The probability of getting 31 in Mus

The probability of being dealt exactly 31 with your first four cards in the eight-reyes (eight-kings) version of Mus (the Spanish card game) is 8,384 out of 91,390, or 9.17% — roughly one in eleven hands. If we count any hand with juego (a total of 31 or more), the probability is around 26.7%.

How juego is counted

Reyes (kings), caballos (knights), sotas (jacks) and treses (threes) are worth 10. Ases (aces) and doses (twos) are worth 1. The remaining cards are worth their face value. There are only four ways to reach 31 with four cards:

• 10 + 10 + 10 + 1: 4,480 combinations. This is the most common way to get 31.
• 10 + 10 + 7 + 4: 1,920 combinations.
• 10 + 10 + 6 + 5: 1,920 combinations.
• 10 + 7 + 7 + 7: 64 combinations. The rarest way.

That makes 8,384 hands out of a possible 91,390.

Why knowing the odds helps

If you’re dealt 31, you’re in the group of 9% of hands most sought after for juego. If you don’t have juego, remember that three out of four hands don’t either, so punto (the point round) matters too. It’s useful to know this before placing a bet.

The role of doses

Since doses count as ases in eight-reyes Mus, there are eight cards worth 1. That’s what makes the 10 + 10 + 10 + 1 combination so common. We explain this in why doses count as ases.