SPR and Commitment

You cannot shove

The SPR — stack-to-pot ratio — is the effective stack behind divided by the pot, and in pot-limit it decides something no amount of courage can override. Here is the largest bet available at each ratio, with a pot of 100:

• SPR 1: bet 100, which is 100% of your stack. All in, and the ratio behind is 0.
• SPR 1.5: 67% of your stack. Ratio behind after a call: 0.17.
• SPR 2: 50%. Behind: 0.33.
• SPR 4: 25%. Behind: 1.
• SPR 8: 13%. Behind: 2.33.
• SPR 13: 8%. Behind: 4.

Rule of the game: a bet may not exceed the pot. In no-limit any stack can go in at any time, which is why the phrase "shove or fold" exists at all.

Every figure above came out of js/core/plo-pot.js, the same legal-raise calculator behind the pot-odds lesson, whose formula was verified against three independent public rule pages (docs/M2-SOURCES.md, section T20).

Above SPR 1, going all in is not an available action. Plan in streets, not in one motion.

Pot-limit, and when nobody has bet yet on this street. A raise can be larger than a bet, but it is still capped by the same rule.

SPR 4 is the depth at which players say "we are short, let us just get it in". The largest thing you can actually do there is 25% of your stack, and after it is called there is still a full pot behind. Nothing got resolved.

The ladder: 1, 4, 13, 40

Bet the whole pot and get called. The pot triples and your stack drops by one pot, so the new ratio is the old one minus one, divided by three. Iterate that and you get the only four numbers you need:

• All in on one street: SPR up to 1.
• Two streets: up to 4.
• Three streets: up to 13.
• Four streets: up to 40 — and postflop has only 3 streets, so that row is a fact about arithmetic, not about poker.

This is our own derivation, checked line by line against the betting calculator. It is not a piece of received wisdom and we are not citing anyone for it.

To have any chance of playing for stacks by the river, you need a flop SPR of 13 or less. Above that, three full-pot bets in a row still do not get there.

Pot-limit, every street bet full pot, every bet called. It is an upper bound on what is reachable, not a recommendation to bet that way.

It does not follow that you must bet full pot every street. From a flop SPR of 8 the sequence runs 8 → 2.33 → 0.44: by the river you are all in with room to spare, so there was slack for a smaller bet somewhere. At 13 the sequence is 13 → 4 → 1, exactly on the line, and there is none. At 20 it is 20 → 6.33 → 1.78 and the plan was never available.

Three bands, and what commitment costs

Our three bands: at SPR 1.5 or below, commitment is mechanical — the money is going in and the only question is with what. Between 1.5 and 4 it is planned: you decide on the flop and execute on the turn. Above 4 you have a genuine three-street game.

The lower edge is 1.5 rather than 1 because at 1.5 one full-pot bet, called, leaves 0.17 — seventeen percent of a pot behind, which is no folding room at all.

What it costs to call off the whole stack at each of those ratios. One caveat this course owes you: beyond one pot deep, that money cannot arrive as a single all-in bet — pot-limit caps any bet at the size of the pot — so a deep stack goes in across streets, not in one shove. The price is the same either way; the number of decisions it takes to get there is not.

• SPR 0.5 → 25.0% · 1 → 33.3% · 1.5 → 37.5% · 2 → 40.0%
• SPR 3 → 42.9% · 4 → 44.4% · 6 → 46.2% · 10 → 47.6%

SPR decides whether a hand can be played to the end. It does not decide whether it should be.

Heads up only. A pure draw at the mechanical band is exempt: there the question is not commitment but whether to attack at all, and that is the previous lesson's threshold.

One ratio, two opposite answers. At SPR 4 on 9♥8♦2♣: J♠T♥7♦6♣ (20/14) is 54.9% against the proxy range, so building the pot now means the turn finishes it. 7♣6♥5♦4♠ (13/3) is 38.2%, and the same bet builds a pot it will have to fold on the turn. A rule that reads only the ratio is wrong at every value you could pick for it.

What to take away, and what we did not measure

• Shoving does not exist above SPR 1. Plan in streets.
• The ladder is 13 for three streets. Above it, stacks do not go in however hard you try.
• Three bands: 1.5 and 4. Mechanical, planned, and a real three-street game.
• The ratio never decides alone. Two draws at the same ratio wanted opposite actions.

What this course will not tell you: where those band edges move in a multiway pot. We have never measured it, so we give no number — inventing an adjustment factor would be exactly the kind of made-up figure this product exists to avoid. A measured calibration needs multiway equity and a multiway betting tree, neither of which we have, and there is no date on either. Until then, treat the bands as heads-up numbers and adjust through the nut requirement instead.

What we can give you is three things we did measure, all by full enumeration:

• With 4 opponents holding trips or better, somebody actually has the absolute nuts only 29.3% of the time (250 river boards, all 178,365 hands enumerated per board, opponents treated as independent). More players does not mean somebody has it.
• A nut wrap does not lose value multiway. J♠T♥7♦6♣ against top set is 54.4%; add a middle set and it goes up to 57.2% over all 666 run-outs, because the two sets take chips from each other.
• A dominated draw is halved. 7♣6♥5♦4♠ against top set is 43.9%; add a nut wrap and it falls to 20.9% in the same 3-way spot.

The mechanism in one line — and like everything else here it is a rule of this course, not an equilibrium solution: extra players do not change the arithmetic of SPR, they change the chance that somebody is contesting the same nuts you are. Which is why multiway adjustments belong to the nut requirement and not to the bands.