Solution to July 14, 2017 Riddler Classic

Riddler Classic - July 14, 2017.R

# Set the parameters which are beyond the player's control
  prob_win <- 0.6
  alpha <- 1000000L
  beta <- 10000L

# List the possible choices available to the player
  minimum_games <- 1L:50L

# List the series lengths which result from each available choice
# and, for each choice, list the corresponding probability of winning the series
  series_lengths <- (2*minimum_games) - 1
  
  prob_win_champ <- 1 - pbinom(q = minimum_games - 1,
                               size = series_lengths,
                               prob = prob_win,
                               lower.tail = TRUE)
                               
# For each choice available to the player, define the payoffs if they win or, alternately, lose
  payoff_if_win <- alpha - beta*minimum_games
  payoff_if_lose <- 0

# Calculate the expected payoff for each choice
  expected_payoff <- (prob_win_champ)*payoff_if_win + (1 - prob_win_champ)*payoff_if_lose

# Return the choice of series length which maximizes the player's expected payoff
  series_lengths[expected_payoff == max(expected_payoff)]

# Return the best expected payoff
  max(expected_payoff)

# Plot the payoff curve
  plot(series_lengths, expected_payoff)