When I was about five-years old, I learned a game called “War.” Two players are dealt 26 cards face down. Each then simultaneously shows the top card, and the player showing the higher value takes both exposed cards and places them at the bottom of his or her stack. If both cards are of equal value, there is a “war.” Each combatant places the next three cards face down, and the fourth face up. The card showing higher value captures all the cards played and puts them at the bottom of his or her stack. The war ends when one person has all 52 cards. I was very good at “War,” or so I thought. I hadn’t yet heard about “confirmation bias,” which was why I remembered my victories more than my defeats.
When I finally realized that the game was skill-free, I lost interest. Knowing that the outcome is completely determined once the deck is shuffled and dealt, I began to invent variations. For instance, I’d put all 4 aces (the highest value) in one stack and the remaining 48 cards in the other stack, and play. After playing five times, the stack that started with 4 aces won all but once. I concluded that it was better to start with the 4-ace stack. I hadn’t known at the time that I was applying a naïve version of a Monte Carlo method, a mathematical procedure in which a large number of repeated trials produce reasonably accurate predictions about the actual probability of the outcome of an event. (For instance, if you flipped a fair coin 1000 times, you would probably get approximately 500 heads, give or take 20.)
When I was about five-years old, I learned a game called “War.” Two players are dealt 26 cards face down. Each then simultaneously shows the top card, and the player showing the higher value takes both exposed cards and places them at the bottom of his or her stack. If both cards are of equal value, there is a “war.” Each combatant places the next three cards face down, and the fourth face up. The card showing higher value captures all the cards played and puts them at the bottom of his or her stack. The war ends when one person has all 52 cards. I was very good at “War,” or so I thought. I hadn’t yet heard about “confirmation bias,” which was why I remembered my victories more than my defeats.
When I finally realized that the game was skill-free, I lost interest. Knowing that the outcome is completely determined once the deck is shuffled and dealt, I began to invent variations. For instance, I’d put all 4 aces (the highest value) in one stack and the remaining 48 cards in the other stack, and play. After playing five times, the stack that started with 4 aces won all but once. I concluded that it was better to start with the 4-ace stack. I hadn’t known at the time that I was applying a naïve version of a Monte Carlo method, a mathematical procedure in which a large number of repeated trials produce reasonably accurate predictions about the actual probability of the outcome of an event. (For instance, if you flipped a fair coin 1000 times, you would probably get approximately 500 heads, give or take 20.)