Treebeard's Homepage : Stumpers

# Treebeard's Stumper9 May 2003

Sackcloth and Ashes

Today is the Dunn Middle School Renaissance Faire! We have a village with peasants, craftsmen, royalty, minstrels, and more. You meet a gray-bearded penitent in sackcloth who offers a simple game of chance. He has three cards. One is black on both sides, one is red on both sides, and one has a red and a black side. You reach in his bag and pull a card to the table. It's black on top. The bearded man bets even money that the hidden side is the same. "It can't be red-red, so there are only two choices. We have an equal chance of winning." Is this a fair game or a con?

Here is that crusty gray-bearded penitent in sackcloth at the DMS RenFaire. This was a fun day!

I played my "game of chance" with three cards that I made by gluing some old playing cards together face-to-face and marking them like this on each side:

Show the cards to the player and shuffle them in the bag. Have the player reach in to pick a random card and put it down without looking at the bottom. Suppose the top is black. Either way, you bet that the bottom is the same color. Explain how that eliminates the red-red card, so it must be an honest wager since only two cards remain. As soon as you see their money, the player can turn the card for judgement. The game is especially vicious if you "double or nothing" every time you lose.

For added effect, you can reach into the bag and remove the red-red card (after the player draws black) to demonstrate that there are only two choices remaining. How does it effect the odds if you allow the player to switch cards at this point?

Wearing sackcloth and ashes is an ancient symbol of penance and humility. In my "game of chance", who should be mournful and why? What other games is this related to?

Answer

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Copyright © 2003 by Marc Kummel / mkummel@rain.org