Facing a Three-Bet

The only question is the stack-to-pot ratio

Coverage note: our reference range now covers facing a three-bet in exactly one seat pairing — you open the button, the big blind three-bets — and the table there gives four-bet, call or fold. The worked example below is a different pairing (cutoff open, button three-bet), so its numbers are arithmetic, not a lookup: they come from the pot calculator and the equity engine. Other pairings, and facing a four-bet, are still not covered, and there is no date on them.

You open the cutoff to 7. The button three-bets the full pot to 24. You have two lines, and they lead to two different games:

• Call. Pot 51, 176 chips behind. Stack-to-pot ratio 3.5 — three streets of real poker.
• Four-bet the pot to 75 and get called. Pot 153, 125 behind. Stack-to-pot ratio 0.8 — one decision, made on the flop at the latest.

That is the whole choice. You are not picking between "strong enough" and "not strong enough"; you are picking the ratio you want to play this hand at. Aces want the second line because a low ratio removes the streets where a pair stops being good. A rundown wants the first, because it needs those streets to become something.

The one pairing our table covers says the same thing in its own words. Open the button, get three-bet by the big blind: A♥A♦K♥K♦ four-bets, Q♦Q♣8♦7♣ sits on the four-bet/call line, J♠T♠9♥8♥ calls. And 2♠7♦9♣J♥ is not marked as a fold — it is marked as a spot that cannot happen, because you never opened it. That distinction matters: a table that answered "fold" there would be answering a question nobody asked.

With aces, four-bet to lock in a low stack-to-pot ratio.

At 100 big blinds or shallower, heads-up, when the opponent will actually put the money in, and when the aces are the good kind (C5).

0.8 is not zero. There are still 125 chips to play after the flop, and the hands that call your four-bet are not helpless — the three rundowns we measured all hold 41.2% or better against a range of aces, which is the next page. The four-bet also narrows your own range to something close to face-up. If you want the ratio genuinely locked you need to be shallower: the same line at 50 big blinds leaves a ratio of 0.2 (C12).

Calling the four-bet is the normal answer

Coverage note: our reference range now covers the opener's side of a three-bet — you open the button, the big blind three-bets, and the table tells you to four-bet, call or fold. This page is the other side: you were the three-bettor and now face a four-bet. That direction is still not covered — there is no date on it, and it is only worth building alongside the seat pairings around it. The pot maths below comes from the calculator and the equities from the engine; the opponent range is one we constructed and named on the page, not one we looked up.

Now sit on the other side. You three-bet the button to 24 and the cutoff four-bets to 75. The pot is 102 and it costs you 51: break-even 33.3%.

Assume the four-bet is exactly what it looks like — any two aces plus any two non-aces, 6768 combinations. Our engine against that range, 300000 simulations each:

• K♠Q♠J♥T♥: 41.2%.
• J♠T♠9♥8♥: 43.3%.
• 8♠7♠6♥5♥: 44.2%.

All three clear 33.3% with room to spare. Calling a four-bet with a rundown is the ordinary play here, not a hero call.

And look at the order. Against a random hand the height ladder was clear: K♠Q♠J♥T♥ at 58.9% beat 8♠7♠6♥5♥ at 48.8% by ten points (C6). Against a range of aces the ladder inverts — the low rundown does best. The aces already occupy the top of the deck, so a hand that competes up there is fighting for cards the opponent is holding, while the low rundown overlaps with him hardly at all. Which hand is better has no answer until you name the opponent's range.

Facing a four-bet that represents aces, call with a rundown.

When you have position, the price is met, and you are content with the ratio the call leaves you.

The price being met is only a floor — that was C8, and it is still true here. If calling leaves you so short that the flop is automatic, you have bought a one-shot coin flip at 41.2 to 44.2%, not a hand you get to play. And the moment his four-betting range is wider than pure aces, every number on this page moves.

Blockers, before the flop

These are counted, not estimated. A four-bettor holding any two aces plus any two non-aces has 6768 combinations. How many survive depends on the cards in your hand:

• You hold no ace, e.g. J♠T♠9♥8♥: 5676 combinations left.
• You hold one ace, e.g. A♠J♠T♥9♥: 2970 left — 52.3% of the previous line.
• You hold two aces, e.g. A♠A♥J♠T♥: 1035 left — 18.2%.

One ace in your hand cuts his aces roughly in half. That is what a blocker looks like before the flop: not a feeling about what he has, but an integer you can count.

Holding an ace makes it much less likely he has aces — downgrade his four-bet accordingly.

When his four-betting range really is aces-heavy. Against someone who four-bets other holdings too, your ace blocks a smaller share of it.

Halved is not gone: 2970 combinations is still a lot of aces, and "less likely" gets misread as "unlikely" every time. The blocker also has a price. That ace costs your hand connectedness — our classifier counts an ace as sharing at most 1 five-card straight window with any other card in your hand, where a king shares 2 (C6). You are paying for the blocker with your straight potential, so an ace is not a free upgrade to a hand.

What to take away

• Calling a three-bet leaves a ratio of 3.5; four-betting the pot leaves 0.8. Pick the one your hand wants, and stop asking whether the hand is "strong enough".
• Facing a four-bet, the price is 33.3% and rundowns hold 41.2% to 44.2% against a range of aces. Calling is the normal answer.
• Against aces the height ladder inverts. Hand rankings are relative to a range, always.
• One ace halves his aces to 52.3% of the combinations — and costs you straight potential to hold.

None of this came from a range table, because we do not have one for these spots yet. Take the arithmetic, keep the mechanism, and treat the specific lines as worked examples rather than as a chart.