p_vec <- seq(from = .6, to = .8, by = .025)
great_wins3_mean <- rep(NA, length(p_vec))
great_wins3 <- rep(NA, 500)
for (k in 1:length(p_vec)){

  for (j in 1:500){

   ## run scenario 2 1000 times and extract sample mean
    ## for great players winning it all
    win_vec3 <- rep('none', 500)

    for (i in 1:length(win_vec3)){
      while (win_vec3[i] == 'none'){
        win_vec3[i] <- scenario3(p_vec[k])
      }
    }
    great_wins3[j] <- length(which(win_vec3 == 'great'))
  }
  great_wins3_mean[k] <- mean(great_wins3)
}
plot(p_vec, great_wins3_mean/500, type = 'l', col = 'red', lwd = 3, ylab = 'Win Percentage of Great Player',
     xlab = 'Good vs Bad Win Percent', main = 'Sensitivity Analysis')
abline(h = mean(great_wins1) / length(great_wins1), col = 'blue', lty = 3, lwd = 3)
legend('topright', legend = 'Baseline from Scenario 1', col = 'blue', lty = 3, lwd = 3)