Your coach

The book, as something you can ask — and the solver that graded it, as something you can run. Paste your table below and the same machinery that graded every problem and puzzle in the book ranks your legal first plays. Ask the coach for rules, rulings and the measured numbers.

What the solver is

It is the machinery of Chapter 3, unchanged: paired rollouts under common random numbers over the evolved policy's candidate plays, with the per-player-count weights the book was written from, under Hasbro's 2024 rules. It plays your position out from every candidate first play with the same shuffles and the same opponents, so the differences between plays are measured far more tightly than the levels are, and it reports both. This is the promise printed in the book: the solver that graded every problem and puzzle in it will grade your table.

What it is not is an oracle. Every estimate arrives with the number of rollouts behind it and a 95% margin, and at the sample size a web request can afford, a single play's estimate is worth about seven points either way while the gap between two plays is worth two or three. Trust the ranking before the decimals. It also grades the first play and lets the policy finish the turn, so it can miss a win that needs two plays in the right order — the case Chapter 15's Puzzle 11 is about. Look for one yourself.

Programs are welcome: POST /play/api/solve takes the position notation directly and GET /play/api/solve returns the schema, the limits and an example. No key, no sign-in, a few requests a minute per address, and nothing that identifies anyone is logged.

What the coach does

• Rules, from the current sheet. Hasbro's 2024 instruction sheet (G0351) is the printed rule, and the coach quotes it. Chapter 1 fills in what the sheet leaves implicit.
• The rulings nobody has settled. Eight questions went unanswered in print for fifteen years. The 2024 sheet settled four. For the other four the coach will tell you plainly that Hasbro has never settled it, what Hasbro has said and when, how this book plays it, and that you should agree at the start of the game rather than in the middle of a hand. It also knows the finding that ends most of those arguments: settle them whichever way you like and no headline number moves by more than 0.14 points.
• Strategy with the number attached. Ask whether to bank before you build and you get the chapter, the measured cost at every player count, the experiment ID, and the 95% confidence interval from the results log — not a rule of thumb.
• Your table, graded. The coach reads a position and tells you which play the book's rules point at and why. For a number on that play it sends you to the grader at the top of this page, which is the solver itself. The coach does not estimate; the solver measures.

What it will not do

The coach will not invent a number. Every figure it gives is read off the manuscript, the 2024 rulebook, the claim verdicts or the results log, with its player count and its margin, and it is under instruction never to estimate one, never to carry a number to a player count it was not measured at, and never to round a margin away. Ask it something the study did not measure and the answer is that the book does not measure it.

The coach is not the solver, and it cannot run it. Galley, which hosts the coach, gives a book's bot no way to call an outside service mid-conversation, so rather than let it approximate one we kept the two apart: the coach quotes a printed solver estimate as printed and names the puzzle it came from, and for a new position it points here. A grade from this page says how many rollouts it ran; a number from the book says which puzzle it was printed in. Those are different things and neither is dressed up as the other.

What is open, and the one thing that is not

Everything above is open to anyone, signed in or not. The grader, the rules, the rulings, the strategy with its numbers, and your table graded. That is the whole coach, and it is the bonus the book promises.

One thing sits behind the book, because it is the book: the problems at the end of every chapter and the twenty puzzles of Chapter 15, worked through with the solver estimates printed beside them. Tell the coach you have the book and it will ask for a photo of a receipt or an order page. The image is read and thrown away; what is kept is a score and a hash of the order number, which is what stops the same receipt being used twice. It is a one-time thing and it does not expire.

Try the coach

• Does a Just Say No on my own turn cost a play?
• Can two Double the Rents make it ×4?
• How much does banking before building cost?
• Whom should I charge first?
• Walk me through a puzzle

Where its answers come from

Four documents, and nothing else: the manuscript; Hasbro's 2024 instruction sheet; the claim-verdict tables, which score every community claim at two, three, four and five players; and the results log, which carries all 861 measured cells with their sizes and margins. The last two are on this site in full — the results log, the claim verdicts and the rulings tracker — and the site is the living record. The numbers in the printed book were frozen at press; the site's move.

One example, from Chapter 8

Two players, turn 10, and you are behind, holding a Forced Deal; on your table sit an Orange, a Red, a Yellow, a Light Blue/Brown wild and a Railroad/Utility wild, and his Green is the one card that would complete your set. Give the Light Blue/Brown wild for the Green and the solver scores it 62.5%; give the Orange, the Red or the Yellow and it is 50.0%; give the Railroad/Utility wild, which is the folk play, and it is 37.5%, worst of the lot, because his Utility is one card from a set of its own. It is about what you give, not what you take. That is the kind of turn the book was written for, and the kind to bring the coach.

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