Chuck-a-luck is a popular dice game played with three standard dice that are kept in a device shaped somewhat like an hourglass that resembles a wire-frame bird cage and that pivots about its centre.

The dealer rotates the cage end over end, with the dice landing on the bottom.A player may bet on any one of the numbers 1,2,3,4,5,6. If the player's number appears on one, two, or three of the dice, he receives respectively one, two, or three times his original stake plus his own money back; otherwise he loses his stake.

What is the chance of winning this game ?

[provided you bet for any one number and atleast one die comes up with the number is considered as a win]

Suppose you have selected Number 3

There are 6 x 6 x 6 = 216 ways for the dice to come up, and 5 x 5 x 5 = 125 of these

ways have no threes coming up.

Thus the probability of winning are (216-125) / 216 = 91/216

Thanks for the comment. Answer corrected!!

216 - 125 = 91, not 86.