// spot check · river
Top pair, weak kicker, river bet: how many bluffs does villain need?
Villain bets 15 bb into 20 bb on the river.
Your hand
K♣4♦Board
K♥9♠5♣2♦7♥Facing
15 bb into 20 bbVillain range: custom · 50 of 84 combos live
AK,KQ,KJ,K9s,99,55,86s,QJs,JTs,T8s,64sVillain bets better kings, sets, and the 86s straight for value, and missed draws (QJs, JTs, T8s, 64s) as bluffs. With your cards removed that is 50 combos.
Break-even0.00 bb either way
30.0% equity against 30.0% needed
What it shows
Your king-four beats every bluff and nothing else, so your equity is simply the bluff share. A 15 bb bet into 20 needs 30%, and 15 bluffs out of 50 combos is exactly 30%: you are indifferent to the chip. One more bluff combo makes it a call, one fewer a fold.
The working
- Range. The stated range is 84 combos. 34 of them use a card you can see (your hand or the board), which leaves 50.
- Equity. You win 30.0% and chop 0.0%, so equity is 30.0% + 0.0% ÷ 2 = 30.0%. 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) = 15 ÷ (20 + 2 × 15) = 30.0%.
- EV. equity × (pot + bet) − (1 − equity) × bet = 0.3000 × 35 − 0.7000 × 15 = 0.00 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 | 6.0% | 0.0% | 0.0% | 0.0% |
| 86s | 4 | 8.0% | 0.0% | 0.0% | 0.0% |
| 99 | 3 | 6.0% | 0.0% | 0.0% | 0.0% |
| AKo | 6 | 12.0% | 0.0% | 0.0% | 0.0% |
| AKs | 2 | 4.0% | 0.0% | 0.0% | 0.0% |
| K9s | 1 | 2.0% | 0.0% | 0.0% | 0.0% |
| KJo | 6 | 12.0% | 0.0% | 0.0% | 0.0% |
| KJs | 2 | 4.0% | 0.0% | 0.0% | 0.0% |
| KQo | 6 | 12.0% | 0.0% | 0.0% | 0.0% |
| KQs | 2 | 4.0% | 0.0% | 0.0% | 0.0% |
| 64s | 3 | 6.0% | 100.0% | 0.0% | 100.0% |
| JTs | 4 | 8.0% | 100.0% | 0.0% | 100.0% |
| QJs | 4 | 8.0% | 100.0% | 0.0% | 100.0% |
| T8s | 4 | 8.0% | 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
- The same ace-high river call against a balanced regularA♣Q♦ again, now against The Reg’s range.Call · 27.8% vs 25.0% · +0.90 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