R help - Mar 2005 - Beginner - simple simulation

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

a simple approach could be:

n <- seq(10, 5000, 10)
means <- numeric(length(n))
for(i in seq(along=n)){
    mat <- sample(1:6, 2*n[i], TRUE); dim(mat) <- c(n[i], 2)
    means[i] <- mean(ifelse(!mat[,1]%%2, mat[,1], -mat[,2]))
}
means
plot(n, means, xlab="sample size", ylab="mean")


I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/16/336899
Fax: +32/16/337015
Web: http://www.med.kuleuven.ac.be/biostat/
     http://www.student.kuleuven.ac.be/~m0390867/dimitris.htm




----- Original Message ----- 
From: "Jacob van Wyk" <jlvw at na.rau.ac.za>
To: <r-help at stat.math.ethz.ch>
Sent: Tuesday, March 01, 2005 9:25 AM
Subject: [R] Beginner - simple simulation

> 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
>
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