Nim games are two player strategy games where players take turns removing objects by some rules until none remain.
For this version, place N counters in a row numbered 1 to N.
A player's turn consists of taking either one counter or two counters from consecutive positions.
Whomever takes the last counter loses (this is called a misère game.)
If you were to play this game, for what values of N would you prefer go first and what should be your first move?
For N<9 I would want to go first except for N=1 and N=4
My opening move for N=2 is (naturally) to remove 1 object
My opening move for N=3,5,6,7,8 would be to remove the
center object for odd N and the center 2 objects for even N.
I should state this more strongly: given my play, I would be guaranteed a win. Against a reasonable player, starting with N=4, I would lose.
I think things may change starting at N>8, but I
am still working on it... TBC
Edited on December 16, 2021, 11:37 am
partial soln
