This is a simulation study of gambling…..
Gambling1 <- function(p, Bet, Capital, Maxit=101, Fig=F)
{
X <- numeric(Maxit)
X[1] <- Capital
for(j in 2:Maxit)
{
if(X[j-1]>0) X[j] <- X[j-1] + sample(Bet*c(-1,1),1,prob=c(1-p,p))
}
if(Fig==T)
{
plot(X, type="l", ylim=c(0, max(X)*1.2), xlab="Trial", ylab="State")
abline(Capital, 0, lty=2, col="red")
}
}
par(mfrow=c(2,2), mar=c(3,3,3,3))
Gambling1(p=0.5, Bet=1, Capital=20, Fig=T)
Gambling1(p=0.5, Bet=1, Capital=20, Fig=T)
Gambling1(p=0.5, Bet=1, Capital=10, Fig=T)
Gambling1(p=0.5, Bet=1, Capital=10, Fig=T)
Gambling2 <- function(p, Bet, Capital, Maxit=101, Nsim=100)
{
X <- array(0, c(Nsim, Maxit))
for(i in 1:Nsim)
{
X[i,1] <- Capital
for(j in 2:Maxit)
{
Tmp <- X[i,(j-1)] + sample(Bet*c(-1,1),1,prob=c(1-p,p))
if(Tmp >0) X[i,j] <- Tmp
if(Tmp<=0) X[i,j] <- -10
}
}
plot(X[1,], type="l", ylim=c(0, max(X)*1.2),
xlab="Trial", ylab="State", col="grey")
for(i in 1:Nsim) points(X[i,], type="l", col="grey")
abline(Capital, 0, lty=2, col="red")
hist(X[,Maxit], col="orange", xlab="Final state", main="")
return(X)
}
par(mfrow=c(2,2), mar=c(3,3,3,3))
Res <- Gambling2(p=0.5, Bet=1, Capital=20, Maxit=100, Nsim=100)
Res <- Gambling2(p=0.5, Bet=1, Capital=20, Maxit=1000, Nsim=100)