Originally Posted by

**Soroban** This is the basis for a "Sucker Bet".

I have four playing cards, one of each suit, face down on the table.

You pick any two of them.

You will bet that the cards are of the same color.

I will bet that they have opposite colors.

. . And we bet "even money".

Are you being hustled?

Let's reason it out . . .

There are only two outcomes: the colors match or they do not match.

. . Since these outcomes are equally likely, the bet is "fair".

Okay, there are *four* outcomes: (Red, Red), (Red, Black), (Black, Red), (Black, Black)

. . Since we each win half the time, the bet is fair.

The above explanations are comforting and reasonable . . . but *wrong!*

. . There are **six** outcomes: .$\displaystyle (\heartsuit\,\diamondsuit),\;(\heartsuit\,\spadesu it),\;(\heartsuit\,\clubsuit),\;(\diamondsuit\,\sp adesuit),\;(\diamondsuit\,\clubsuit),\;(\spadesuit \,\clubsuit)$

. . And in only **two** of them, $\displaystyle (\heartsuit\,\diamondsuit),\;(\spadesuit\,\clubsui t)$, the colors match.

Your probability of winning is: .$\displaystyle \frac{2}{6}\:=\:\frac{1}{3}$

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