A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG),[1] is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's seed (which may include truly random values). Although sequences that are closer to truly random can be generated using hardware random number generators, pseudorandom number generators are important in practice for their speed in number generation and their reproducibility.[2]
The random number generator is based mainly on the randomSeed value, found in the save file. The randomSeed is the main seed used for drawing cards, trader options, sigil odds, etc. This is shared between the main game and KCM.
The randomSeed value is incremented at certain points in the code after being used, but most of the time, when you exit a run and then continue, the randomSeed value is not changed. This is why your opening hand in battles normally does not change - the randomSeed value stays the same.
However, sometimes one of those events that increments the randomSeed is called, and the game saved. This is why on occasion, when save scumming, you end up with a new starting hand. Also, after your hand changes once, it usually stays that way - the game is now saved with the new randomSeed.
Unfortunately, we don't have a comprehensive list of what changes/saves the seed. This makes it difficult to purposefully avoid/force changes.
However, we did discover that at least previously, starting a new main game - going into the main menu > chapter select > and starting a game from Act 1 - would 100% reroll it, likely because the game uses the randomSeed when rolling map stuff for the new game.
Ultra save scumming
Start the battle and view your starting hand
Exit to the KCM main menu by using the “Start Screen” card in the pause menu
Exit to the base game by using the “Exit Mod” option in the KCM main menu
Use the chapter select (the SD card button) to start a new base game save
Exit to the main menu by using the “Start Screen” card in the pause menu
Use the red skull button to return to the KCM main menu
Continue your run
When you restart the battle, your topdeck will have changed.
See here for the discovery confirmation video, by ham#1234.
See here for a comparison to regular exiting/restarting. The video also demonstrates it happening twice in a row.