The author

Keith Adler

Keith Adler writes fiction and non-fiction, and has an unhelpful habit of building the thing his books are arguing about before he will write a word of the argument.

He loves mathematics - his brother teaches it, so the arguing started early and has never entirely stopped - and he loves this game. The two are the same interest approached from different directions. Win at 3 Card Poker came out of wanting to know how something so simple has held casino floors for thirty years and kept both sides of the table coming back to it. That is a hard thing to design. It is worth understanding rather than resenting.

So the book is not an attack on the game. It is an admiring look at a very well-built machine, and at the small number of places where a player who pays attention does better than one who does not. He wrote the solver first - a program that counts every hand in the game against every hand that can beat it - and only then wrote the book, using what the count said rather than what gets repeated.

The aim is the most comprehensive analysis of Three Card Poker ever put together - the history, every jurisdiction it is spread in, the complete mathematics worked out from the deck up, and an honest account of where the game is weak and where it is not.

The solver is on this site as The Simulator, free to use any time, no account and nothing to install.

And every figure the book quotes can be checked. The enumeration is published as a standalone reference implementation in Python - plain, commented, standard library only - so that anyone who wants to audit a number can run it themselves rather than take it on trust. It is written independently of the code behind The Simulator, and a figure only appears in the book when the two agree exactly. Two programs reaching the same digits is worth more than one program being confident.

The project

The most comprehensive analysis of this game ever assembled - and all of it checkable.

Six hundred years of history, every jurisdiction the game is spread in, the complete mathematics counted rather than estimated, and a straight account of where it is weak. Nothing in it has to be taken on trust: the enumeration behind every figure is published as a reference implementation anyone can run, at github.com/keithadler/win-at-3-card-poker.

Use The Simulator free

Also by Keith Adler

The fiction

Novels, mostly about people in situations that do not have a clean way out.

Novel

The Aura Principle

Science fiction. Singapore, 2072.

theauraprinciple.com

Novel

The Saga for Donna

Akron, Ohio, summer 1987. A boy sent to live with an uncle he has never met, and the girl next door the book is named for.

thesagafordonna.com

Novel

Thirty-One Mirrors

A story told in reflections, and the one he is least willing to summarise.

thirtyonemirrors.com

Novel

Young Cop

The first, and the one the rest came out of.

youngcop.com

Each has its own site. Availability varies; several are in production.

On this book

Is this an advantage play book?

No. There is a part of it that looks at where the mathematics is weak, because that is the interesting question and because you cannot admire a design without knowing where it bends. But the motive is respect rather than exploitation. This game has held a floor for three decades and kept players sitting at it, which is a genuinely difficult thing to build - and taking it apart carefully is how you find out why it works.

Why a casino game?

Because it is small enough to be answered completely, and almost nobody has bothered. Three cards from fifty-two is twenty-two thousand one hundred hands. That is a number a computer can walk through exhaustively in under a second - so there is no reason to estimate anything, and yet estimates are mostly what is out there.

Does the book teach you to beat the game?

No, and it says so on the first page. Nothing beats the house edge at this game. What the book does is show the gap between playing it well and playing it the way almost everyone does, which is a real gap, a large one, and entirely inside the player's control.

Why the long history section?

Because the rule that makes this game work - the one about the dealer needing a certain hand to qualify - is not obvious, and it is a lot easier to understand once you know what the game is descended from and what problem its inventor was trying to solve. Six hundred years of cards turn out to be relevant to a decision you make in two seconds.

Why give The Simulator away?

Because a book full of numbers that you have to take on faith is a worse book. The Simulator runs the same computation the book is built on, in the browser, while you play. If a figure in the book is wrong, The Simulator will disagree with it - and I would rather find that out than not.

How do I get in touch?

contact@winat3cardpoker.com. I read everything, and I particularly want to hear two things: a figure you think is wrong, and a pay table or a house rule you have actually seen on a felt that this book does not cover. Both make the next edition better, and the first one makes it correct.