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Name: Jonathan
Status: other
Age: 40s
Location: N/A
Country: N/A
Date: N/A 


Question:
My goal is to simulate the rolling of large numbers of dice without a recursive formula. I can generate "random" numbers between 0 and 1 and i need an euqation that can allow me to, using one random number, simulate the rolling of x numbers of y sided dice.



Replies:
Don't do it. Use a separate "random" number to simulate each roll of each die. Your method for generating random numbers is probably a linear congruence generator, which is fine for most applications. However, if you try to break it doen into separate "random" regions (low byte, high byte, for example), it turns out that not all regions will pass the "randomness" tests equally well.

In fact, when I use a linear congruence generator for my own Monte Carlo codes, I combine several computer-generated variates into one number to assure me that my numbers are as free from structure as possible.

I'm guessing that what you really want here is a formula to calculate the probabilities of each possible sum of die rolls, say rolling two six-sided dice in a craps game. Remember that all sides of a fair die have the same probability; thus, the 36 possible permutations of rolling dice A and B also all have equal probabilities of 1/36. To fin the probability of each SUM (2-12), you need to find out how many different rolls lead to the same sum.

Richard Barrans Jr., Ph.D.
Chemical Separations Group
Chemistry Division CHM/200
Argonne National Laboratory
9700 South Cass Avenue
Argonne, IL 60439



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