Riddle:
You have 52 playing cards, 26 red, and 26 black. You draw cards one by one. A red card pays you a dollar. A black one fines you a dollar. You can stop any time you want. Cards are not returned to the deck after being drawn. What is the optimal stopping rule in terms of maximizing your expected payoff? Also, what is the expected payoff following this optimal rule?
Answer: The solution to this problem is, in my opinion the most difficult to understand of all the puzzles. Indeed I was unable to solve it and didn't receive a complete solution until two years after originally posting it. The final solution, in the form of the spreadsheet was sent to me by Han Zheng. For this reason I have left on the page the thoughts i had before I had the final solution as they represent an easier to understand and more simplistic approach. Also the reasoning may help you arrive at the final solution by yourself or help you understand it. I would recommend reading that answer before you dive into the full answer. But an important thing to note are that as the player we can't lose this game as we can gamble till all the cards are drawn and our net position is zero. From our earlier analysis it is clear we need a dynamic quit rule. A singal value is not sufficent. We must, at each stage consider what cards are remaining, and therefor the probability of a positive or negative outcome from drawing again. For the explanation i will ask you first to consider a deck containing only 6 cards, 3 +ve & 3 -ve (note i'm no longer calling the cards black and red, it confuses me.)
Riddle:
I’m filled with air and hide under your seat; sit down, and I’ll give you a treat. What am I?
Answer: A whoopee cushion.
A classic prank tool, it’s a staple of April Fools' Day mischief.
Riddle:
What is it that goes through the woods and never touches a twig?
Answer: Sound.
Riddle:
Make me thy lyre, even as the forests are. What if my leaves fell like its own -- The tumult of thy mighty harmonies Will take from both a deep autumnal tone. What am I?
Answer: The west wind.
Riddle:
What do you get when you cross a dog with a trickster’s day?
Answer: April Drool’s Day.
A playful pun on “April Fools’,” this reflects the holiday’s goofy humor.
Riddle:
A man crosses a desert in 10 days with no water. How?
Answer: He's a camel named Abdul.
The unexpected twist (a camel, not a man) mirrors the surprise element of April Fools' pranks.
Riddle:
If you counted 20 houses going to school, and then 20 houses on the left, going home. How many houses have you counted?
Answer: 20. They're the same houses going back.
Riddle:
I saw a creature: his stomach stuck out behind him, enormously swollen. A stalwart servant waited upon him. What filled up his stomach had travelled from far, and flew through his eye. He does not always die in giving life to others, but new strength revives in the pit of his stomach; he breathes again.
What is he?
Answer: Bellows.
Riddle:
What’s the best day to monkey around with your pals? It starts with “Ape” and ends with laughs!
Answer: Ape-ril Fools' Day!
A pun on “April,” this highlights the silly, mischievous fun of the day.
Riddle:
What’s the difference between Thanksgiving and a prankster’s delight? One’s full of thanks, the other’s full of fright!
Answer: April Fools' Day.
This contrasts Thanksgiving’s gratitude with April Fools' Day’s playful scares and tricks.
