great_wins1 <- rep(NA, 1000)
great_wins2 <- rep(NA, 1000)

## run sim 1000 times to look at sample means
for (j in 1:1000){

  ## run scenario 1 1000 times and extract sample mean
  ## for great players winning it all
  win_vec <- rep('none', 1000)

  for (i in 1:length(win_vec)){
    while (win_vec[i] == 'none'){
      win_vec[i] <- scenario1()
    }
  }
  great_wins1[j] <- length(which(win_vec == 'great'))

  ## run scenario 2 1000 times and extract sample mean
  ## for great players winning it all
  win_vec2 <- rep('none', 1000)

  for (i in 1:length(win_vec)){
    while (win_vec2[i] == 'none'){
      win_vec2[i] <- scenario2()
    }
  }
  great_wins2[j] <- length(which(win_vec2 == 'great'))
}

t.test(x = great_wins1, y = great_wins2, 'less')

hist(great_wins1/length(great_wins1), xlab = 'Percentage of Great Player Wins: Scenario 1',
     main = 'Histogram of Win Percentage')

hist(great_wins2/length(great_wins2), xlab = 'Percentage of Great Player Wins: Scenario 2',
     main = 'Histogram of Win Percentage')