# EinStein würfelt nicht!

EinStein würfelt nicht! (... does not play dice) is a board game, designed by Ingo Althöfer, a professor of applied mathematics in Jena, Germany. It is the official game of an exhibition about Einstein in Germany during the Einstein Year (2005).

The name of the game in German has a double meaning:

• When you only have one cube (ein Stein) remaining, you no longer need to 'play dice', but simply move your cube.
• It is a play on Einstein's famous quote "I am convinced that He (God) does not play dice." (See Criticisms of the Copenhagen interpretation)

## Rules

The starting board

The game is played on a square board with a 5×5 grid. Each player has six cubes, numbered one to six, which are placed as illustrated in the image. During setup, each player can arrange the cubes as he/she sees fit.

The players take turns rolling a six-sided die and then moving the matching cube. If the matching cube is no longer on the board, the player moves a remaining cube whose number is next-highest or next-lowest to the rolled number. The player starting in the top-left may move that cube one square to the right, down, or on the diagonal down and to the right; the player starting in the bottom-right may move that cube one square to the top, left, or on the diagonal up and to the left. Any cube which already lies in the target square is removed from the board.

The object of the game is to either get one of your cubes to the far corner square in the grid (where your opponent started) or to remove all of your opponent's cubes from the board.

## Strategy

The fewer cubes you have, the "more mobile" they are, since more die rolls can result in moving the same piece. Therefore it can be helpful to aim to remove one's own cubes in order to be able to move them with a higher individual probability than having multiple cubes remaining.

### Schwarz Tables

The "mobility" of pieces given the removal of one or more pieces can be quantified with probability. The Schwarz score of a set of pieces on the board is defined as the expected number of remaining moves, assuming no capturing takes place, for one of the pieces to reach its goal. In general, players should minimize the Schwarz score of their pieces and maximize the Schwarz score of their opponent's pieces. As there are six pieces, and each piece can be 1, 2, 3, or 4 moves away from their goal, or out of play, there are 15,625 distinct situations in which Schwarz scores can be precomputed. http://www.minet.uni-jena.de/preprints/althoefer_06/rockNroll.pdf

## Variants

The game can also be played on a 6x6 board with ten piece on each side, labeled 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12. A pair of 6-sided dice are rolled. The game can also be played in rounds with a doubling cube as in backgammon.