tavolo=function(theta,y0,k){
  plot(theta,10*y0,xlim=c(0,1),ylim=c(0,10),type = "o",pch=19,
       yaxt="n",xlab="theta",ylab="",main=paste("Biliardo n=",k),
       cex.main=1)
  rect(0,0,1,10)
  lines(c(theta,theta),c(0,10),lwd=1)
}
biglie=function(theta,x,y){
  x.L=x[x<=theta];y.L=10*y[x<=theta]
  x.R=x[x>theta];y.R=10*y[x>theta]
  points(x.L,y.L,col='red',cex=4,pch='.')
  points(x.R,y.R,col='blue',cex=4,pch='.')
}
dens_beta=function(theta,xp,L,R,col){
  plot(theta,xlim=c(0,1),ylim=c(0,40),pch='.',
       xlab="theta",ylab="Densità beta")
  points(xp,dbeta(xp,L,R),ty='l',col=col)
  lines(c(theta,theta),c(0,40),lty="dashed")
}
pausa=function(){
  cat("\npremere enter\n")
  scan()
}
biliardo=function(n){
  x=numeric();y=numeric()
  theta=runif(1);y0=runif(1)
  xp=seq(0,1,by=0.0001)
  par(mfrow=c(2,1),mar=c(4,4,1.5,1))
  passo=n/10 
  k1=1; L1=0; R1=0
  set=seq(passo,n,by=passo)
  for(k in set){
  tavolo(theta,y0,k)
  for (i in k1:k){
      x[i]=runif(1);y[i]=runif(1)
      biglie(theta,x,y)
  }
  L=length(x[x<=theta]);R=length(x[x>theta])
  dens_beta(theta,xp,L+1,R+1,"red")
  k1=k+1
  pausa()
}
  print(L)
  print(R)
  print(theta)
}