Saki’s epic win over Koromo in episode 19 was unquestionably amazing, with lots of lens flare, typhoons back and forth across the mahjong table, fiery Terminator eyeball glare, and LOL MAHJONG IS FUN LOL. It was also completely ridiculous and unrealistic (surprise!).

Obviously that’s par for the course with this series, when we’ve just seen a hanchan played that had multiple haitei raoyue (bottom of the ocean) and rinshan kaihou (drawing your winning tile from the dead wall after a kan) declarations made. I was curious, though, just how unlikely this last game really was.

Warning – lots of mahjong diagrams and math ahead. Read on if you have questions about what exactly happened in that last round of Saki 19, or if you’re curious about just how incredibly unlikely Saki’s win really was. If you don’t care about any of that, go ahead and just go straight to the end for the fanservice pictures.

OK, so first let’s consider Saki’s hand on the final turn of the game, and the sequence of events that leads up to her absolutely ridiculous win over Koromo. You can skip past this and right to the math if you already understand the details of what happened in that last game. This is Saki’s hand on the final turn, right before Koromo discarded:

So she’s in tenpai (needs only one tile to win) for a chinitsu hand (all one-suit), and she’s waiting on either a 1-pin or 4-pin. Basically, if she gets 4-pin she can win like this: Read the rest of this entry »