Nachbin's theorem

Nachbin's theorem is like a math super power. It lets us look at two different kinds of things to figure out if they are the same. It can be used with probabilities and statistics.

Let's say you want to know if you have the same chance of winning a game of luck-based card games if you use two different decks of cards. Nachbin's theorem helps you figure out whether the two decks are really the same, so you can be sure you have the same chance of getting lucky either way.

To do this, Nachbin's theorem looks at two sets of numbers. It looks at the chances of getting a certain outcome from each of the decks, like getting a card from a specific suit or getting a card from a certain card number. It then checks to see if the same numbers appear in both sets. If they do, then Nachbin's theorem says the two decks are the same, so they give you the same chance of success in a game.