*To*: mathgroup@smc.vnet.net*Subject*: [mg12065] RE: [mg11971] A Monte Carlo Simulation with loop structure*From*: Richard Finley <rfinley@netdoor.com>*Date*: Fri, 24 Apr 1998 01:52:35 -0400

Hi Daniel, //This is the quick and dirty way I did it....define a function to simulate rolling the three dice m times:// TripleDiceSim[m_] : able[ {Random[Integer,{1,6}], Random[Integer,{1,6}], Random[Integer,{1,6}]}, {n,1,m}]; //Then define a function that counts the number of times the dice sum to nine or ten:// Count9[ expr_] :ount[ Apply[ Plus, expr, 2 ], 9 ] Count10[expr_]:ount[ Apply[ Plus, expr, 2], 10 ] //Then create a simulation of an ensemble of experiments...each experiment rolling the three dice 1000 times...and repeating for 200 experiments:// sim able[ TripleDiceSim[ 1000 ], {n,1,200} ]; //Then count the number of times the results sum to 9 or 10 for each experiment, take the ratio, and compute the relevant statistics (make sure you load "Statistics`" first):// sim9 ap[ Count9, sim ]; sim10 ap[ Count10, sim ]; ratio im10/sim9 // N; Mean[ ratio ] StandardErrorOfSampleMean[ ratio ] //Doing this gave me the result Mean[ ratio ] .082 with a standard error 009 which is close to the theoretical value of 1.08// Hope that helps. RF -----Original Message----- From: Daniel Sanders [SMTP:dman777@worldnet.att.net] To: mathgroup@smc.vnet.net Sent: Friday, April 17, 1998 1:21 AM To: mathgroup@smc.vnet.net Subject: [mg11971] A Monte Carlo Simulation with loop structure Hi, I'm learning Mathematica programming in AutoDidactic [mode], and I'm working on conditionals and loop structures. The problem that follows is prototypical, and perhaps I can benefit from seeing some of your solutions. I owe the problem to J. Laurie Snell from his book, "Introduction to Probability". In the early 1600s, Galileo was asked to explain the fact that, although the number of triples of integers from 1 to 6 with sum 9 is the same as the number of such triples with sum 10, when three dice are rolled, a 9 seemed to come up less often a 10 supposedly in the experience of gamblers. Can you suggest native Mathematica code not emulating a procedural language for a Monte Carlo simulation experiment that runs many times keeping track of the proportions of 9s and 10s? Thanks in advance, I'm interested in the looping mechanism. Daniel Sanders