Читать книгу Informatics and Machine Learning. From Martingales to Metaheuristics онлайн

80 страница из 101

16

If using loaded dice, but with dice that have no interaction, then they are still independent of eachother, and their probabilities are thus still independent, reducing to the product of two simpler probability distributions (with one argument each) as shown above. In games of dice where two dice are rolled (craps) it is possible to have dice that individually roll as fair, having uniform distribution on outcomes, but that when rolled together interact such that their combined rolls are biased. This can be accomplished with use of small bar magnets oriented from the “1” to “6” faces, such that the dice tend to come up with their magnets anti‐aligned one showing its “1” face, the other showing its “6” face, for a total roll count of “7” (where the roll of a “7” has special significance in the game of craps). In the instance of the dice with magnets, the outcomes of the individual die rolls are not independent, and the simplification of P(X, Y) to P(X)P(Y) cannot be made.