Dealing cards

A Long Introductory Note
I wrote this puzzle with the characters Alice, Bob and Charlie. Last week a math logic puzzle went viral with the characters Albert, Bernard and Cheryl (see how math people always use names conveniently starting with the letters A, B and C?). My video answer was one of the first posted and has already gotten over 60, 000 views.

One thing I’ve learned is many people really do hate math. I’ve gotten an unusual amount of negative comments about how stupid the problem is, or why the correct official answer is wrong.

Another thing I’ve learned is people seem to hate women even more than math. Leave Cheryl alone. I’m surprised at how many big sites have called her derogatory names.

This blog is not the best place to elaborate on the topic. But since I write puzzles, I am including characters Albert, Bernard and Cheryl in more adventures so they are not judged only by that one incident.
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The Puzzle

On a lazy Sunday, Cheryl and Bernard were dividing up weekly chores. To make things interesting, they made it a game of chance.

First, they would shuffle a standard deck of cards (52 cards). Then they would draw cards alternately, with Cheryl going first. The person who draws an unlucky card would have to do the chore.

But, as these games go, they disagreed about the rules.

Cheryl proposed Rule 1, that the game would end when the Ace of Spades is drawn (and Cheryl draws first).

Bernard, an avid reader of MindYourDecisions, proposed Rule 2, that the game would end when any ace was drawn (again, Cheryl draws first).

Cheryl, also a fan of MindYourDecisions, was suspicious. So they discussed a possible compromise. In Rule 3, the game would end with the Ace of Spades, but Bernard would be the first to draw the cards. Cheryl said she would only agree to this if she could insert an extra card, a Joker, into the deck before it is shuffled as a good luck charm.

Now Albert, who was watching the entire drama, felt this was all a huge fuss about nothing. Clearly all the rules are equally fair to both people, right?

They need your help to figure out the probabilities. What’s the answer? Are the rules fair or is there an unfair edge to one of the players? Answer To You Might Be Dealing Cards Wrong

Let’s recap the rules.

Rule 1: Cheryl draws first, first person to draw the Ace of Spades gets the chore.

Rule 2: Cheryl draws first, first person to draw any ace gets the chore.

Rule 3: Bernard draws first, first person to draw the Ace of Spades gets the chore. Before shuffling, a Joker is inserted so the deck has 53 cards total.

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