This little book comes out of an evening at the table. Every example in it is a real hand played in this room against the ship's own bot — a bot whose preflop play is solved (it plays Cepheus's published strategy, the program that essentially closed heads-up limit hold'em in 2015) and whose river play is computed exactly, hand by hand, while you sit there deciding. When the chart in these pages says check 98%, that is not a pundit's opinion. It is what equilibrium does.
You could read a hundred strategy books and not find that sentence. Poker literature is mostly folklore — good folklore, tested folklore, but folklore: distilled experience, argued by analogy. This room is different. The game you practice here has been solved by machines, the solution is wired into the table you play on, and a meter measures — exactly, in big blinds — what your decisions cost against it. The folklore era gave us maxims. The solver era lets us check which maxims were true.
It turns out the true ones fit in one short book.
Everything else is commentary.
Before any bet you ever make, there is one question, and this book is mostly that question wearing different hats:
A bet earns money in exactly two ways. Either a worse hand pays it — that's a value bet — or a better hand folds to it — that's a bluff. That's the whole list. A bet that does neither — that folds out only the hands you already beat and gets called only by hands that beat you — is not aggression. It is a donation with good posture.
From this one question, the entire shape of correct play unfolds into three families:
Players lose most of their money by misfiling the middle. The anxious instinct with a mediocre pair is to bet it — “to find out where I stand,” “to protect it.” The chart's cold answer, hand after hand: stand still. You find out where you stand for free at showdown. What follows are four hands from one evening that teach the three families and their consequences better than any abstraction could.
Second pair, out of position, and the urge to “find out.”
Second pair on a king-high board is the textbook middle. Run the question: who pays a bet? Every king calls and beats you. Fives and tens have you in bad shape or crushed. And everything you're ahead of — queen-high, jack-high, the whiffed connectors — folds the moment you bet, paying you nothing. The bet can't get value and can't bluff anything out that mattered. It only builds a pot for the times you're behind.
The check, meanwhile, is not surrender. It is a trap with the safety off. Your opponent's range is full of exactly that air you can't get paid by — and air wants to bluff at a checked flop. Second pair is a premium bluff-catcher: it beats every bluff he can invent. So you check, he stabs, and you call — and his bluffs, which would have folded to your bet for free, pay you a street of value instead.
When he did bet that flop, the chart read: fold 0% · call 90% · raise 10%. Fold zero — you're getting five to one against a range bloated with worse. Call ninety — raising would just re-open the betting and fold out the very bluffs you fished for. The plan begun by checking is completed by calling. The middle stands still, twice.
The same two cards are not the same hand on every street.
The jack of spades fell, and the chart flipped from near-pure passivity to near-pure aggression with the same two cards. Nothing is inconsistent. The hand changed category. Count what that one card did: the 9♠ now carries a flush draw (nine outs), the 9-10 now needs one queen for a straight (four more), and the pair of tens still beats all his air. Roughly a third of the deck now improves you to a hand that beats nearly everything.
That class of holding — big equity, not yet best — is the semi-bluff, and it is the happiest hand in poker, because it profits both ways. When he folds, you win a pot you had no right to yet. When he calls, you're drawing at a third of the deck with the pot already swollen. Compare the flop bet we refused: that one had neither consolation. The middle checks; the draw bets. Same cards, different street, opposite family.
Junk, therefore weapon.
The natural read of seven-high is “junk, give up.” The chart folds it two percent of the time. Two percent! The rest divides between calling — you're getting five to one, and any six makes you a straight nobody will see coming — and, remarkably, raising almost half the time. Understand why, and you understand bluffing better than most people who play for money.
An equilibrium strategy must bluff — if its raises were only ever strong, opponents could fold everything else and never pay them. So it needs bluff candidates, and it chooses them by three criteria. First, no showdown value to waste: a hand like ace-high wins showdowns, so spending it as a bluff throws away real equity; seven-high has nothing to waste. Second, outs as a backup: when the bluff gets called, the gutshot still arrives sometimes, and arrives disguised. Third, no blockers to his folds: seven-five holds none of the cards he needs to have in the hands you want him to fold. Your worst holdings meet all three tests. The almost-good ones fail the first.
The outs are spent. What remains is the truth.
On the river there are no more outs, no more categories to change into. Every hand is finally just a number. And the chart — which on this street is an exact solve of your hand against his precise range — says something that looks like a misprint: call thirty percent. With seven-high.
It is not a misprint; it is the sharpest lesson in the book. Showdown value is relative, not absolute. To call a river bet you don't need a good hand — you need to beat his bluffs, and his bluffs are drawn from the same population as yours: busted draws. On this board his bluffing range is full of six-five, five-trey, missed hearts — and seven-high is a monarch among busted draws. The solver counted his exact combos against your exact cards and found that, at nine to one, calling with the best of the trash shows a profit. Folding is still the headline — the bluff's story failed, and 53% of the time you accept that. And 18% of the time seven-high tells one last lie, raising to fold out the thin hands that beat you at showdown.
Three actions, all correct. Which brings us to the strangest habit of solved poker.
What 53/30/18 actually asks of you.
When the chart splits an action three ways, it is not hedging. At equilibrium, every action it mixes has exactly equal expected value — that equality is the mathematical condition that makes the strategy unexploitable. The mixing exists to deny your opponent information: if you raised every strong hand and folded every weak one, your frequencies would tell him what you hold.
This licenses two practical rules that sound contradictory and aren't:
The expensive decisions are neither of these. They are the 98/2 spots where you take the 2. Which is why this room has a meter.
Results are luck-soaked. Decisions are not.
A poker result tells you almost nothing — a 40-hand match between a master and a novice is close to a coin flip. This is poker's great pedagogical curse: the feedback is a liar. Chess punishes your blunder on the spot; poker pays your blunders for weeks, then fines your best play, and lets you learn the wrong lesson from both.
The Wardroom's answer is to grade the decision, not the result. On every river you play, the exact solver computes what each action was worth against the opponent's real range and charges you the difference between what you chose and the best available, in big blinds. The running total, per hundred hands, is your leak — the 🎯 number in the top bar. It cannot be flattered by winning or slandered by losing. It is the rate at which you give chips away, measured in the only currency that compounds.
| Player | River leak, bb/100 |
|---|---|
| Cepheus (solved play) | ~0.1 |
| This room's bot | ~0 by construction |
| Estimated peak humans | 1–5 |
| The historical pro bar | < 5 |
The training loop, then — the whole method of this room in four steps:
Do this for an evening and you'll have what almost no poker player in history had before 2015: an exact, luck-free measurement of your own skill, drifting downward as you learn. Keep it under five and you are making decisions at a rate the folklore era would have called professional.
Why learn a solved game first.
Fixed-limit heads-up is the right first game precisely because it is solved and small: the bets are fixed, so every lesson is about frequencies — when to bet, not how much. That is the skeleton of all poker. No-limit adds one enormous axis — bet sizing — which roughly doubles the theory but changes none of the bones. Ranges, polarization, bluff-candidate selection, relative showdown value: everything in this book survives the crossing intact.
When you're ready for the crossing, the advanced shelf, in reading order:
A field guide to the instruments.
| Instrument | What it does | Key |
|---|---|---|
| 💡 hint | shows the chart's mix for one decision (flagged, not counted) | |
| 🎓 coach | shows the mix on every decision — training wheels | 4 |
| 🎯 leak chip | live running river leak, bb/100 | 5 |
| 📋 chart room | accuracy, leak headline, every graded decision | |
| scorecard | on the trophy screen: hand · cards · river EV paid; click any row to replay | |
| 📋 copy (in replay) | the annotated hand as plain text, for any analyst | |
| 🏅 rated | assistance structurally removed; your rating on the line; everything revealed only after | |
| fold / call / raise | the only three verbs in the language | 1 2 3 |
One habit recommendation to close. Play your learning sessions casual with the coach off and the leak chip on — make real decisions, watch the real bill. Save the coach for reviewing concepts, and save rated for when you want your number to mean something. The chart will still be there when the hand is over, patient as arithmetic, ready to tell you who was supposed to pay.
⚓
written aboard, between hands