Puzzle: The Pirate’s Dilemma

Captain Montgomery Hall, the famous pirate, was getting ready to retire, and wanted to be sure he had a qualified successor, so one morning he came on deck with three buckets, their tops covered. As the crew watched he hoisted each of them overhead on separate halyards.

“To be a captain,” he said, “Ye have to be smart. Who amongst ye is the smartest?”

The pirates conferred a bit, and then pushed forward their reluctant choice.

“All right, we’ll see how smart ye are. There’s a gold doubloon in one a’them buckets. There’s a piece of stale, weevily bread in the other two. Pick the right bucket, and you get the doubloon, and the command. Pick the wrong one, ye get yer usual breakfast.”

“But captain,” said the sailor, “No matter how smart I might be, I could only pick the right bucket by luck.”

“Just by sayin’ that, it shows that at least ye aren’t stupid. But pick one anyway.”

So the sailor chose one of the buckets, walked over to the pin its halyard was on, and prepared to cast off.

“Wait just a minute,” said the captain, “Let’s make this more interesting.” And he went over to one of the other pins, lowered one of the other buckets to deck, and removed its cover. Inside was a piece of stale, weevily bread.

“This means that the doubloon is either in the bucket ye chose, or in the third bucket,” said the captain. Could be either one, right?”

“Ye-e-ss,” said the sailor thoughtfully.

“I’ll let ye change your mind, if ye want,” said the captain.

After the sailor considered the matter for a while, he walked away from his first choice, and lowered the third bucket to deck.

So here is the puzzle: Was this the smart thing to do? By changing his mind, did the sailor improve his chances, or make them worse, or did they stay the same?

If you think you know the answer, send it to puzzle@briontoss.com. Give a reason for your choice. Even if your answer isn’t correct, your courage alone qualifies for a drawing for a Rigger’s Apprentice T-shirt. There will be a bonus prize for the best explanation of the correct answer. Entries must be submitted by noon, Pacific Time, January 22^nd. We will announce the winners on January 24^th.