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  3. Zen Mahjong: Part I - Perfect
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  6.  
  7. Zen Mahjong is a thought experiment that arose from a simple question: "Is a perfect game of
  8. mahjong possible?" As it turns out, that question has a very simple null hypothesis answer.
  9. With a ruleset that allows busting, a Tenhou + 1 Double Yakuman tsumo on the first turn would
  10. result in the simultaneous busting of all three other players, and would constitute a perfect game.
  11.  
  12. With that out of the way, we can begin asking ourselves the real tough questions. "When does a
  13. perfect game cease to be perfect?" and "What constitutes a perfect play?" To answer these
  14. questions, we need to dive into and explore exactly what we mean when we say "perfect" when talking
  15. about games. To do that, we need to define some axioms, which will prove to be the pillars and
  16. foundation for Zen Mahjong.
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  18. ---------------------------------------------------------------------------------------------------
  19.  
  20. "Perfect" doesn't always mean perfect
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  22. When I was a young lad, I was fascinated to death with a mini-game NPC that exists in the video
  23. game Tales of Phantasia. If my memory serves me correctly, this certain NPC appears in the past
  24. city of Alvanista, and challenges you to a game he calls "Ishi-Tori". The premise of the game is
  25. simple; starting with a randomised number of counters, take turns pilfering either one, two, or
  26. three counters from the community pot. The last person who takes a counter is the loser.
  27.  
  28. Beating the so called "Ishi-Tori" master was quite challenging for my infant brain. The NPC seemed
  29. to play flawlessly every time, and I always ended up being the one to take the last counter.
  30. Frustrated, I swallowed my pride and went online to find a perfect strategy to defeat the NPC. The
  31. strategy, which seems so obvious to me today was roughly as follows:
  32.  
  33. "The number of counters at the beginning of the game will always be of the form (x * 4) + 1. When
  34. challenging the Ishi-Tori master, always elect to go second. When the Ishi-Tori master takes his
  35. turn, note how many counters Y he takes. Then, simply take (4 - Y) counters from the community
  36. pot. The Ishi-Tori master will be forced into taking the last counter every time."
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  39.  
  40. I. Axioms
  41.   a.)
  42.   b.)
  43.   c.) tales of phantasia ishitori
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  45. ---------------------------------------------------------------------------------------------------
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  48.  
  49. A famous mahjong pro once stated that a WWYD problem has no correct answer, since the correct
  50. answer would always depend on the players that you're playing against. While this statement is
  51. almost always true, it is vacuously incorrect; there are obvious edge cases. The Double Yakuman
  52. tsumo, for example, is a WWYD problem with only one answer; take the tsumo! Sure, you might be able
  53. to win the hanchan without taking the Yakuman tsumo, in the same way that you might be able to win
  54. a chess game without taking a forced checkmate
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  56.  
  57.  
  58.  
  59. II. The Fundamental Theorem of Mahjong
  60.  
  61. III. Practical Results
  62.  
  63. Axioms:
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  65. Playing "the game" perfectly vs. playing "that game" perfectly.
  66.  
  67. Practical Results:
  68.  
  69.   - EV Calculator for riichi battles that has.
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