Simulate the card game "War" with R

war.R

g <- function(){
  deck = rep(1:13, each=4)
  deal <- sample(length(deck))
  p1 <- deck[deal[1:26]]
  p2 <- deck[deal[27:52]]
  hands <- 1
  wins <- matrix(NA, 0, 4)
  while(length(p1) > 0 & length(p2) > 0){
    hands <- hands + 1
    wins <- rbind(wins, c(p1[1], p2[1], length(p1), length(p2)))
    if(p1[1] == p2[1]) player <- rbinom(1,1,0.5) else player <- p1[1] > p2[1]
    if(player) {p1 <- c(p1[-1], p1[1], p2[1]); p2 <- p2[-1]} else
               {p2 <- c(p2[-1], p2[1], p1[1]); p1 <- p1[-1]}
  }
  plot(wins[,3],type='l',ylim=c(0,52))
  lines(wins[,4],col='tomato')
  return(hands)
}

g()

This simulation treats ties randomly

If you simulate thousands of games the number of hands played averages to around 350 with a maximum in the thousands.

Here's a condensed version without the plot:

g <- function(deck = sample(rep(1:13, each=4))){
  p1 <- deck[deal[1:26]]
  p2 <- deck[deal[27:52]]
  while(length(p1) > 0 & length(p2) > 0){
    if(p1[1] == p2[1]) player <- rbinom(1,1,0.5) else player <- p1[1] > p2[1]
    if(player) {p1 <- c(p1[-1], p1[1], p2[1]); p2 <- p2[-1]} else
    {p2 <- c(p2[-1], p2[1], p1[1]); p1 <- p1[-1]}
  }
}