About this 3D model

The ModelThree dice used to demonstrate an element of game theory. The dice are all six sided but have different numbers on them. The first die has a number four on every side, the second die has a number six on four sides and is blank on the other two sides, the third die has a number one on four sides and a number ten on the two remaining sides. The GameThe game is played with two players and all three dice are placed in the middle of the table. Each player takes a die from the table leaving one die unused on each turn and rolls it at the same time as their opponent. The highest score wins a point. After rolling the players can decide whether to keep the die that they have for the next round or put it back into the middle of the table and choose again. The first to 10 points wins. The total of the sides of each die is 24 and so the average rolled with each die is therefore 24/6 = 4. Since each die has the same average score of four the object of the game is to try to determine whether there is an optimum strategy that will allow you to maximize your chance of winning (this is where the game theory comes in). The MathThe die with four on every side will beat the one that has 1s and 10s two thirds of the time. The die with 6s and 0s will beat the one with four on every side about two thirds of the time. The one with 1s and 10s will beat the one with 6s and 0s about five ninths of the time. This means that there is no one die that is "the best" option as another die can always be chosen that has a greater than 55% probability of beating it (and could therefore be said to be "better" than the one you choose). There is still always a random element to the game and it is always possible for the "better" dice to roll less than the die it is supposed to beat, but if you play for long enough it should become apparent which of the two being rolled is the best.The winning strategy is then to allow your opponent to pick first as you can always pick one of the remaining two that has a slightly better chance of winning. It is very much the dice equivalent of rock, paper, scissors, a game in which your opponent knows they should never show you their chosen play before you choose yours! In game theory these are called Intransitive, Non-transitive or Cyclical Dice as A beats B, B beats C and C beats A.The dice are 20mm x 20mm x 20mm and print in a single color, no support structure is needed. The picture shows the three printed dice in red PLA and three painted versions.