Skinny's Casino

This puzzle was written by Gomez and Logain, and originally appeared in their puzzle competition last year.

Skinny Dakota has recently opened his own Casino and he has put you on the VIP list for opening night. This seeming act of kindness almost makes you reevaluate your opinion of him as a conniving little dung beetle but you soon grow suspicious that he is merely trying to get you to lose at one of his (almost certainly rigged) casino games. Curiosity inspires you to go to the Casino anyway and when you get there Skinny comes to meet you and leads you over to what looks like a Craps table. However, it’s a craps table with a slight difference and Skinny explains the rules.

“Okay, here at Chez Dakota we like to do things a little differently. Here we play with three dice and each of the three dice has twenty sides. The first two dice are the “House’s” dice and the third dice is yours. The croupier over there throws the two house dice and then you roll your lone dice. If the number on your dice is inbetween the numbers on the houses dice, you win. If it is not, the house wins. Fancy a try?”

Knowing Skinny, it’s no surprise to discover that the odd are not in your favour. Since Skinny is such a well known con merchant there wouldn’t be much point in asking if the game was fair at all. However, what is more challenging is the question; What, exactly, are your chances at winning Skinny’s new game?