Data commit

Task/Monty-Hall-problem/R/monty-hall-problem.r

@@ -0,0 +1,58 @@
+set.seed(19771025)   # set the seed to set the same results as this code
+N <- 10000  # trials
+true_answers <- sample(1:3, N, replace=TRUE)
+
+# We can assme that the contestant always choose door 1 without any loss of
+#    generality, by equivalence.  That is, we can always relabel the doors
+#    to make the user-chosen door into door 1.
+# Thus, the host opens door '2' unless door 2 has the prize, in which case
+#    the host opens door 3.
+
+host_opens <- 2 + (true_answers == 2)
+other_door <- 2 + (true_answers != 2)
+
+## if always switch
+summary( other_door == true_answers )
+## if we never switch
+summary( true_answers == 1)
+## if we randomly switch
+random_switch <- other_door
+random_switch[runif(N) >= .5] <- 1
+summary(random_switch == true_answers)
+
+
+
+## To go with the exact parameters of the Rosetta challenge, complicating matters....
+##  Note that the player may initially choose any of the three doors (not just Door 1),
+##     that the host opens a different door revealing a goat (not necessarily Door 3), and
+##     that he gives the player a second choice between the two remaining unopened doors.
+
+N <- 10000  #trials
+true_answers <- sample(1:3, N, replace=TRUE)
+user_choice <- sample(1:3, N, replace=TRUE)
+## the host_choice is more complicated
+host_chooser <- function(user_prize) {
+    # this could be cleaner
+    bad_choices <- unique(user_prize)
+    # in R, the x[-vector] form implies, choose the indices in x not in vector
+    choices <- c(1:3)[-bad_choices]
+    # if the first arg to sample is an int, it treats it as the number of choices
+    if (length(choices) == 1) {  return(choices)}
+    else { return(sample(choices,1))}
+}
+
+host_choice <- apply( X=cbind(true_answers,user_choice), FUN=host_chooser,MARGIN=1)
+not_door <- function(x){ return( (1:3)[-x]) }  # we could also define this
+                                                # directly at the FUN argument following
+other_door  <- apply( X = cbind(user_choice,host_choice), FUN=not_door, MARGIN=1)
+
+
+## if always switch
+summary( other_door == true_answers )
+## if we never switch
+summary( true_answers == user_choice)
+## if we randomly switch
+random_switch <- user_choice
+change <- runif(N) >= .5
+random_switch[change] <- other_door[change]
+summary(random_switch == true_answers)