Think of a number, and keep a running total starting at 0. Each turn, add your number on to the total. Then, if the old total was a multiple of your number, add one to your number. Otherwise, subtract 1.
The game ends when your number is 1.

Which starting numbers eventually get to 1? In the video, it looks like starting at 4 doesn't, but starting at 2 does.

My new sequence, oeis.org/A338807, lists the numbers that eventually reach 1. I'd love to know if there's a pattern!

You could think of this game as "the Collatz sequence with a running total" - what happens next doesn't just depend on which number you're on now, it also depends on all the numbers you've seen before.

(my enemies might like to look at the editing history of the OEIS entry to see what a mare I had trying to compute it correctly and then format it properly)