We Solved the Worst Minigame in Zelda's History (2020) [YouTube]

[This is a rough summary of the video, which explains things much more clearly and thoroughly (using animated plots). I have no affiliation with the creators of the video.]

The goal is to be able to quickly solve a particular mini-game (Sploosh Kaboom) in the game The Legend of Zelda: The Wind Waker (WW). Sploosh Kaboom is like a 1 player version of battleships.

WW uses the Wichmann-Hill random number generator, and always seeds it with (100, 100, 100). A single generator is used globally for all kinds of things, and each call causes the generator state to update.

One of the things the generator is used for is to determine the (hidden) position of the 'squids' in Sploosh Kaboom.

However, on average, each frame of WW calls Wichmann-Hill dozens of times. It isn't possible to know exactly where in the sequence of generated numbers we are.

However, given the time that the game has been running for, and the first state of the game Sploosh Kaboom, it is possible to massively narrow down the estimate of where in the random number generator the game is (although there may be multiple gaussian curves on the line of possible positions in the sequence).

By then trying out different squares on the Sploosh Kaboom board it is possible to determine where in the sequence of random numbers we are, and determine the state of the board before it is fully revealed (allowing the mini-game to be beaten).