1_1_Martingale.r

martingale <- function(max_round = 1000, init_token = 100, bid = 1, 
                       rouletee_prob = c(19/37, 18/37)) {
  ## max_round: number of bidding
  ## init_token: initial # of chip
  ## bid: bidding chip when winning
  ## rouletee_prob: c(win, lose)
  
  if (sum(rouletee_prob) != 1) stop("sum of 'rouletee_prob' must be 1")
  
  capital = init_token 		## current # of chip
  PL <- 0 # the profit vector of the game
  
  i=1			
  while (capital >= bid && i <= max_round) {	# the requirement of bidding on the table
    rout = sample(0:1, size = 1, prob = rouletee_prob, replace = T)	# rouletee simulation
    
    if(rout == 1) {
      PL[i] = bid	## win "bid" chips
      bid = 1	 # bidding 1 chip in the next game
    } else {
      PL[i] = -bid  # lossing "bid" chips
      bid=bid*2 	# double bid
    }	
    
    capital = capital + PL[i]		## the capital 
    i=i+1
  }	
  
  init_token + cumsum(PL)
}

## Plot
plot(martingale(),
     lwd=3,font=2,
     type="l", col="red",
     xlab="The # of Bidding",
     ylab="Cumulative Chips",
     main="Martingale")
abline(h=init_token,col="green",lwd=2)


## Simulation
survival_round <- integer(10000)
final_token <- integer(10000)
for (i in 1:10000) {
  mar_result <- martingale(max_round = 80, init_token = 10)
  survival_round[i] <- length(mar_result)
  final_token[i] <- tail(mar_result, n=1)
}

hist(survival_round, breaks=100)
hist(final_token, breaks=100)