Question

1. A standard deck of cards has 52 cards, four each of 2,3,4,5,6,7,8,9,10,J,Q,K,A. In blackjack, a player gets two cards and adds their values. Cards count as their usual numbers, except Aces are 11 (or 1), while K, Q, J are all 10.
   1. “Blackjack” means getting an Ace and a value ten card. What is probability of getting a blackjack?
   2. What is probability of getting 19? (The probability that the sum of your cards is 19, using Ace as 11)

   Use R to simulate dealing two cards, and compute these probabilities experimentally.

Answer 1

solution:

ptm <- proc.time()
deck<-rep(c("A", "K", "Q", "J", "10", "9", "8", "7", "6", "5", "4", "3", "2"), 4)
prob_blk<-c()
prob_19<-c()
for (i in 1:500) {
draw<-matrix(, nrow = 5000, ncol = 2, byrow = T)
countblk=0
count19=0
for(j in 1:5000) {
draw[j,]<-sample(deck, 2)
ifelse((draw[j, 1] == "A" & draw[j, 2] == "10") | (draw[j, 1] == "10" & draw[j, 2] == "A") | (draw[j, 1] == "A" & draw[j, 2] == "K") | (draw[j, 1] == "K" & draw[j, 2] == "A") | (draw[j, 1] == "A" & draw[j, 2] == "Q") | (draw[j, 1] == "Q" & draw[j, 2] == "A") | (draw[j, 1] == "A" & draw[j, 2] == "J") | (draw[j, 1] == "J" & draw[j, 2] == "A"), countblk <- countblk + 1, ifelse((draw[j, 1] == "A" & draw[j,2] == "8") | (draw[j, 1] == "8" & draw[j, 2] == "A") | (draw[j, 1] == "9" & draw[j, 2] == "10") | (draw[j, 1] == "10" & draw[j, 2] == "9") | (draw[j, 1] == "9" & draw[j, 2] == "K") | (draw[j, 1] == "K" & draw[j, 2] == "9") | (draw[j, 1] == "9" & draw[j,2] == "Q") | (draw[j, 1] == "Q" & draw[j, 2] == "9") | (draw[j, 1] == "9" & draw[j, 2] == "J") | (draw[j, 1] == "J" & draw[j, 2] == "9"), count19 <- count19 + 1, count19))
  
}
prob_blk[i] = countblk/5000
prob_19[i] = count19/5000
}
mean(prob_blk)
mean(prob_19)
proc.time() - ptm

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