The Mathematics of the Cards

Use this rigged game to cheat your friends twice in a row! The game functions just like 31, only this time you'll always win if you follow the instructions in this video.

From Revision3:
This week we're learning a rigged game that combines principles we learned from both the "nim" and "advanced nim" episodes, and combines them with an added twist that allows you to beat your mark even after he knows the secret!

The fame goes by several names (we're calling it "31"), and both the setup and rules are simple...

The setup: pull out all the aces through sixes in a deck of cards, an set them into piles by value (a pile of four aces, four twos, four threes, etc.)

The rules: each player takes turns picking up cards and adding them to "the pot", increasing it's total amount by the value of each card. The first player to take to pot OVER 31 loses.

The trick: as in advanced nim, there are "pole positions" you want to reach on your turn: 3, 10, 17, and 24. Once you've hit a pole position, make sure that each round afterward the total of your draw PLUS the sucker's draw equals 7. This will keep you hitting the pole positions right up until you hit 31.

The twist: the best part about this scam is that you can actually teach the whole trick to your sucker and STILL beat him! Let him go first and achieve one of the pole positions. Once he does, continue to burn the same card over and over (in our case a 4, forcing him to use up the 3's). Once he's run out of the right cards, he'll have no way to properly respond to your plays, allowing you to win the game!