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Monty Hall Problem and probability, simulated in R, Bayes Nets, bayesian nets.
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library(ggplot2) | |
montyHall <- function(maxDoors = 3, switch = T, tries = 10) { | |
plays <- data.frame() | |
for (i in 1:tries) { | |
# Create the doors. | |
doors <- 1:maxDoors | |
# Choose a winning door. | |
winningDoor <- sample(doors, 1) | |
# Choose the player door. | |
playerDoor <- sample(doors, 1) | |
o <- playerDoor | |
if (playerDoor == winningDoor) { | |
# The player has the winning door, so Monty reveals one of the other doors, containing a goat. | |
montyDoor <- sample(doors[-playerDoor], 1) | |
} else { | |
# The player has a goat, so Monty reveals one of the other doors, not including the winning door. | |
montyDoor <- unlist(sample(as.list(doors[-c(playerDoor, winningDoor)], 1))) | |
} | |
# Let the player switch doors. | |
if (switch == T) { | |
playerDoor <- unlist(sample(as.list(doors[-c(playerDoor, montyDoor)], 1))) | |
} | |
plays <- rbind(plays, data.frame(o, playerDoor, winningDoor, switch, playerDoor == winningDoor)) | |
} | |
colnames(plays) <- c('originalDoor', 'playerDoor', 'winningDoor', 'switch', 'win') | |
plays$win <- as.logical(plays$win) | |
plays | |
} | |
switch <- data.frame() | |
for (count in seq(from=100, to=1000, by=100)) { | |
result <- montyHall(switch = T, tries = count) | |
switch <- rbind(switch, c(count, sum(result$win) / count)) | |
} | |
names(switch) <- c('count', 'wins') | |
stay <- data.frame() | |
for (count in seq(from=100, to=1000, by=100)) { | |
result <- montyHall(switch = F, tries = count) | |
stay <- rbind(stay, c(count, sum(result$win) / count)) | |
} | |
names(stay) <- c('count', 'wins') | |
p = ggplot() + | |
geom_line(data = switch, aes(x = count, y = wins, color='Switch')) + | |
geom_line(data = stay, aes(x = count, y = wins, color='Stay')) + | |
xlab('# of Games') + | |
ylab('Win Percentage') + | |
theme(legend.position = 'bottom') + | |
labs(colour='Type') + | |
scale_color_manual(values = c('red', 'blue')) | |
print(p) | |
result1 <- montyHall(switch = F, tries = 500) | |
result2 <- montyHall(switch = T, tries = 500) | |
print(sum(result1$win) / nrow(result1)) | |
print(sum(result2$win) / nrow(result2)) |
Author
primaryobjects
commented
Dec 18, 2019
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