The Paradox of Coincidence

If you are surprised by the first hand you draw, be surprised by the first hand you draw.

I was playing poker or some other card game, and I turned over the first five cards I was dealt, and lo and behold!

♠1-♠2-♠3-♠4-♠5

I thought to myself, "Yay! Something good might happen!" or "I used my luck, I'll have to be careful on the way home," you can be as optimistic or pessimistic as you want.

The probability of getting ♠1-♠2-♠3-♠4-♠5 together is the same as the probability of getting ♥2-♠J-♣5-♦9-♣7 or ♦9-♦A-♣8-♣7-♠10, which have no regularity whatsoever.

If there are 54 cards in a deck of cards, the probability of drawing a certain 5 cards when dealt 5 cards at random without considering the order of drawing is

(54 x 53 x 52 x 51 x 50) / (5 x 4 x 3 x 2 x 1) = 3162510 ways

Therefore

If the probability of getting ♠1-♠2-♠3-♠4-♠5 is 1 / 3162510 possible outcomes, then

If ♥2-♠J-♣5-♦9-♣7, then there are 1 / 3162510 probabilities that ♥2-♠J-♣5-♦9-♣7 will also occur.

We tend to feel that when random events are combined, only those that are clearly regular, such as ♠1-♠2-♠3-♠4-♠5, are seldom found, but those that are not regular are just as seldom found. Of course, it is more fun to play card games if you forget about the probabilities and just be happy.

References

• Signal & Noise: The "Predictive Science" of a Genius Data Analyst