Hallo to everybody. I am new to the list and would appreciate some help in a basic "first demo" of how to use R for simulating a simple game; I would like my students to use R and this may stimulate their interest.
The problem is simply: Two players (A and B) play the following game. Each player rolls a die (fair, 6-sided) and they write down the result: say A rolls nA and B rolls nB. If nA is even, A pays B $nB: if nA is odd, B pays A $nA (we think of A paying B a negative amount). The amount that A pays B is a random variable X. Find the expectation of X. Theoretically it is 1/4 - B is ahead on average with 25c. Would anybody be prepared to help a little. I want to avoid loops and vectorize the computations, simulate the value of X for various sample sizes and preparea basic plot to show that the average value of X "converges" to 1/4. I would start with, say, sample(1:6,2,replace=T) for one simulated roll of the two dice. I want to repeat this n times, where n is, say, 10:2000 in steps of 10. Put the results in a matrix and work columnwise - choosing when the first roll is even, selecting the corresponding value of the second roll, and computing the payoff as described, etc. But I need help to put this together. In Matlab I would, for example, do the following to display the average payouts of A and B: c=1; samplesizes=[10:10:2000]; for s=samplesizes rolls=ceil(6*rand(s,2)); a_pays_b_index=find(mod(rolls(:,1),2)==0); a_pays_b_value=rolls(a_pays_b_index,2); b_pays_a_index=find(mod(rolls(:,1),2)==1); b_pays_a_value=rolls(b_pays_a_index,1); a_pays_average(c)=mean(a_pays_b_value); b_pays_average(c)=mean(b_pays_a_value); c=c+1; end Then do the plotting, etc. (One could also take differences, and so on.) I would really appreciate if anybody would be kind enough to help. I thought it might be a nice example to introduce students (in general, perhaps - because it is a kind of interesting game) to simulation in R. Thank you ! Jacob (PS Any credit would be respected, i.e. my students will know who helped me with this introduction.) Jacob L van Wyk Department of Mathematics and Statistics University of Johannesburg APK P O Box 524 Auckland Park 2006 South Africa Tel: +27-11-489-3080 Fax: +27-11-489-2832 ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
