Zelda speedrunners have long stumbled over a particular point in the 2002 game "Legend of Zelda: The Wind Waker". About thirty minutes into it, you have to play a minigame called "Sploosh Kaboom", which is basically a version of the famous board-game "Battleship".
The problem is, even when you're using optimum strategy in a Battleship-type game, it involves some random guessing — which means, in the case of Sploosh Kaboom, that in a majority of times you lose. This seriously slows down any attempt to speedrun the game, which is why speedrunners hate Sploosh Kaboom.
But recently a group of gamers did a close analysis of "The Wind Waker", examining how it generates the Sploosh Kaboom game boards. They learned how the game generates random numbers, the points in the game at which it generates a new Sploosh Kaboom board … and did some terrific statistical analysis.
The upshot is they created the "Sploosh Kaboom Probability Calculator", which anyone can use to help beat that minigame. Basically, when you reach Sploosh Kaboom, you input the information about your shots into the tool, and it crunches stats to help you predict — on the next board, and the next one — the location of your opponents. It rapidly narrows things down, so you can pass the minigame quickly.
The creators made that video, above, describing their reverse-engineering of the game's random-number generation and their statistical analysis. They're wonderfully clear — they get deep in the weeds but keep it so crisp and step-by-step that it's eminently follow-able.