What is the best way to play if you want to maximize your winnings? The catch is, these chances are unknown to you, and so you do not know which machine will give you a higher chance of winning. For machine 1, this chance is 50%, and for machine 2 it is slightly lower at 40%. For an individual machine, the chances of winning are the same every time you play it, and it is not affected by the results of your previous plays. When you play a game, you either win (get $1) or lose (get nothing). At each time you can pull the arm of either slot machines, but not both, and we assume you can play this game 2,000 times. You have two slot machines / one-armed bandits (the number of machines can be changed). If we make some assumptions, we can view the problem of choosing penalty takers as a Multi-armed Bandit (MAB) problem, and we will learn whether Van Gaal’s policy is optimal. The player that missed will go down to the bottom of the list, and will be back at the top after the four other players have missed their penalties. While most football teams appoint one or two players to take penalty kicks in all matches, Van Gaal has a list of five players that rotates whenever a player misses a penalty. Manchester United, under Dutch coach Louis van Gaal, has an unconventional policy on which player takes a penalty during a match.
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