Tip the Die, a Two-Person Game

Philip B. Yasskin

Department of Mathematics
Texas A&M University


This is the student version of this article.


Tip the Die is a two player game similar in style to the Subtraction Game or NIM but with more (or just different) strategy.


I don't know much about the history of this game. My son has worked at the local Renaissance Festival since high school. Several years ago, he came home and said one of the staff was playing a game after hours and no one could beat him. He asked me if I could analyze the game and give him a winning strategy. When I looked at the game I found it has a very interesting structure and complex strategy. While it has a similar structure to the Subtraction Game or NIM, it is significantly more complex. He said that the game was called the Game of 31, but since the number 31 is not significant to the strategy, I have come to call it Tip the Die because you tip a die to one of the adjacent sides without turning it over or rolling it.


Start by rolling a six-sided die. The number on top is the current total which is shared by both players and will grow as the game proceeds. The players alternate turns. On a player's turn, the player tips the die to one of the four sides other than the top or bottom, adds the new top to the current total and announces the new current total. The goal is to be the player who makes the current total become 31. If a player makes the current total go over 31, s/he loses. If the previous current total is under 31, the player must move. So the winner is the person who makes the current total become 31 or forces their opponent to go over 31.

First Sample Game:

Second Sample Game:


After you play the game a couple of times you will see there is a lot of strategy to the game. The real question is "What is the strategy for developing a strategy?" You will have a strategy when you know what play or plays to make for each current total and number showing on the top.

In analyzing the game, there are a couple of simple facts you should know:

After you find a strategy, there two facts you should notice:

Game Variations

Have fun.

Last Updated: April 18, 2015, PBY
Copyright © 2015 Philip B. Yasskin