A Third Cousin of Nim

A slight modification of an earlier puzzle: From a pile of checkers, each player removes one, two or three checkers but is forbidden to take the same number of checkers removed by the previous opponent. The player who takes the last checker or is prevented from playing loses. There are originally 30 checkers in the pile. What is the best strategy to assure you won't lose in a 2-player game? In a 3-player game? What if there are N checkers to begin?

Source: Original. Based on Nim puzzles from four and two years ago.

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