Pi by coin tossing

pie.R

one_pie<-function(N,n){
	coins<-rbinom(n,1,.5)
	means<- cumsum(coins)/(1:n)
	if (any(means>0.5)) return(means[min(which(means>0.5))])
	coins2<-c(coins,rbinom(N,1,.5))
	means2<-cumsum(coins2)/(1:(N+n))
	if (any(means2>0.5)) return(means2[min(which(means2>0.5))])
	return((1/2)+(1/(N+n+1)))
}

pie_story.Rt

> system.time(r<-replicate(100000,one_pie(1000,10)))
   user  system elapsed 
  1.072   0.046   1.115 
> system.time(r<-replicate(100000,one_pie(1000,50)))
   user  system elapsed 
  0.761   0.040   0.800 
> system.time(r<-replicate(100000,one_pie(1000,100)))
   user  system elapsed 
  0.838   0.050   0.887 

##looks like n=50 is the sweet spot on my computer