Winning strategy for choosenim (n) player 2

None

Winning strategy for choosenim (n) for player one

On first move choose the multiple of n+1

Winning strategy for RNim (m,n) player 1

Has w.s. If m is not a multiple of one more than n+1. The strategy is to reduce m to one more than a multiple of n+1 on first move. Subsequent moves respond to j with (n+1)-j.

Winning strategy for RNim(n) player two

Has w.s. If m is a multiple of one more then n+1. The strategy is to respond to j with (n+1)-j.

Winning strategy for Nim(m,n) player one

Has w.s. If m is not a multiple of n+1. First move reduce running sum to a multiple of n+1. Subsequent moves respond to j with (n+1)-j.

Winning strategy for Nim(m,n) player 2

Has w.s. If m is a multiple of (n+1). Subsequent moves respond to j with (n+1)-j.

What does TFGWT stand for?

Totally Finite Games Without Ties

Properties of TFGWT

1- two players, I and II, move alternately, I going first.

2- no randomizing mechanisms are used

3- whenever a play ends, exactly one winner exists

4- each play ends after finitely many moves

5- at any moment in any play, there are only finitely many options for a legal next move.

Strategy in alternating move games

A set of rules that specify a single move for players for every partial play leading up to their turn.

Winning strategy in alternating move games

A strategy that is impossible for a player to lose a play of the game by following the rules.