It's about time I claim my title as the Math gay. I just listened to a video about manipulating RNG in Paper Mario the Thousand Year Door (video here) and it is all about how the game calculates RNG values based on the previous value with a formula and the values are in a sequence so you can reverse engineer it to find where in the sequence it is as well as the current values position in the sequence.
Because the RNG value increments once with a jump or twice for every character of text on screen each frame, you can actually take specific actions in order to rapidly increment your RNG value and make the specific number of steps to get from the original value to the necessary one.
This turned what was a roughly 1/46000 chance into something they could guarantee and only waste 12 frames. All to get 2 fights to have Hammerbros holding Mega Rush badges. But now this can be used for so much more.
This has made my little math nerd heart very happy. This tech absolutely fascinates me. I love how games fake randomness and the brilliant people who reverse engineer it and make it bend to their wills.