AliceBob2.R

library(MASS)
rm(list = ls())
options(warn=-1)
set.seed(1234)
Nrep <- 1e05
maxT <- 1e05
As <- rep(0, Nrep)
TAs <- rep(0, Nrep)
Bs <- rep(0, Nrep)
TBs <- rep(0, Nrep)
for (n in 1:Nrep) {
  A <- sample(c(-1, 1), maxT, prob = c(49, 51), replace = TRUE)
  B <- sample(c(-1, 1), maxT, prob = c(51, 49), replace = TRUE)
  AA <- c(100, 100 + cumsum(A))
  BB <- c(100, 100 + cumsum(B))
  TA <- min((0:maxT)[AA <= 0], maxT)
  TB <- min((0:maxT)[BB <= 0], maxT)
  As[n] <- AA[TA + 1]
  TAs[n] <- TA
  Bs[n] <- BB[TB + 1]
  TBs[n] <- TB
}
NAbusts <- sum(As == 0)
NAbusts

## [1] 1782

if (NAbusts > 0) truehist(TAs[As == 0], prob = FALSE)

NBbusts <- sum(Bs == 0)
NBbusts

## [1] 100000

if(NBbusts > 0) truehist(TBs[Bs == 0], prob = FALSE)

if(NAbusts < Nrep) truehist(As[As > 0], prob = FALSE)

if(NBbusts < Nrep) truehist(Bs[Bs > 0], prob = FALSE)
sum(As == 0 & Bs == 0)

## [1] 1782

sum(TAs > TBs & As == 0 & Bs == 0)/sum(As == 0 & Bs == 0) # Bob bust before Alice given both went bust

## [1] 0.5112233

sum(TAs < TBs & As == 0 & Bs == 0)/sum(As == 0 & Bs == 0) # Alice bust before Bob given both went bust

## [1] 0.4887767