Defending Against an Open

Why pot odds filter nothing here

The button opens to 7 and the small blind folds. You are in the big blind: the pot is 10 and it costs you 5 to call. Break-even equity is 33.3%. The hold'em habit says: find 33.3% and defend.

So we measured. The button's opening range is 126165 combinations opened outright, plus a mixed tier it opens only part of the time; counting that mixed tier at half weight, the button opens 48.6% of all starting hands. (Two different quantities: the first is a count of pure raises, the second a weighted share — one does not divide into the other.) Against that whole range (300000 simulations, standard error 0.09 points), 2♣2♦3♥3♠ has 37.1%. That is comfortably over the line, and our reference range folds it from the big blind anyway.

It is not an outlier. Equities in this game are compressed (that was C3), so almost anything clears a one-in-three price. And yet the table defends only 36.1% of hands. If pot odds decided it, the number would be somewhere north of ninety.

The missing term is equity realisation: you do not get to see all five cards for free. You will be out of position for three streets against a player with the betting lead, folding some of that 37.1% away on every card that misses you.

If the pot odds are there, defend.

When you have position, or the hand can walk itself down after the flop — a nutted, connected holding that knows what it is doing on the turn.

2♣2♦3♥3♠ is 37.1% and folds everywhere. In hold'em pot odds are a real filter because equities are spread out; here they are met almost always, which makes them a necessary condition and never a sufficient one. Any rule that ends at "the price is right" will have you defending the whole deck out of position.

Three-bet or call — not sorted by equity

Of the 36.1% this table defends, 10% is a three-bet and the rest is a call. Here is what those hands are worth against the button's opening range (300000 simulations each), next to the action the table gives them:

• A♥A♦K♥K♦ — 70% — three-bet.
• K♠Q♠J♥T♥ — 54.1% — three-bet.
• J♠T♠9♥8♥ — 50.3% — three-bet or call, both defensible.
• J♠T♥9♠2♥ — 47.8% — call or fold, both defensible.
• 8♠7♠6♥5♥ — 45.5% — call.

Read the last two rows again. The hand with more equity gets the weaker action. That is not a bug in the table; it is the table pricing in something equity cannot see. 8♠7♠6♥5♥ is four connected ranks, double-suited: after the flop it knows what it is doing, and when it gets there it usually has the nuts. J♠T♥9♠2♥ has a 2♥ hanging off the bottom and spends most flops being almost something.

The more equity a hand has, the more aggressively you should defend it.

Between hands of similar shape — two rundowns, two pairs-plus-suits — where the structure is not doing anything different.

J♠T♥9♠2♥ beats 8♠7♠6♥5♥ by more than two points of equity and sits one full step lower in the table. Preflop equity is one input, not the sort key. Nuttiness and playability are the other two, and neither shows up in a percentage.

The small blind, where we have no table

Coverage note, up front: our reference range does now cover this seat — small-blind defence against a button open — and you can look any hand up in the range table. Two things to know before you do. It is modelled as three-bet or fold, with no calling tier at all: no public source gives a small-blind calling frequency we could anchor to, and an invented tier is worse than a missing one. And it covers this pairing only, six-handed at 100 big blinds; other opening seats are not in the table, and there is no date on adding them. The arithmetic below is the pot calculator, and the shape argument is still an argument — where we are reasoning rather than measuring, we say so.

Start with the part that is certain. The button opens to 7. In the big blind the pot is 10 and you owe 5: break-even 33.3%. In the small blind the pot is the same 10, but you have only 1 chip out there, so you owe 6: break-even 37.5%. The small blind gets a worse price than the big blind, on the same hand, against the same raise.

Three things stack up in the same direction:

• Worse price, as above.
• You do not close the action. Call, and the big blind is still to speak — and can squeeze. You have paid without buying certainty.
• Worst seat postflop. You act first on every street, ahead of both the raiser and the big blind.

So the small blind's defending range wants to be shaped differently from the big blind's: fewer flat calls, more of a split between re-raising and folding.

The reference table is shaped exactly that way, and you can go read it. A♥A♦K♥K♦ and K♠Q♠J♥T♥ three-bet. J♠T♠9♥8♥ sits on the boundary — three-bet or fold, both defensible. And here is the pair worth staring at: 8♠7♠6♥5♥ defends by calling in the big blind and is a fold in the small blind. Same hand, same raise, one seat apart.

From the small blind facing an open, three-bet or fold rather than flat calling.

Six-handed, around 100 big blinds, facing a late-position open with the big blind still to act behind you.

Notice what the table is: a curated reference range that agrees with the shape argument above, not a measurement of how often to do anything — and the missing calling tier is a modelling decision of ours, not a discovery. The rule also breaks in two ordinary spots. Deeper stacks reward implied odds, so calling with a hand that flops big gets better rather than worse. And a big blind who almost never squeezes removes the second reason entirely. Run this as a lean, not a law — "only aces from the small blind" is exactly the over-fold this lesson is trying to prevent.

What to take away

• Pot odds are a floor, not a filter. The price in the big blind is 33.3%; even 2♣2♦3♥3♠ clears it at 37.1%, and the table still defends only 36.1%.
• What actually decides it is realisation. Out of position, against the betting lead, you keep far less of your equity than the number says.
• The defending range splits about one to three. 10% three-bets, the rest calls — and the split is by structure, not by equity: 47.8% can rank below 45.5%.
• The small blind is a different problem at a worse price (37.5%), and one we do not have a table for yet.

Next lesson takes the three-betting half of this and asks what it is actually for — because the answer you brought with you is the wrong one.