# New Dice Table at the Casino [closed]

You walk up to a dice table in the casino.

A woman bets on $12$, throws the dice and they come up: 6 5 3 2

She shouts with glee as the dealer hands her the winnings.

She then bets on $14$ and rolls: 5 2 6 1

The dealer hands her winnings again.

Deciding to get in on the action you bet on $15$. She then rolls: 3 4 1 5

Did you win? Why/why not?

• This feels very underspecified; I bet it's possible to come up with lots of possible explanations, some of which make the answer yes and some of which make the answer no. (Two simple theories consistent with the observations: 1. Everyone always wins. 2. You win if and only if a 6 comes up, whatever you bet on.) – Gareth McCaughan Feb 15 '18 at 17:05
• I believe the way this is tagged gives appropriate information on what possible solutions should entail. But it would make for a more complete puzzle to have at least one counter-example where the woman loses her money. – user41531 Feb 15 '18 at 17:19
• @Bilkokuya Good call, this is an initial iteration of this puzzle. Futher iterations will have a roll that she loses. Thanks! – Vamphri Un'Goro Feb 15 '18 at 17:21

You win.
The aim of this game is to reach the number face-down (i.e. opposite sides) on each of the dice.
For the roll (6,5,3,2) this is (1,2,4,5) which equals 12.
For the roll (5,2,6,1) this is (2,5,1,6) which equals 14.
For the roll (3,4,1,5) this is (4,3,6,2) which equals 15. As such, you win.