Planning a Whole Hand

The ratio is set before the flop

Full-street practice in this course is a heads-up table: two seats, and the button is the small blind. Both stacks are 100 big blinds; the blinds are 0.5 and 1. Nothing below is a matter of taste — every raise size on this page is the pot-limit maximum, computed rather than chosen.

Rule of the game: the largest legal raise is your own current bet, plus the pot, plus twice what you owe. A raise size in pot-limit is therefore a fact about the pot, not a style.

Computed by js/core/plo-pot.js — the same function that draws the ceiling on the Bet button in full-street play, so the numbers on this page and the numbers on that screen cannot drift apart.

Three preflop lines, each raise at the maximum. Both players end up matching, so the flop pot is twice the last number:

• Button opens to 3, big blind calls → flop pot 6, 97 behind, ratio 16.17.
• Big blind three-bets to 9, button calls → flop pot 18, 91 behind, ratio 5.06.
• Button four-bets to 27, big blind calls → flop pot 54, 73 behind, ratio 1.35.

Nobody has seen a card yet, and the ratios already span more than an order of magnitude: 16.17, 5.06, 1.35. Ask the rule layer how many more bets fit before the stacks are gone and the same three lines answer 4, 3 and 2. Each extra raise preflop deletes a street of postflop play.

Work out the flop ratio before you put the first chip in, not after the flop arrives.

Heads-up, 100 big blinds deep, every raise at the pot-limit maximum. Smaller raises land between these numbers, and a different stack depth moves all three of them; the arithmetic is the same, the values are not.

Low is not the same as good. At 1.35 the hand is only 2 bets long, which protects a hand that is already ahead and pins a hand that needed the flop to help it. The four-bet line commits you in both directions at once — which is exactly what the next page is about.

One hand, two flops, two games

Take A♥A♦K♥K♦ against J♣T♣9♠8♠ and deal two different flops. Each one is enumerated all the way to the river — 820 runouts per flop, no sampling, no estimate:

• 2♣7♦3♥ — the aces have 83.5%.
• 9♥8♦2♣ — the aces have 32.4%.

Same two hands, 51.1 points apart, and the only thing that changed is three cards on the table. That gap is the whole reason the ratio matters. A hand whose value is concentrated on a subset of flops wants a short tree: at 1.35 the hand is 2 bets long, so the flops where it is behind cost it less. A hand that needs the flop to arrive wants the opposite — at 16.17 there is room to fold cheaply on the bad flops and to build on the good ones.

Pick the preflop line by what the hand needs from the flop, not by how strong it looks before the flop.

Heads-up, both stacks deep enough that all three lines exist. The comparison above is exact for these two specific hands on these two specific flops; other pairs of hands move both numbers, and a pair of hands that runs close together everywhere barely moves at all.

"Aces always want a small ratio" is the version of this rule that costs money. On 9♥8♦2♣ the four-bet line locks 32.4% into a pot it cannot leave — a low ratio does not protect a hand that is already behind, it commits it. The rule is about the shape of the hand, not about the label on it, and these are the rules of this course, not an equilibrium solution.

Which decisions we can grade — and which we cannot

We ran the scripted opponent for 120 hands against a fixed probe — it calls whenever it faces a bet and alternates check and bet when nobody has — and counted every point where a player is asked to act. 505 decision points; 113 of the 120 hands went all the way to the river. Of those 505 points, 269 came back with a verdict. That is a judgement coverage of 53.3%.

Where the coverage is, and where it is not:

• Preflop — 148 points, all graded. There is a reference range table behind every preflop node on this table.
• Facing a bet — 56 points, 98.2% graded. Your equity against the opponent's range at that node and the price you are being laid are both computable. The single point that got nothing had too few live combinations left to call the remainder a range.
• The flop with nobody betting — 107 points, 61.7% graded. The rest fell outside the rule's own stated conditions: a paired board, a monotone board, a ratio too low — or you had already made a hand. That last one matters: the flop rule this course calibrated is a rule about draws. Ask it about a flopped set and its first hard gate (no outs to the nut straight) files the hand under “control the pot” — which would have us telling you that betting top set is wrong. It is not that we grade that leniently; we do not grade it at all.
• Leading the turn or the river, and every raise anywhere — 194 points, 0 graded. Not graded generously, not graded harshly: not graded.

That last line is the honest half of this trainer. Our rule layer is a set of classifiers, not a strategy. Ask it whether a draw may attack a flop and it answers; ask it whether you should bet this turn and it has nothing to say, because nothing in this project has ever calibrated that question. Grading you there would mean grading you against a script we wrote ourselves — you would be learning to guess our script, not to play. So those nodes show the facts we can actually compute (equity, outs, the nut ladder, the ratio) and no grade colour at all.

The rule layer refuses in smaller ways too, and you will meet them: a pure draw at a ratio of 1.35 gets no commitment band, because that band was only ever calibrated for hands that have something made. These are the rules of this course, not an equilibrium solution, and a rule that knows where it stops is worth more than one that always has an answer.

On a node marked as having no verdict, read the facts and ignore the missing colour.

The share above was measured with that one probe. A human plays a different mix of actions — more raises, fewer leads, or the other way round — so the share you personally see will differ. It is a property of the node you are standing on, not a score for the session.

"No verdict" does not mean "anything goes". The facts on the screen still rule some actions out: folding the effective nuts is wrong whether or not anything grades it, and the equity curve in the review will show you exactly where a line stopped making sense.

This course gives no grade on a turn lead, a river lead, or any raise. We have no calibrated criterion there, and inventing one would mean judging you against a script of our own making. There is no date on it, and it only happens if calibration data ever exists. One more limit belongs on this page rather than buried in a document: full-street play is a heads-up table, but the preflop tables it reads were built for a six-handed game. Real heads-up ranges are wider than that. It is a data limit of this version, not a claim about how heads-up should be played.

What to take away

• Four questions, in this order. What ratio did my preflop line just create? What does this hand want from the flop? Which kind of node am I standing on? How many bets are left?
• The ratio is preflop arithmetic. 16.17, 5.06, 1.35 — three lines, three different games, decided before a card is dealt.
• The same hand is not the same hand. Two flops, 51.1 points apart. Strength preflop tells you almost nothing about which flops you will still like.
• Know what the short tree asks. At 1.35 the hand is 2 bets long and getting the rest in needs 36.5%; that is a threshold for the chips, not a licence to shove.
• Know what we cannot grade. Judgement coverage was 53.3% on our probe, and the uncovered part is not random: turn and river leads, every raise, and a flop where you have already made a hand. On those, read the facts.

Every number above comes from js/core/plo-pot.js, js/core/plo-equity.js or a live run of js/fullstreet/engine.js, and each is locked into test/fixtures/learn-numbers-postflop.js by the same gate that guards the rest of this book. The thresholds are the rules of this course, not an equilibrium solution.