Suppose I'm forced to enter the game of nim with two players who are perfectly logical people. The rules is simple:
- We play a set number of rounds.
- In every round, a random number of marbles (between 25-40) are put inside the box, but the contents of the box will always be visible during the duration of the round.
- The first player will takes the box and can take 1, 2, or 3 marbles from the box. After that, he/she must pass the box to second player.
- The second player can also take 1, 2, or 3 marbles from the box and must pass the box to third player.
- The third player will do the same thing and the round will continue until someone takes the last marble. When that happens, the round ends.
- The player who takes the last marble loses 1 point and the last player who successfully passes the box gains 5 points. (Ex. If third player takes the last marble, second player will gains 5 points and third player will loses 1 point.)
- After a set number of rounds have been played, the player with the most points wins the game.
The problem is that I will go second in every round.
What is the strategy I must take to maximize my score and what is the minimum number of rounds to be played so I will be guaranteed to win the game, if possible?