If a gambler and the casino keep going forever, how come the casino is always the winner?
In: Mathematics
Say you have a single die (one of a pair of dice). It has 6 sides, right?
Let’s invent a game where a player can bet $5 that a throw of the die will be either 3 or 6. If it’s one of those numbers, they get to keep their $5, and the house pays them another $5. But if it lands on 1, 2, 4, or 5, they lose, and their $5 goes to the house.
A player can easily double their money in a single roll. How exciting!
But it’s not a good bet, because their odds of winning are only 2 in 6 (one third). So a third of the time they will win $5, but two thirds of the time they’ll lose $5.
An individual throw of the die is random. It can land on any of the 6 sides. But over time, the ratio will look closer and closer to what you expect based on the die having six sides, 1/6th of the rolls l will be a “1”, 1/6th will be a “2”, and so on.
The gambler (irrationally) hopes to get lucky on a few rolls. But the house is playing a long game. As long as there are enough rolls of the die, they are guaranteed to win 2/3rds of them.
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