Simulating Snakes and Ladders in R - r

Question

I am a beginner in R and I have to simulate a snakes and ladders game in R for an assignment. The board has 100 squares. The only winning square is 100, for example if you’re on square 98 and roll a 6 you would go forward 2 spaces to 100 and then bounce back 4 spaces to 96. My difficulty is insterting the snakes/ladders transitions in the complete transition matrix, and coding the winning condition. Here is my code so far:
snakesNladders <-
function()
{
transitions <- rbind(
c(40, 3),
c(4, 25),
c(27, 5),
c(13, 46),
c(43, 18),
c(54, 31),
c(33, 49),
c(99, 41),
c(42, 63),
c(66, 45),
c(50, 69),
c(89, 53),
c(76, 58),
c(62, 81),
c(74, 92))
transmat <- 1:100
names(transmat) <- as.character(1:100)
transmat[transitions[,1]] <- transitions[,2]
firstpos <- 0
curpos_player1 <- NULL
curpos_player2 <- NULL
while(curpos_player1 & curpos_player2 < 100) {
curpos_player1 <- firstpos + curpos_player1 + sample(1:6, 1, replace=TRUE)
curpos_player2 <- firstpos + curpos_player2 + sample(1:6, 1, replace = TRUE)
curpos_player1 <- transmat[curpos_player1]
curpos_player2 <- transmat[curpos_player2]
if(curpos_player1 | curpos_player2 == 100){
print(win)
}else if(curpos_player1 > 100){
return()
}else if(curpos_player2 > 100){
return()
}
}
}
}
}
Not sure what I should put in the return brackets to simulate the winning condition. Also if the rest of the code seems ok. I would really appreciate any help.

Answer 1

Here's how I might approach it. Maybe you can get some ideas by walking through the code.
library(data.table)
set.seed(1633654196) # for reproducibility
# for the transitions, position 1 is the start position, position 2 is the
# square at the bottom left of the board, position 101 is the winning position
# get a vector of snake/ladder transitions (where a player moves after
# landing on each square)
trans <- 1:101
trans[c(40, 4, 27, 13, 43, 54, 33, 99, 42, 66, 50, 89, 76, 62, 74) + 1] <-
c( 3, 25, 5, 46, 18, 31, 49, 41, 63, 45, 69, 53, 58, 81, 92) + 1
# get a matrix of all possible starting/ending positions (based on die
# roll 1 through 6)
m <- c(sequence(rep(6L, 100), 2:101), rep(101L, 6))
# handle overshooting the winning square
blnBounce <- m > 101
m[blnBounce] <- 202 - m[blnBounce]
# add in the snake/ladder transitions
# (faster to index moves as a list of vectors than as a matrix)
to <- asplit(m <- matrix(trans[m], 6), 2)
simgame <- function(nplayers = 1, to, blnPrint = TRUE, turns = 50L, start = rep(1L, nplayers)) {
# turn 1 is the starting position, and won't be retained in the output, so
# add 1 to turns
turns <- as.integer(turns) + 1L
# sample the rolls for all players up front
rolls <- matrix(sample(6, nplayers*turns, TRUE), ncol = 2)
# initialize the output matrix
out <- matrix(0, turns, nplayers)
out[1,] <- start
for (j in 1:nplayers) {
for (i in 2:turns) {
out[i, j] <- to[[out[i - 1L]]][rolls[i, j]]
if (out[i, j] == 101L) {
turns <- i
break
}
}
}
# subtract 1 so "1" corresponds to square 1 and "100" corresponds to the
# winning square
out <- out[2:turns,,drop = FALSE] - 1L
turns <- turns - 1L
winner <- match(100L, out[turns,], 0L)
if (winner) {
if (blnPrint) print(paste("Player", winner, "wins"))
out
} else {
# no winner yet, recursively call simgame
rbind(out, Recall(nplayers, to, blnPrint, turns, out[turns,]))
}
}
# simulate a 2-player game
(game <- simgame(2, to))
#> [1] "Player 2 wins"
#> [,1] [,2]
#> [1,] 25 6
#> [2,] 31 30
#> [3,] 32 32
#> [4,] 34 34
#> [5,] 3 36
#> [6,] 25 6
#> [7,] 5 28
#> [8,] 11 10
#> [9,] 46 14
#> [10,] 52 51
#> [11,] 31 31
#> [12,] 35 37
#> [13,] 39 38
#> [14,] 3 41
#> [15,] 8 7
#> [16,] 12 12
#> [17,] 46 17
#> [18,] 69 48
#> [19,] 75 71
#> [20,] 78 77
#> [21,] 84 83
#> [22,] 87 53
#> [23,] 93 92
#> [24,] 96 94
#> [25,] 41 100
# simulate the number of rounds for 15k games
system.time(turns <- replicate(15e3, nrow(simgame(2, to, FALSE))))
#> user system elapsed
#> 1.18 0.01 1.06
hist(turns)
# Probability of single player finishing by turn
dt <- data.table(from = c(col(m)), to = c(m))[, .(prob = .N/6), from:to]
# full transition matrix
m1 <- matrix(0L, 101, 101)
m1[as.matrix(dt[, 1:2])] <- dt$prob
# calculate the probabilities for 300 turns
mm <- m1
prob1 <- numeric(300)
for (i in 1:300) {
mm <- mm %*% m1
prob1[i] <- mm[1, 101]
}
plot(prob1, xlab = "Roll number", main = "Probability of winning by turn")
# for a 3-player game:
prob3 <- 1 - (1 - prob1)^3