The Devil’s Card Game

In this episode, we’ll analyze a card-counting game called The Devil’s Card Game. This exercise can teach us many key concepts related to economics, investor and market psychology, and probability. The game goes like this: suppose we have 11 cards in front of us: 10 “double” cards and 1 “devil” card. The “double” cards all have a 2 written on them. The “devil” card has 1/2048 written on it. The cards are thoroughly shuffled, and we get to pick them one by one. So, we know all the cards in the deck, but we don’t know which *order* we’ll get them in. All possible orders are equally likely. And there’s no “replacement”; once we pick a card, it’s put aside, NOT returned back to the deck. So, each time we draw a “double”, the odds of the next card also being a “double” could go down. We start with $1M. Each time we pick a card, our money gets multiplied by the number written on the card. So, if we get a “double” card, our money doubles. And if we get the “devil” card, our money gets divided by 2048. At any time, we’re free to stop picking cards and walk away with whatever money we have. What should our strategy be for playing this game? When should we walk away? Some questions to ponder: 1) Does it matter whether the initial $1M is our own hard earned money or “house” money? 2) Would our strategy for playing the game change if the initial sum were $1 instead of $1M? 3) If our sole objective were to maximize the *expected value* of the money we walk away with, what strategy would we play? 4) If we were to play this game in real life, would we adopt “expectation maximization” as our strategy? 5) How does the game look from the standpoint of our counter-party? Is it more favorable to them or us — assuming the initial $1M comes from us? 6) How do we expect most market participants to play this game? Would they use a strategy different from ours? 7) Extending the game: What if we could decide *how much* to bet on each card just before drawing it? In this case, only the portion of money that we bet is multiplied by the card we draw. Any “un-bet” money stays intact. Some key concepts we can learn from this exercise: 1) The “House Money” effect, 2) “Prospect Theory” and Loss Aversion, 3) The Marginal Utility of money, 4) Expectation Maximization, 5) Expected Utility Maximization, 6) Kelly Style Betting, 7) Markowitz Style Betting, 8) The fundamentals of Card Counting, etc. Download the Callin app for iOS and Android to listen to this podcast live, call in, and more! Also available at callin.com