Run Buster

Two players, Red and Blue, sit across from each other at an initially cleared table. They each begin with a dice cup containing six dice of their own color. Definitions Straight: Collection of one or more dice, numbered sequentially, such as (2, 3, 4), (3, 4, 5, 6), and (1). [A straight is always as long as it can be. It’s never a sub-straight of a longer straight.] Full straight: (1, 2, 3, 4, 5, 6) Complement (or Run Buster): The set of dice which, when combined with a non-full straight, completes a full straight. For example, the complement of (2, 3, 4) is (1, 5, 6). Play Starting with Red, players take turns rolling their dice, one roll per turn, and adding some of their newly rolled dice into their own hand (if they can. See below.) Players sometimes kill their opponent's hand. To win, your hand must be a full straight. It's possible to win on your first turn, with a probability of 1.54%, or about 1 in 65 plays. Red's first turn Red rolls the dice in his cup, and, selecting from his rolled dice, forms his hand. His hand must consist of exactly one straight. [Hands are always comprised of exactly one straight.] For example, if Red rolls (2, 2, 4, 5, 5, 6), his hand option are (2), (4), (4, 5), (4, 5, 6), (5), (5, 6), and (6). After forming his hand, Red must deposit his remaining dice back into his cup, concluding his turn. Blue's first turn Blue rolls the dice in his cup. If Blue's rolled dice contain the complement of Red's straight, Blue must remove Red's hand from the table and drop it into Red's cup. For example, if Red's hand is (1, 2, 3, 4), and Blue rolls (1, 3, 3, 5, 6, 6), Blue's roll contains (5, 6), which is the complement of Red's (1, 2, 3, 4). Blue must then place Red's hand in Red's cup. Then Blue (whether or not he killed Red’s hand), selecting from his rolled dice, forms his own hand, consisting of exactly one straight. In this example, from his (1, 3, 3, 5, 6, 6), Blue’s hand options are (1), (3), (5), (5, 6), and (6). Blue must then put his remaining dice back in his cup, concluding his turn. All remaining turns Begin your turn by rolling the dice in your cup. If your newly rolled dice contain the complement of your opponent's straight, you must remove his hand from the table and deposit it in his cup, as described above. Then (whether or not you've killed your opponent's hand) you must extend your straight with at least one of your newly rolled dice, if you can. For example, say your hand is (4, 5) and you've rolled (3, 4, 4, 6). Your new, extended straight options are (3, 4, 5), (3, 4, 5, 6), and (4, 5, 6). But say that, instead, you've rolled (1, 2, 4, 5). In this case, there's no way to extend your (4, 5) straight. As always, put your remaining dice back in your cup, concluding your turn. Variants Monocolor: Each player must have their own hand, but not necessarily their own color. All of the dice can be standard white dice with black pips for example. Just try to keep the hands separated if they're all the same color. Multiplayer: Run Buster can actually accommodate any number of players. Remove all of your opponents’ hands for which you have complements in your newly rolled dice. Randomly choose Player 1 and proceed clockwise. In successive rounds, the new Player 1 is to the left of the previous Player 1. The round winners drop out, one by one, and the last remaining player buys the next round of drinks. Design notes The challenge was to design a simple dice game with a certain symmetry: Six faces on a die, six dice, and a goal of six different numbers. It took me a few weeks of trance-like concentration. Inventing concepts. Morphing and recombining them. Eventually the solution came together in the form of this very satisfying mechanism.