Why do some hands seem impossible?

Some hands seem impossible because they catch our attention and stick in our memory, like four aces, four kings or a perfect 31. Yet every specific 4-card hand has exactly the same chance of being dealt: 1 in 91,390, even a combination as unremarkable as the dos de copas (two of cups), cinco de bastos (five of clubs), sota de oros (jack of coins) and siete de espadas (seven of swords).

How our brains trick us

Our brains lump all the ‘ordinary’ hands together and only single out those with a name or special meaning. There are thousands of unremarkable hands, so they feel like the norm. Special hands are few and far between, which makes them seem impossible.

An example

If you’re dealt four aces, you think, ‘What are the chances!’ If you’re dealt a nothing hand, you don’t give it a second thought. But that particular nothing hand was just as unlikely. It’s simply that there are countless others like it.

What really is different

The probability of getting any good hand really is lower than that of getting any ordinary hand, simply because there are fewer good hands. We work it out in the hardest hand to get and the probability of getting four kings. And we explore more tricks our minds play in impossible coincidences that can actually happen.