// spot check · river
The same ace-high river call against a balanced regular
The Reg bets 8 bb into 16 bb on the river.
Your hand
A♣Q♦Board
J♠8♥5♠3♣2♦Facing
8 bb into 16 bbVillain range: The Reg · 124 of 172 combos live
AA,KK,QQ,JJ,TT,99,88,77,66,55,AKs,AQs,AJs,ATs,A5s,A4s,KQs,KJs,KTs,QJs,QTs,JTs,T9s,98s,87s,76s,AKo,AQo,AJo,KQoVillain bets every hand in The Reg’s range from /opponents. A real regular would check some of these, which would change the answer; paste a narrower range into the calculator to see by how much.
Call+0.90 bb for calling
27.8% equity against 25.0% needed
What it shows
A tighter range makes the call much thinner than against the maniac, but it is still a call at this price. Change the bet to pot and see where it flips.
The working
- Range. The stated range is 172 combos. 48 of them use a card you can see (your hand or the board), which leaves 124.
- Equity. You win 24.2% and chop 7.3%, so equity is 24.2% + 7.3% ÷ 2 = 27.8%. The river is dealt, so every combo is evaluated once and the number is exact.
- Price. Calling risks the bet to win the pot plus the bet, so break-even is bet ÷ (pot + 2 × bet) = 8 ÷ (16 + 2 × 8) = 25.0%.
- EV. equity × (pot + bet) − (1 − equity) × bet = 0.2782 × 24 − 0.7218 × 8 = +0.90 bb. Folding is 0, so that is the whole difference between the two options.
Where the equity comes from
Your equity against every hand class in the range, with how much of the range each one is. The total above is these rows averaged by combo count.
| Villain | Combos | Share | Win | Chop | Your equity |
|---|---|---|---|---|---|
| 55 | 3 | 2.4% | 0.0% | 0.0% | 0.0% |
| 66 | 6 | 4.8% | 0.0% | 0.0% | 0.0% |
| 77 | 6 | 4.8% | 0.0% | 0.0% | 0.0% |
| 87s | 3 | 2.4% | 0.0% | 0.0% | 0.0% |
| 88 | 3 | 2.4% | 0.0% | 0.0% | 0.0% |
| 98s | 3 | 2.4% | 0.0% | 0.0% | 0.0% |
| 99 | 6 | 4.8% | 0.0% | 0.0% | 0.0% |
| A4s | 3 | 2.4% | 0.0% | 0.0% | 0.0% |
| A5s | 2 | 1.6% | 0.0% | 0.0% | 0.0% |
| AA | 3 | 2.4% | 0.0% | 0.0% | 0.0% |
| AJo | 7 | 5.6% | 0.0% | 0.0% | 0.0% |
| AJs | 2 | 1.6% | 0.0% | 0.0% | 0.0% |
| AKo | 9 | 7.3% | 0.0% | 0.0% | 0.0% |
| AKs | 3 | 2.4% | 0.0% | 0.0% | 0.0% |
| JJ | 3 | 2.4% | 0.0% | 0.0% | 0.0% |
| JTs | 3 | 2.4% | 0.0% | 0.0% | 0.0% |
| KJs | 3 | 2.4% | 0.0% | 0.0% | 0.0% |
| KK | 6 | 4.8% | 0.0% | 0.0% | 0.0% |
| QJs | 2 | 1.6% | 0.0% | 0.0% | 0.0% |
| 3 | 2.4% | 0.0% | 0.0% | 0.0% | |
| TT | 6 | 4.8% | 0.0% | 0.0% | 0.0% |
| AQo | 7 | 5.6% | 0.0% | 100.0% | 50.0% |
| AQs | 2 | 1.6% | 0.0% | 100.0% | 50.0% |
| 76s | 4 | 3.2% | 100.0% | 0.0% | 100.0% |
| ATs | 3 | 2.4% | 100.0% | 0.0% | 100.0% |
| KQo | 9 | 7.3% | 100.0% | 0.0% | 100.0% |
| KQs | 3 | 2.4% | 100.0% | 0.0% | 100.0% |
| KTs | 4 | 3.2% | 100.0% | 0.0% | 100.0% |
| QTs | 3 | 2.4% | 100.0% | 0.0% | 100.0% |
| T9s | 4 | 3.2% | 100.0% | 0.0% | 100.0% |
// settle the thread
The link encodes the whole spot. Anyone who opens it gets these numbers, recomputed in their own browser.
Disagree with the range, or want to see where the answer flips? Open this spot in the calculator and change anything: cards, bet size, villain range.
Change the numbers →// what is computed, and what is assumed
- Computed: card removal, equity (exact on the river, sampled with fixed seeds before it), the break-even price, and the EV of calling. Same engine, same seeds, same numbers for anyone who opens the link.
- Assumed: the range. Villain bets every combo in it, all equally often. The four archetype ranges are our assumptions and are printed in full; a pasted range is yours.
- Assumed: this is the last bet. Before the river, the EV counts you as seeing every remaining card with no more money going in. That is exact when the bet is all-in (every worked example below is) and optimistic otherwise, because it ignores implied odds and reverse implied odds alike.
- Pot is everything in the middle except the bet you face; bet is what it costs you to call. Range notation: AA, AKs, AKo, AK (both), TT+, ATs+, 22-55, A2s-A5s. No weights or single combos.
More worked spots
Flop, facing an all-in
- Flush draw vs an overpair, all-in on the flop: call or fold?J♥T♥ on 9♥5♥2♣ against QQ+, pot-size shove.Call · 36.2% vs 33.3% · +0.87 bb
- Nut flush draw vs top pair, all-in on the flopA♥4♥ on K♥8♥2♣ against top pair or better.Call · 41.3% vs 33.3% · +2.38 bb
- Open-ended straight draw vs top pair, pot-size all-in on the flop9♣8♣ on T♠7♦2♥: eight outs twice, against top pair.Fold · 31.7% vs 33.3% · −0.49 bb
- Gutshot on the flop facing a half-pot all-in6♠5♠ on 9♣8♦2♥: four outs to a straight.Fold · 19.6% vs 25.0% · −1.09 bb
- Combo draw vs top pair: are you the favourite all-in on the flop?9♥8♥ on T♥7♥2♣: flush draw plus open-ender.Call · 54.6% vs 33.3% · +6.38 bb
- Two overcards vs a pair, pot-size all-in on the flopA♥K♦ on 9♣6♠2♥, no draw: six outs.Fold · 18.3% vs 33.3% · −4.51 bb
- Pocket aces on a monotone flop facing an overbet all-inA♠A♦ on K♥8♥4♥ without the ace of hearts.Call · 59.5% vs 42.9% · +11.65 bb
- Bottom two pair against a range full of draws, all-in on the flop9♠5♠ on 9♥5♦2♥ facing a 2× pot shove.Call · 75.2% vs 40.0% · +17.60 bb
Turn, facing an all-in
- Flush draw on the turn facing a pot-size all-inSame draw, one card later: J♥T♥ on 9♥5♥2♣3♦.Fold · 19.3% vs 33.3% · −12.65 bb
- Is a flush draw ever a call on the turn? Facing a third-pot all-inJ♥T♥ on the turn, villain all-in for a third of the pot.Fold · 19.3% vs 20.0% · −0.36 bb
- Open-ended straight draw on the turn facing a pot-size all-in9♣8♣ on T♠7♦2♥3♠ with one card to come.Fold · 17.8% vs 33.3% · −9.34 bb
- Middle pair against a maniac’s turn all-in7♠6♠ on 9♥7♣2♦K♥ against a range that bets everything.Call · 49.3% vs 30.0% · +5.80 bb
- Ace-king with a gutshot on the turn facing an all-inA♥K♦ on Q♣J♠4♦2♥: gutshot plus overcards.Fold · 15.3% vs 28.6% · −4.66 bb
River bets
- Calling the maniac’s river bet with ace highA♣Q♦ on J♠8♥5♠3♣2♦, half-pot bet.Call · 42.0% vs 25.0% · +5.45 bb
- Top pair, weak kicker, river bet: how many bluffs does villain need?K♣4♦ on K♥9♠5♣2♦7♥, 15 bb into 20 bb.Break-even · 30.0% vs 30.0% · 0.00 bb
- Overpair facing a river overbet: call or fold?Q♠Q♦ on J♣8♥2♠5♦3♣, 30 bb into 20 bb.Fold · 32.4% vs 37.5% · −4.05 bb