// spot check · preflop
Ace-king offsuit vs a nit’s 20 bb shove from the small blind
The Nit open-shoves 20 bb from the small blind; you are in the big blind. That is 21 bb in the middle with 19 to call, so the pot before the part you have to match is 2 bb.
Your hand
A♦K♣Board
preflopFacing
19 bb into 2 bbVillain range: The Nit · 36 of 50 combos live
AA,KK,QQ,JJ,TT,AKs,AQs,AKoVillain shoves The Nit’s range from /opponents: TT+, AQs+, AKo. That is far tighter than the solved 20 bb shoving range on the push/fold charts.
Fold−1.86 bb for calling
42.8% equity against 47.5% needed
What it shows
Against a range this tight even ace-king falls short of the 47.5% the price demands: two thirds of the range is a pocket pair, which has you at a coin flip or worse, and against AA and KK you are crushed. The solved 20 bb calling range assumes a much wider shover.
The working
- Range. The stated range is 50 combos. 14 of them use a card you can see (your hand or the board), which leaves 36.
- Equity. You win 30.5% and chop 24.6%, so equity is 30.5% + 24.6% ÷ 2 = 42.8%. Each hand class gets 20,000 sampled runouts with its own fixed seed, weighted by live combos. Sampling error is about ±0.13 points (one standard error).
- Price. Calling risks the bet to win the pot plus the bet, so break-even is bet ÷ (pot + 2 × bet) = 19 ÷ (2 + 2 × 19) = 47.5%.
- EV. equity × (pot + bet) − (1 − equity) × bet = 0.4285 × 21 − 0.5715 × 19 = −1.86 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 |
|---|---|---|---|---|---|
| AA | 3 | 8.3% | 6.1% | 1.4% | 6.8% |
| KK | 3 | 8.3% | 29.7% | 0.9% | 30.2% |
| TT | 6 | 16.7% | 42.7% | 0.4% | 42.9% |
| 6 | 16.7% | 43.0% | 0.5% | 43.2% | |
| JJ | 6 | 16.7% | 43.1% | 0.4% | 43.3% |
| AKs | 2 | 5.6% | 2.3% | 90.6% | 47.6% |
| AKo | 7 | 19.4% | 1.6% | 96.8% | 50.0% |
| AQs | 3 | 8.3% | 67.8% | 4.5% | 70.0% |
// 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
- 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