The Turn: Barrel, Give Up, Build

One card, one division

The turn is where the arithmetic gets simple and the mistakes get expensive. There is exactly one card left, and there are exactly 44 cards you have not seen. So the chance a draw arrives is the number of outs divided by 44 — no rules of thumb, no doubling, one division:

• 8 outs: 18.2%.
• 13 outs: 29.5%.
• 17 outs: 38.6%.
• 20 outs: 45.5%.

Put that beside the price. Half pot asks for 25.0%, three-quarters asks 30.0%, a full pot asks 33.3%. A thirteen-out draw facing a pot-sized turn bet is short — 29.5% against 33.3% — and a seventeen-out draw is not.

On the turn, compare two numbers and stop. The count of outs over 44, against the price the bet is asking. Everything else on this street is a refinement of that comparison, not a replacement for it.

Facing one bet on the turn with a hand whose value is its draw. If your hand also wins some pots unimproved, the comparison understates you and you should be looking for reasons to continue, not to fold.

The comparison is not the whole decision, and the case where it lies is common: the same 13-out draw that folds for 33.3% is a clear call when the two of you are deep enough that arriving wins his stack rather than the current pot. That is implied odds, and the next page says exactly how far we are willing to go with it.

The single-card probabilities come from js/content/postflop-rules.js; the prices come from js/core/plo-pot.js, the same legal-raise calculator behind the pot-odds lesson.

If you want the river all-in, the flop is where you start

Pot-limit takes the sizing decision away from you at the top end, and that turns "how do I get all the money in" into arithmetic. Start with a pot of 100 and bet the maximum every street, each one called:

• Flop: bet 100.
• Turn: bet 300.
• River: bet 900. Final pot 2700.

So the stack-to-pot ratio you can still finish inside 3 streets depends entirely on the size you choose, and the dependence is brutal:

• Full pot every street: up to 13.
• Three-quarters: up to 7.31.
• Half: up to 3.5.
• One-third: up to 1.81.

Reading down that list is reading the price of small bets. Betting maximum, one street gets you in at 1, two at 4, three at 13, four at 40. Betting half pot, three streets only reach 3.5 — a quarter of the range.

Rule of the game: a bet may not exceed the pot, so the largest bet available is computed, not chosen. In no-limit the same plan can be executed from any depth by simply betting more; here the ladder above is a hard ceiling.

The amounts come from js/core/plo-pot.js and the ladder is a derivation of this project, checked against that calculator street by street (docs/POSTFLOP-RULES.md).

Decide on the flop how the stack is supposed to end up, then pick the size that gets it there. If the answer is "all-in by the river", small bets on the flop have already made that impossible.

Whenever you hold a hand that wants the stack in and the ratio is above the mechanical band — that is, whenever you actually have a choice.

The ladder is not an argument for always betting the maximum. It is an argument for betting the size your plan needs: if the plan is two streets and then giving up, betting 100 into 100 builds a pot you will have to abandon. The mistake it does rule out is the popular one — habitually betting small when stacks are deep, which quietly removes the option of ever getting the money in.

Giving up, and the number we will not give you

Two-thirds of the hands you barrel on the turn should end there, and the reason is on the previous page: the turn bet is 300 into 300, so a third barrel commits a stack. The question is which hands are allowed to continue, and it splits cleanly in two.

The part we can compute. A draw with 13 outs arrives 29.5% of the time and a pot-sized bet asks 33.3%. Against the pot in front of you, that is a fold. It is a fold at any depth, on any board, against anybody — the two numbers do not care.

The part we cannot. The reason people call anyway is that arriving does not just win the current pot; it wins some of what is still behind. At a ratio of 13 there is a lot behind. How much of it you actually collect depends on how often he pays you when you get there, how often you are drawing to the second-best hand, and how often the card that helps you kills his willingness to continue.

This project has never calibrated implied odds, so this course does not give you a number for them — not a multiplier, not a rule for how many outs it is worth, not a discount table. Doing that honestly needs to know what an opponent actually holds on the turn, and that is data we do not have and will not fake. There is no date on it, and the postflop range work it depends on does not exist in this project at all; until it does, this course tells you the direction and refuses to tell you the size.

Take the fold the price hands you unless you can say, in one sentence, what you expect to collect that is not in the pot yet. If you cannot finish that sentence, the sentence is the answer.

Turn, heads up, facing a bet with a hand that is a draw and nothing else.

The rule cuts the other way too, and this is the failure people never notice. When his stack is short enough that arriving wins almost nothing extra, the price comparison is generous rather than strict — and the same 13-out hand that everybody calls with in a deep game should be folding without a second thought.

What to take away

• One card, 44 unseen, one division. Thirteen outs is 29.5%, seventeen is 38.6%, and a pot-sized bet asks 33.3%.
• The size you pick on the flop decides whether the river can be all-in. Maximum bets reach a ratio of 13; half-pot bets reach 3.5.
• The turn barrel is 300 into 300. By the time you fire it you are choosing whether the stack goes in, so choose that on the flop.
• Implied odds get a direction from us, never a number. We have not calibrated them and will not invent a multiplier.

The ladder and the prices are arithmetic done with our own pot calculator; the thresholds are rules of this course, not an equilibrium solution. Next: the street where nothing else is coming.