Two teams play a series of games, the chance of winning is 0.5 independently. The winning team is the one that comes first to four wins in a row. How do I calculate the expectation of the number of games in a series using simulation?
I need to create simultation of choise between A,B. one time group A wins and other tome group B. the first group who got 4 wins in a row, she is the winner and we stop the game.
I stated like this - (don't judge me I started ussing R just in the last week)
# 2 Teams play each other, each Team has a chance to win p = 0.5
# Only the Team wining in a row of 4 strikes wins
# How many times need to be played till the chance is very high that this will happen
#how many games
c_nb_of_games <- 1e2L
#how many times to simulate
c_index = 1:100
for(j in 1:length(c_index)){
#Create a vecor that a team wins by chance of 0.5, => 1 = win game, 0 = lose game
c_wins <- rbinom(c_nb_of_games, 1, 0.5)
#check for the index (number of games till one team wins 4 times in a raw)
for(i in 4:length(c_wins)){
if(sum(c_wins[seq(i-3,i,1)]) == 4){
#print(i)
c_index[j] <- i
break
}
}
}
hist(c_index)
I know it's not a good code, but I dont know how to create a "if" to stop if one group get to 4 wins in a row.. help?