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Zen Mahjong: Part I - Perfect

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Zen Mahjong is a thought experiment that arose from a simple question: "Is a perfect game of
mahjong possible?" As it turns out, that question has a very simple null hypothesis answer.
With a ruleset that allows busting, a Tenhou + 1 Double Yakuman tsumo on the first turn would
result in the simultaneous busting of all three other players, and would constitute a perfect game.

With that out of the way, we can begin asking ourselves the real tough questions. "When does a
perfect game cease to be perfect?" and "What constitutes a perfect play?" To answer these
questions, we need to dive into and explore exactly what we mean when we say "perfect" when talking
about games. To do that, we need to define some axioms, which will prove to be the pillars and
foundation for Zen Mahjong.

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"Perfect" doesn't always mean perfect

When I was a young lad, I was fascinated to death with a mini-game NPC that exists in the video
game Tales of Phantasia. If my memory serves me correctly, this certain NPC appears in the past
city of Alvanista, and challenges you to a game he calls "Ishi-Tori". The premise of the game is
simple; starting with a randomised number of counters, take turns pilfering either one, two, or
three counters from the community pot. The last person who takes a counter is the loser.

Beating the so called "Ishi-Tori" master was quite challenging for my infant brain. The NPC seemed
to play flawlessly every time, and I always ended up being the one to take the last counter.
Frustrated, I swallowed my pride and went online to find a perfect strategy to defeat the NPC. The
strategy, which seems so obvious to me today was roughly as follows:

"The number of counters at the beginning of the game will always be of the form (x * 4) + 1. When
challenging the Ishi-Tori master, always elect to go second. When the Ishi-Tori master takes his
turn, note how many counters Y he takes. Then, simply take (4 - Y) counters from the community
pot. The Ishi-Tori master will be forced into taking the last counter every time."



I. Axioms
  a.)
  b.)
  c.) tales of phantasia ishitori

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A famous mahjong pro once stated that a WWYD problem has no correct answer, since the correct
answer would always depend on the players that you're playing against. While this statement is
almost always true, it is vacuously incorrect; there are obvious edge cases. The Double Yakuman
tsumo, for example, is a WWYD problem with only one answer; take the tsumo! Sure, you might be able
to win the hanchan without taking the Yakuman tsumo, in the same way that you might be able to win
a chess game without taking a forced checkmate




II. The Fundamental Theorem of Mahjong

III. Practical Results

Axioms:

Playing "the game" perfectly vs. playing "that game" perfectly.

Practical Results:

  - EV Calculator for riichi battles that has.