4s B 100 % K3s Not in this range here K2s Not in this range here
Q AQo B 100 % KQo B 52 % QQ Not in this range here QJs Not in this range here QTs X 63 % Q9s B 100 % Q8s B 100 % Q7s B 100 % Q6s Not in this range here Q5s B 100 % Q4s B 100 % Q3s B 100 % Q2s B 100 %
J AJo Not in this range here KJo B 100 % QJo Not in this range here JJ B 100 % JTs Not in this range here J9s Not in this range here J8s Not in this range here J7s Not in this range here J6s B 100 % J5s Not in this range here J4s B 100 % J3s Not in this range here J2s Not in this range here
T ATo X 100 % KTo B 100 % QTo X 51 % JTo Not in this range here TT Not in this range here T9s B 54 % T8s X 100 % T7s X 100 % T6s B 100 % T5s X 100 % T4s Not in this range here T3s Not in this range here T2s Not in this range here
9 A9o B 100 % K9o X 97 % Q9o B 100 % J9o Not in this range here T9o B 59 % 99 Not in this range here 98s B 100 % 97s B 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 B 99 % K8o X 100 % Q8o Not in this range here J8o Not in this range here T8o X 100 % 98o B 100 % 88 Not in this range here 87s B 100 % 86s Not in this range here 85s B 100 % 84s Not in this range here 83s Not in this range here 82s Not in this range here
7 A7o B 73 % K7o X 100 % 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 Not in this range here 76s Not in this range here 75s B 100 % 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 B 100 % 65s Not in this range here 64s B 100 % 63s Not in this range here 62s Not in this range here
5 A5o B 68 % 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 Not in this range here 54s B 100 % 53s Not in this range here 52s Not in this range here
4 A4o B 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 B 100 % 43s Not in this range here 42s Not in this range here
3 A3o B 75 % 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 B 100 %
  • Check: 23.82% of the range (5.38 combos)
  • Bet ⅒ pot (3 bb): 0.00% of the range (0 combos)
  • Bet 0.34 pot (11 bb): 6.87% of the range (1.55 combos)
  • Bet 0.6 pot (19 bb): 11.79% of the range (2.66 combos)
  • Bet 0.85 pot (27 bb): 16.22% of the range (3.66 combos)
  • Bet 1½ pot (48 bb): 6.50% of the range (1.47 combos)
  • All-in (84.3 bb): 34.79% of the range (7.86 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.

Every hand class in the button's range: combos and how often it takes each action
Hand class Combos CheckBet ⅒ pot (3 bb)Bet 0.34 pot (11 bb)Bet 0.6 pot (19 bb)Bet 0.85 pot (27 bb)Bet 1½ pot (48 bb)All-in (84.3 bb)
AA 0.549 0.0%0.0%0.6%38.3%60.0%0.7%0.3%
AKs 0.277 0.0%0.0%0.6%81.4%13.5%0.2%4.3%
AQs 0.898 0.0%0.0%1.3%4.7%5.4%6.6%82.1%
ATs 0.373 99.9%0.0%0.0%0.0%0.0%0.0%0.1%
A9s 0.001 0.0%0.0%0.0%0.0%0.2%70.5%29.3%
A8s 0.034 0.0%0.0%0.0%1.0%70.8%27.6%0.6%
A7s 0.02 11.3%0.0%0.4%13.3%56.6%15.5%2.9%
A5s 0.178 12.5%0.0%8.6%25.4%12.4%11.1%29.8%
A4s 0.009 0.0%0.0%0.1%0.1%0.3%20.0%79.5%
A3s 0.179 0.3%0.0%0.8%32.5%44.5%13.8%8.1%
A2s 0.274 0.1%0.0%0.3%10.5%54.7%20.3%14.1%
AKo 0.687 0.0%0.0%0.5%82.2%13.7%0.2%3.4%
KK 0.698 0.0%0.0%21.2%42.2%17.1%0.1%19.4%
KQs 0.527 38.3%0.0%44.8%12.2%4.7%0.0%0.0%
KJs 0.177 0.0%0.0%0.9%4.3%1.0%0.4%93.3%
KTs 0.545 0.0%0.0%0.8%3.7%21.7%17.3%56.5%
K9s 0.344 95.8%0.0%4.2%0.0%0.0%0.0%0.0%
K8s 0.204 99.8%0.0%0.2%0.0%0.0%0.0%0.0%
K6s 0.363 0.0%0.0%0.2%0.0%54.9%44.9%0.1%
K4s 0.476 0.0%0.0%0.6%7.2%50.7%41.4%0.1%
AQo 1.147 0.0%0.0%1.2%5.0%6.3%7.3%80.2%
KQo 1.695 47.6%0.0%38.8%11.6%1.9%0.0%0.0%
QTs 0.259 62.5%0.0%0.1%0.0%0.0%0.1%37.3%
Q9s 0.479 0.0%0.0%5.6%9.4%33.2%0.8%51.0%
Q8s 0.18 0.0%0.0%36.1%0.4%35.8%0.2%27.5%
Q7s 0.144 0.1%0.0%5.0%0.6%0.5%0.6%93.1%
Q5s 0.283 0.1%0.0%2.2%0.5%0.5%0.6%96.2%
Q4s 0.029 0.0%0.0%0.2%0.1%0.2%0.4%99.2%
Q3s 0.302 0.1%0.0%14.3%0.6%0.5%0.6%84.0%
Q2s 0.369 0.0%0.0%19.7%0.5%13.1%0.6%66.0%
KJo 0.46 0.0%0.0%1.0%12.4%11.5%1.3%73.8%
JJ 0.584 0.0%0.0%0.6%0.5%0.3%11.9%86.8%
J6s 0.3 0.0%0.0%0.0%14.6%65.4%20.0%0.0%
J4s 0.37 0.0%0.0%0.2%1.6%82.6%15.6%0.0%
ATo 0.561 99.9%0.0%0.0%0.0%0.0%0.0%0.1%
KTo 1.038 0.0%0.0%0.8%2.7%22.9%16.9%56.7%
QTo 0.835 51.0%0.0%0.1%0.0%0.0%0.2%48.7%
T9s 0.264 45.7%0.0%0.0%0.0%0.1%3.7%50.4%
T8s 0.012 99.7%0.0%0.0%0.0%0.0%0.1%0.2%
T7s 0.039 99.7%0.0%0.0%0.0%0.0%0.0%0.3%
T6s 0.003 0.0%0.0%1.1%80.1%17.8%0.3%0.7%
T5s 0.018 99.7%0.0%0.0%0.0%0.0%0.0%0.3%
A9o 0.011 0.0%0.0%0.0%0.0%0.2%72.6%27.1%
K9o 0.768 96.7%0.0%3.3%0.0%0.0%0.0%0.0%
Q9o 0.58 0.0%0.0%8.5%8.3%32.2%0.7%50.3%
T9o 0.544 41.3%0.0%0.1%0.0%0.1%3.5%55.0%
98s 0.008 0.0%0.0%0.0%0.2%37.4%62.1%0.4%
97s 0.014 0.0%0.0%0.0%0.3%36.0%62.7%1.0%
A8o 0.149 1.4%0.0%0.0%1.3%75.8%20.9%0.6%
K8o 0.239 99.8%0.0%0.2%0.0%0.0%0.0%0.0%
T8o 0.092 99.7%0.0%0.0%0.0%0.0%0.1%0.3%
98o 0.039 0.0%0.0%0.0%0.2%35.6%63.8%0.4%
87s 0.015 0.0%0.0%7.7%21.0%65.3%5.8%0.2%
85s 0.098 0.0%0.0%18.3%68.0%11.8%1.6%0.3%
A7o 0.467 27.0%0.0%0.4%5.9%45.4%10.4%11.0%
K7o 0.001 100.0%0.0%0.0%0.0%0.0%0.0%0.0%
75s 0.008 0.0%0.0%33.1%53.8%5.1%4.9%3.2%
66 0.253 0.0%0.0%0.7%0.6%0.3%0.5%98.0%
64s 0.15 0.0%0.0%0.8%10.7%86.1%2.0%0.3%
A5o 1.818 32.2%0.0%4.7%22.1%9.0%6.9%25.0%
54s 0.005 0.0%0.0%0.2%0.2%1.5%39.8%58.3%
A4o 0.519 0.1%0.0%0.1%0.2%0.3%7.4%91.8%
44 0.259 0.0%0.0%0.9%0.8%0.2%0.3%97.7%
A3o 0.356 24.7%0.0%0.4%11.7%37.6%10.1%15.5%
22 0.001 0.0%0.0%1.8%11.2%86.3%0.5%0.2%
The solver's strategy for A♠Q♠ on K♦ J♠ 6♥ 4♣ T♦: check 0%, bet ⅒ pot (3 bb) 0%, bet 0.34 pot (11 bb) 1%, bet 0.6 pot (19 bb) 3%, bet 0.85 pot (27 bb) 9%, bet 1½ pot (48 bb) 9% and all-in (84.3 bb) 78%.
The solver's strategy for A♠Q♠ on K♦ J♠ 6♥ 4♣ T♦: check 0%, bet ⅒ pot (3 bb) 0%, bet 0.34 pot (11 bb) 1%, bet 0.6 pot (19 bb) 3%, bet 0.85 pot (27 bb) 9%, bet 1½ pot (48 bb) 9% and all-in (84.3 bb) 78%.

What each action is worth with A♠Q♠

Action How often Expected value
Check 0.00% 31.201 bb
Bet ⅒ pot (3 bb) 0.00% 47.004 bb
Bet 0.34 pot (11 bb) 1.15% 52.267 bb
Bet 0.6 pot (19 bb) 3.23% 52.505 bb
Bet 0.85 pot (27 bb) 8.47% 52.475 bb
Bet 1½ pot (48 bb) 8.77% 52.464 bb
All-in (84.3 bb) 78.38% 52.486 bb

Ranges, pot and stacks

  • The hand so far: 6-max cash, 100 big blinds · Button opens to 2.5 bb, big blind calls · Flop K♦ J♠ 6♥: big blind checks, button bets 1.8 bb, big blind calls · Turn 4♣: big blind checks, button bets 11.4 bb, big blind calls · River T♦: big blind checks · Pot 31.9 bb · Button to act, 84.3 bb behind
  • Pot at this decision, including the bets in front: 31.9 bb
  • The button: 84.3 bb behind
  • The big blind: 84.3 bb behind
The button's range: 22.6 combos
AKQJT98765432
A AA 9 % AKs 9 % AQs 22 % AJs Not in this range here ATs 12 % A9s <1 % A8s 1 % A7s 1 % A6s Not in this range here A5s 4 % A4s <1 % A3s 5 % A2s 7 %
K AKo 8 % KK 23 % KQs 18 % KJs 9 % KTs 18 % K9s 12 % K8s 7 % K7s Not in this range here K6s 18 % K5s Not in this range here K4s 24 % K3s Not in this range here K2s Not in this range here
Q AQo 10 % KQo 19 % QQ Not in this range here QJs Not in this range here QTs 9 % Q9s 12 % Q8s 5 % Q7s 4 % Q6s Not in this range here Q5s 7 % Q4s 1 % Q3s 8 % Q2s 9 %
J AJo Not in this range here KJo 7 % QJo Not in this range here JJ 20 % JTs Not in this range here J9s Not in this range here J8s Not in this range here J7s Not in this range here J6s 15 % J5s Not in this range here J4s 19 % J3s Not in this range here J2s Not in this range here
T ATo 6 % KTo 17 % QTo 9 % JTo Not in this range here TT Not in this range here T9s 9 % T8s <1 % T7s 1 % T6s <1 % T5s 1 % T4s Not in this range here T3s Not in this range here T2s Not in this range here
9 A9o <1 % K9o 9 % Q9o 5 % J9o Not in this range here T9o 6 % 99 Not in this range here 98s <1 % 97s <1 % 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 1 % K8o 3 % Q8o Not in this range here J8o Not in this range here T8o 1 % 98o <1 % 88 Not in this range here 87s <1 % 86s Not in this range here 85s 3 % 84s Not in this range here 83s Not in this range here 82s Not in this range here
7 A7o 4 % K7o <1 % 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 Not in this range here 76s Not in this range here 75s <1 % 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 8 % 65s Not in this range here 64s 8 % 63s Not in this range here 62s Not in this range here
5 A5o 15 % 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 Not in this range here 54s <1 % 53s Not in this range here 52s Not in this range here
4 A4o 6 % 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 9 % 43s Not in this range here 42s Not in this range here
3 A3o 3 % 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 <1 %

Each cell shows the share of the class's possible combos in the range.

The big blind's range: 68 combos
AKQJT98765432
A AA Not in this range here AKs Not in this range here AQs Not in this range here AJs Not in this range here ATs 12 % A9s Not in this range here A8s Not in this range here A7s Not in this range here A6s 7 % A5s Not in this range here A4s 27 % A3s Not in this range here A2s Not in this range here
K AKo Not in this range here KK Not in this range here KQs Not in this range here KJs <1 % KTs 38 % K9s 44 % K8s 65 % K7s 74 % K6s 35 % K5s 80 % K4s 77 % K3s 89 % K2s 96 %
Q AQo 7 % KQo 36 % QQ Not in this range here QJs 51 % QTs 12 % Q9s Not in this range here Q8s Not in this range here Q7s Not in this range here Q6s 1 % 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 54 % KJo 7 % QJo 41 % JJ Not in this range here JTs 1 % J9s 3 % J8s 75 % J7s 49 % J6s Not in this range here J5s 61 % J4s 49 % J3s 72 % J2s 79 %
T ATo 18 % KTo 54 % QTo 26 % JTo 9 % TT Not in this range here T9s Not in this range here T8s Not in this range here T7s Not in this range here T6s 5 % 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 57 % Q9o Not in this range here J9o 9 % T9o Not in this range here 99 Not in this range here 98s Not in this range here 97s Not in this range here 96s 8 % 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 30 % 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 Not in this range here 87s Not in this range here 86s 45 % 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 Not in this range here 76s 23 % 75s 1 % 74s Not in this range here 73s Not in this range here 72s Not in this range here
6 A6o 2 % 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 18 % 66 7 % 65s 11 % 64s 28 % 63s 12 % 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 Not in this range here 54s 6 % 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 47 % 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 0.6 bb, opens sized by the solver (2.5 bb here) and several bet sizes on each street. The flop and turn follow the most-used sizes, which are also A♠Q♠'s own most-used bets. On the river the button can check, move all in or bet from a tenth of the pot to 1½ times 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-R1.8-C, turn X-R11.4-C, river X
Solver notation
KdJs6h4cTd · AsQs . 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.

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