experiment <- function(doors, isChangeMind=TRUE, experimentTime) {
winTime = 0
lostTime = 0
i = 1
while(i <= experimentTime) {
prize <- sample(doors, 1)
guess <- sample(doors, 1)
delete <- sample(doors[! doors %in% c(prize, guess)], 1)
reserve <- doors[doors != delete]
if (isChangeMind == TRUE) {
guess <- sample(reserve[reserve != guess], 1)
}
if (guess == prize) {
winTime = winTime + 1
} else {
lostTime = lostTime + 1
}
i = i + 1
}
c(experimentTime, winTime, lostTime, winTime/experimentTime)
}
resultNames <- c("doorNum", "ExpTime",
"change_winTime", "change_lostTime", "changeWinRate",
"noChange_winTime", "noChange_lostTime", "noChangeWinRate")
expBoth <- function(doorNum = 3, experimentTime = 1000) {
doors <- LETTERS[1:doorNum]
changeResult <- experiment(doors, isChangeMind = TRUE, experimentTime)
noChangeResult <- experiment(doors, isChangeMind = FALSE, experimentTime)
c(doorNum, changeResult,noChangeResult[-1])
}
drawBar <- function(result) {
names(result) <- resultNames
subResult_names <- c('change_winTime', 'change_lostTime', 'noChange_winTime', 'noChange_lostTime')
subResult <- result[subResult_names]
mtx_result <- matrix(subResult, nrow = 2, dimnames = list(c("win", "lost"), c("change", "noChange")))
print(mtx_result)
barplot(mtx_result
, ylab = "count", col = c("skyblue", "skyblue4")
, main = "times of win or lost")
}
3 doors
# 1000 experiments
result <- expBoth()
drawBar(result)
## change noChange
## win 664 363
## lost 336 637
# 3 doors, 10,000 experiments
result <- expBoth(experimentTime = 10000)
drawBar(result)
## change noChange
## win 6697 3302
## lost 3303 6698
# 3 doors, 100,000 experiments
result <- expBoth(experimentTime = 100000)
drawBar(result)
## change noChange
## win 66523 33403
## lost 33477 66597
10 doors
# 10 doors, 1000 experiments
result <- expBoth(10, 1000)
drawBar(result)
## change noChange
## win 114 100
## lost 886 900
win rate from 3 to 25
# win rate from 3 to 25
df_result <- data.frame()
doorNums <- 3:25
for (doorNum in doorNums) {
result <- expBoth(doorNum, 1000)
df_result <- rbind(df_result, result)
}
names(df_result) <- resultNames
print(df_result)
## doorNum ExpTime change_winTime change_lostTime changeWinRate
## 1 3 1000 680 320 0.680
## 2 4 1000 384 616 0.384
## 3 5 1000 261 739 0.261
## 4 6 1000 191 809 0.191
## 5 7 1000 194 806 0.194
## 6 8 1000 134 866 0.134
## 7 9 1000 125 875 0.125
## 8 10 1000 104 896 0.104
## 9 11 1000 111 889 0.111
## 10 12 1000 87 913 0.087
## 11 13 1000 77 923 0.077
## 12 14 1000 81 919 0.081
## 13 15 1000 69 931 0.069
## 14 16 1000 71 929 0.071
## 15 17 1000 61 939 0.061
## 16 18 1000 58 942 0.058
## 17 19 1000 67 933 0.067
## 18 20 1000 46 954 0.046
## 19 21 1000 57 943 0.057
## 20 22 1000 48 952 0.048
## 21 23 1000 39 961 0.039
## 22 24 1000 42 958 0.042
## 23 25 1000 41 959 0.041
## noChange_winTime noChange_lostTime noChangeWinRate
## 1 311 689 0.311
## 2 257 743 0.257
## 3 213 787 0.213
## 4 159 841 0.159
## 5 152 848 0.152
## 6 155 845 0.155
## 7 105 895 0.105
## 8 106 894 0.106
## 9 78 922 0.078
## 10 89 911 0.089
## 11 80 920 0.080
## 12 72 928 0.072
## 13 68 932 0.068
## 14 71 929 0.071
## 15 62 938 0.062
## 16 46 954 0.046
## 17 48 952 0.048
## 18 57 943 0.057
## 19 44 956 0.044
## 20 45 955 0.045
## 21 37 963 0.037
## 22 40 960 0.040
## 23 38 962 0.038
plot(df_result$changeWinRate, type = "l")
lines(df_result$noChangeWinRate, col="blue")
