Almost exactly a year ago I posed Here is a card puzzle This sparked a frenzy in the comments section. The solution to this puzzle was so counterintuitive that some readers rejected it outright. In honor of the upcoming anniversary, it’s time to stir up more controversy with two more surprising card puzzles.
One of them I learned from Presh Talwalkar and the other from Martin Gardner. So please forward any hate mail their way.
Did you miss last week’s puzzle? check it out here, and find its solution at the bottom of today’s article. If you haven’t solved last week’s question yet, be careful not to read too far into it!
Puzzle #46: The Coming Ace
1. Shuffle a normal deck of 52 face-down playing cards, then turn the cards face up one at a time.
Which card is more likely to appear Immediately after the first Ace Appears: King of Spades or Ace of Spades? In other words, you will turn over the cards until you see an Ace of any suit. Is Next Is the card more likely to be the King of Spades or the Ace of Spades, or are they equally likely?
2. Reshuffle the same deck and start flipping again. This time, before flipping, you have to guess The first black ace Will appear. Which position in the deck is most likely, or are they all the same?
I’ll be back on Monday with answers and new puzzles. Do you know a cool puzzle that you think should be featured here? Leave me a message on X @JackPMurtagh or email me gizmodopuzzle@gmail.com
Solution to Puzzle #45: There’s no place like home
Last week’s puzzle You are asked to play the role of a sports statistician. Do you know how schedule affects the NBA Championship Series?
speak out Adanag 13 Provide you with clear answers.
In a real basketball game, you might think that the order of plays matters for psychological reasons (e.g., enjoying a winning streak might increase your chances of winning the next game), but in our mathematical model, it turns out The order of the games doesn’t matter. It doesn’t matter at all. In both cases, the Celtics are still more likely to win because they have the extra home game, even if they don’t end up using it. We’ll argue for best-of-seven situations, but the same argument applies to other numbers of games.
The key insight is that even if a team wins four games before Game 7, playing the rest of the way just for fun won’t change the outcome of the championship. So we can look at this series as if they always played seven games no matter what and then see who has won more games after all seven games are over. Teams that play more home games have an advantage.
