Create goat.R

# goat.R
#   a numerical approach to the monty hall paradox
#   http://en.wikipedia.org/wiki/Monty_hall_problem

Written after an evening of empirical testing, while watching footy and drinking beer. After about 30 repetitions the results were clearly becoming unequivocal.

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+# goat.R
+#   a numerical approach to the monty hall paradox
+#   http://en.wikipedia.org/wiki/Monty_hall_problem
+#   SJP 25 Oct 2007
+# 
+#   consts
+NUMDOORS <- 3    #
+GOAT <- 0
+PRIZE <- 1
+ITERATIONS <- 100
+#   FUNCTIONS
+###############################################################
+#   select a door
+getDoor <- function(d=NUMDOORS){
+  z <- rep(1, d)      		# vector of 1s
+	z <- cumsum(z) / sum(z)     # vector of props a..1
+  	my_door <- which.min(z < runif(1))   # which door is chosen
+	return(my_door)
+}
+###############################################################
+# put the prize behind a door
+allocPrize <- function(d=NUMDOORS){
+	door <- rep(GOAT, d)                   # vector of goat doors (0)
+	door[getDoor()] <- PRIZE               # put the prize behind a door
+	return(door)
+}
+
+###############################################################
+#  game() function
+#	call game(T) to switch, game(F) to not swap
+#   put a prize behind a door
+game <- function(swap_decision, iter=ITERATIONS){
+	wins <- 0            # counter for winning trials
+	for(i in 1:iter){
+		doors <- allocPrize()
+		#   the contestant chooses a door
+		guess_door <- getDoor()             # could be the same as the prize door
+
+		#   Monty Hall opens a goat door
+		while(T){
+			host_door <- getDoor()          # Monty chooses a door
+			if(host_door == guess_door) next    # Monty not very smart
+			if(doors[host_door] == PRIZE) next   # oops not that one either
+			break
+		}
+		#	extra bit: add in 'toss a coin'
+		swap <- ifelse((class(swap_decision)=='logical'), swap_decision, pr())
+		# test the original guess
+		#! 1: I guessed right AND I swap:        win <- 0
+		#! 2: I guessed right AND I DON'T swap:  win <- 1
+		#! 3: I guessed wrong AND i swap:        win <- 1
+		#! 4: I guessed wrong AND I DON'T swap:  win <- 0
+    	win <- (xor(doors[guess_door]==PRIZE, swap))
+		wins <- wins + win
+	}
+	return(sprintf('Iterations: %i Swap: %5s  Wins: %3.1f%%', iter, swap_decision, wins/iter*100))
+}
+
+cat('\n==========  SWAP or not, to win a car =============\n')
+print(game(swap=T))
+print(game(swap=F))
+print(game(swap='TOSS'))
+cat('===================================================\n\n\n')
+
+
+#  ######################################
+junkYard()			# stop() silently
+#   test functions
+#   have we got a fair distribution of prizes?
+x <- t(replicate(1000, allocPrize()))
+colsum <- apply(x, 2, sum)
+barplot(colsum)