# start with N = number of repetitions, pAB = Pr(A beats B), pAC = Pr(A beats C), pBC = Pr(B beats C)
#
matchup = rep(NA, times = N)
winner = rep(NA, times = N)
loser = rep(NA, times = N)
#
# initial matchup
rand1 = runif(1,0,1)
if (rand1 < 1/3) {matchup[1] = "AB"}
if (rand1 >= 1/3 & rand1 < 2/3) {matchup[1]="AC"}
if (rand1 >= 2/3) {matchup[1] = "BC"}
#
# generate random numbers to determine winners
rand = runif(N,0,1)
#
# conduct loop
for (i in 1:N) {
   if ((matchup[i] == "AB") & (rand[i] < pAB)) {winner[i] = "A"; loser[i] = "B"; matchup[i+1] = "AC"}
   if ((matchup[i] == "AB") & (rand[i] >= pAB)) {winner[i] = "B"; loser[i] = "A"; matchup[i+1] = "BC"}
   if ((matchup[i] == "AC") & (rand[i] < pAC)) {winner[i] = "A"; loser[i] = "C"; matchup[i+1] = "AB"}
   if ((matchup[i] == "AC") & (rand[i] >= pAC)) {winner[i] = "C"; loser[i] = "A"; matchup[i+1] = "BC"}
   if ((matchup[i] == "BC") & (rand[i] < pBC)) {winner[i] = "B"; loser[i] = "C"; matchup[i+1] = "AB"}
   if ((matchup[i] == "BC") & (rand[i] >= pBC)) {winner[i] = "C"; loser[i] = "B"; matchup[i+1] = "AC"}
}
table(matchup)
table(winner)
table(loser)
#
games = table(winner) + table(loser)
propwin = table(winner)/games
proplose = table(loser)/games
propwin; proplose