Pot Odds and Call Discipline

Doing pot odds at the table

Pot odds is one division: what you must call, divided by what the pot will be after you call. That is the equity you need to break even. Working from a pot of 100:

• Quarter pot — call 25, need 16.7%.
• One-third pot — need 20.0%.
• Half pot — call 50, need 25.0%.
• Two-thirds pot — need 28.6%.
• Three-quarter pot — call 75, need 30.0%.
• Full pot — call 100, need 33.3%.

Rule of the arithmetic, and the one piece of this camp that is standard everywhere: required equity = amount to call ÷ (pot after your call). Nothing about Omaha changes it.

It is the same expression our rule layer uses to grade every odds question in this camp, and the same one behind the commitment table in the SPR lesson — one function, js/content/postflop-rules.js, so a change to it can never disagree with itself in four places.

Six numbers, and the useful thing about them is how close together they are. Everything from a quarter pot to a full pot lives between 16.7% and 33.3%.

The ceiling pot-limit gives you

The largest bet anybody can make is the pot. So facing a bet, the most equity you can ever be asked for is 33.3%. There is no sizing in this game that demands more of a caller.

Rule of the game: a bet may not exceed the size of the pot, and the largest legal raise always leaves the original bettor exactly the same price. In no-limit a single overbet removes this ceiling entirely.

Both numbers below come out of the legal-raise calculator, js/core/plo-pot.js, which was checked against three independent public rule pages before a line of it was written (docs/M2-SOURCES.md, section T20).

Watch it survive a raise. Pot 100, you bet 100, he makes the maximum raise to 400. You owe 300 into a pot that will be 900: 33.3%, exactly as before.

Facing a single bet — including the maximum raise back at you after you bet — 33.3% is a hard ceiling on the equity you need.

It holds for "he bets, you act" and for "you bet, he raises, you act". Both cases have your earlier money already working for you.

It breaks the moment a third player is involved and you have not acted yet. Same pot of 100, the first player bets 100, the second raises to 400, and now it is on you with nothing invested this street: you owe 400 into a pot that will be 1,000, and you need 40.0%. In a 3-way pot the ceiling protects whoever bet, not whoever is last to speak.

The band, and the number we do not have

J♠T♥6♣5♣ on 9♥8♦2♣ — 8 outs, all 8 nut outs — is worth 28.0% against top set, enumerated over all 2,625 of them. Now price it:

• Facing three-quarter pot you need 30.0%. You are short by 2.0 points.
• Facing a full pot you need 33.3%. You are short by 5.3 points.

Inside 3 points of the break-even line we call it a marginal spot rather than a call or a fold; outside it we commit.

Everywhere a threshold appears in this camp, so that a number sitting on a line never gets graded as if it were clearly on one side of it.

"Can I call with this hand" is a question missing an argument. Same hand, same board, same opponent: at three-quarter pot it is marginal, at a full pot it is a fold. Only the sizing moved.

One thing this course does not give you: implied odds. Putting a number on "what I win later when I hit" needs a model of how both players bet on future streets, and this project has no such model — so we say nothing rather than guess. There is no date on it. The full-street engine has since shipped and did not bring implied odds with it — a scripted opponent is not a range model, and only a range model could price this. Until then, treat every number in this lesson as the price of seeing the next card only.

What to take away

• One division. Amount to call, over the pot after your call.
• Half pot is 25.0%, full pot is 33.3%. Memorise those two and interpolate.
• Facing a bet, 33.3% is the ceiling. Facing a bet and a raise with nothing invested, it is not — that spot asked for 40.0%.
• Within 3 points of the line, nobody knows. Our all-nut eight-out draw at 28.0% is a genuine coin-toss of a decision at one sizing and a clear fold at another.

These are rules of this course, not an equilibrium solution — the band in particular is our choice about how precisely we are willing to claim to know something.

Pot odds tell you whether calling is profitable. They do not tell you whether attacking is. That is the next lesson, and it is the one that separates the players who survive Omaha from the ones who do not.