Gambling Machine revisited

### Gambling Machine Puzzle
### Author: Corey Chivers
### http://wordplay.blogs.nytimes.com/2013/03/04/machine/
### original code adapted by: annoporci (R newbie), 25 March 2013.
### purpose: use continuous uniform distribution on reals instead of discrete distribution on integers

### Doesn't seem to work as intended...

### Refine computations
### Initialize
rm(list=ls())
xmin = 69
xmax = 72
step = 0.05
df <- data.frame()

for( N in list(10,100,1000,10000,100000) )
#for( N in list(1000000) ) # extra large
  { ### start loop over sample size -N-
    vector.cutoff <- numeric(length=0)
    vector.payoff <- numeric(length=0)

    for( cutoff in seq(xmin, xmax, by = step) )
    { ### start loop over strategies -cutoff-
      set.seed(123456789)
      x <- runif(N, min = 0, max = 100)
      y <- runif(N, min = 0, max = 100)
      payoff <- numeric(N)

      for(i in 1:N)
        { ### start loop over grid values -i-
          ### Correct guess payoff = y
          if( (x[i]>cutoff & y[i]<x[i]) | (x[i]<=cutoff & y[i]>x[i]) )
            payoff[i] <- y[i]

          ### Wrong guess payoff = 0
          if( (x[i]>cutoff & y[i]>x[i]) | (x[i]<=cutoff & y[i]<x[i]) )
            payoff[i] < -0

          ### Tie payoff =  0
          if(x[i] == y[i])
            payoff[i] <- 0
        } ### end loop over grid values -i-

      ### Expected Payoff All Contingencies Considered
      #print(paste(cutoff,mean(payoff)))
      vector.cutoff <- c(vector.cutoff,cutoff)
      vector.payoff <- c(vector.payoff,mean(payoff))
      print(vector.payoff)
      dfN <- data.frame(vector.cutoff, vector.payoff, stringsAsFactors = FALSE)
      colnames(dfN) <- c("Cutoff","Payoff")

    } ### end loop over strategies -cutoff-

  # export pdf plot
  pdfname <- paste0("gamble-payoff-sample-size-",N,".pdf")
  pdf(pdfname)
  par(cex=0.8) # cex = character expansion factor
  plot(dfN, main = paste( "samples of size",  N )
       , xlab = 'Cutoff', ylab = 'Payoff'
       , pch = 20, col = "red", axes = FALSE )
  axis(1, pos = min(vector.payoff))
  axis(2, pos = min(vector.cutoff), las = 1)
  segments(0, max(vector.payoff), which.max(vector.payoff), max(vector.payoff), lty = "dashed")
  segments(which.max(vector.payoff), min(vector.payoff), which.max(vector.payoff), max(vector.payoff), lty = "dashed")
  dev.off()

  assign(paste0("df",N),dfN)
  df <- c(df,dfN)
  print( get(paste0("df",N)) )
  save(dfN, file = paste0("df",N,".RData"))

  } ### end loop over sample size -N-


# clean-up
library(gdata)
# keep only objects with names starting in df
keep(list = ls(pattern = "^df", envir = .GlobalEnv), all = TRUE, sure = TRUE)
rm(dfN)