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Leo designed a maze game (roughly) based on quantum mechanics and entanglement.

Here’s the board (the player tokens are the dime and quarter):

IMG_7744

Each square represents a quantum state, so the maze is a state space.There are six paths out of each state, to some other state (or back to itself). (Well, there are supposed to be six paths out of each state, but Leo was being highly disorganized in drawing the maze, so we ended up with a few less in the latter states, but anyway…)

Both players start out in the start state, entangled together. Rounds are collective, that is, players play together. A round begins by rolling two die: First the count die (the green one, in this case) is rolled, and then the path die (yellow) is rolled the number of times shown by the count die. So, for example, if the count die rolls 3, we would then roll the path die three times. Let’s say that the path results are: 4,2,4. Each player then chooses one of the paths to take from their current state to a new state, trying to reach the end state. BUT, there is an “exclusion” constraint(*) that requires that only one player choose each value. So, in the example above (4,2,4), if one player wants to move on path 4, and the other on path 2, there is no problem. Similarly, if both want to move on path 4, there’s no problem because there are two 4s. However, if both want to move on path 2, you have to roll against one another for priority, and the player with the highest roll gets to choose his or her path first, and the other player is left with whatever paths are left.

Simple, but fun!

We had ideas for a bunch of enhancements, esp. re-entanglement if we ended up on the same state, and I had this fantasy of using <bra|OP|ket> notation to record the paths, but we never got around to these. It would have been  a bit better with a more state space maze.

(*) It occurred to me that it would have made more physical sense for the exclusion constraint to keep the players out of the same state, but that would have required redesigning the board from scratch, with two starts next to one another, or something. We’ll have to think about this for a redesign.