Problematics | Games with matches and jumbled scientists

While planning for your puzzles for the week, I came across an excellent variation of the well-known game ‘Nim’. After that, at every move, once the second player has taken away one, two or three matches, the first player repeats the strategy. They continue this way until only four matches remain; whatever number the second player takes now, the first player sweeps away the rest. If you start with a multiple of 4, the first player’s opening move will have no option but to take one, two or three matches, leaving a remainder that is not a multiple of 4. One, the first player cannot remove all the matches on their opening move, but can remove any other number.