Playing Cards

Two Hands of Cards photo

Q: If we assume that both hands above came from an honest deal (truly random), which one are you more likely to get?


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A: Both hands are equally probable.

Most people will pick hand #2, probably because playing card games has changed the way we look at cards. It makes us instinctively look for patterns and discriminate between two categories: “good” and “bad” hands. And in all games, for all the possible hands in a deck there are many more “bad” hands than “good” ones. Because hand #1 looks like a very good hand using general card game rules of thumb (high cards, same suit, sequential order, etc), it seems less likely to come up than a “bad” hand like #2.

But in an honest deal, any hand of X cards is just as likely as any other hand of X cards. To better see it, just imagine you were dealt a hand from a randomized deck of blank cards; after all, if the deck is truly randomized, it doesn’t matter what’s printed on the cards, each card has a 1 in 52 chances of being in each position of the deck.

The point here is not just about cards. It’s about being careful with what kind of patterns we look for without realizing it. Rules of thumb are good shortcuts for most of every day life, but sometimes you really need to look at things with a set of fresh eyes, as if you were seeing them for the first time.

See also: Rationality

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One Response to “Playing Cards”

  1. jinsei Says:

    Or the point is that we interpret the situation and question based on our experience of the context. There are only four possible hands equivalent to the first, but over a million hands equivalent to the second. So we subconsciously assume the question to mean “which one is your hand more likely to be equivalent to?” This is normal, I think, and a perfectly fine thing to do…

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