WWTBAM Bored

A man in a trench coat approaches you and pulls an envelope from his pocket. He tells you that it contains a sum of money in bills, anywhere from $1 up to $1,000. He says that if you can guess the exact amount, you can keep the money. After each of your guesses he will tell you if your guess is too high, or too low. But! You only get nine tries. What should your first guess be to maximize your expected winnings?

BackInTex wrote:The number would be higher than 500 because you are trying to maximize your winnings, not maximize your chance of winning. So there is higher value in narrowing down a higher number rather than narrowing down a lower number.

In other words, each of the 9 guesses are better spent working towards a number above 500 rather than below.


This is for smarter people than me to figure out, but I think my initial logic is correct.

silverscreenselect wrote:It's somewhat similar to the one a couple of weeks ago that sparked a lot of interest here:

A man in a trench coat approaches you and pulls an envelope from his pocket. He tells you that it contains a sum of money in bills, anywhere from $1 up to $1,000. He says that if you can guess the exact amount, you can keep the money. After each of your guesses he will tell you if your guess is too high, or too low. But! You only get nine tries. What should your first guess be to maximize your expected winnings?

As with the one two weeks ago, the obvious answer would appear to be $500, but I'm almost positive that's wrong. There's no prize other than getting a shoutout on the site next week if you get it right and they pick your entry. Here's the link:

http://fivethirtyeight.com/features/can ... ench-coat/

Bob78164 wrote:

silverscreenselect wrote:It's somewhat similar to the one a couple of weeks ago that sparked a lot of interest here:

A man in a trench coat approaches you and pulls an envelope from his pocket. He tells you that it contains a sum of money in bills, anywhere from $1 up to $1,000. He says that if you can guess the exact amount, you can keep the money. After each of your guesses he will tell you if your guess is too high, or too low. But! You only get nine tries. What should your first guess be to maximize your expected winnings?

As with the one two weeks ago, the obvious answer would appear to be $500, but I'm almost positive that's wrong. There's no prize other than getting a shoutout on the site next week if you get it right and they pick your entry. Here's the link:

http://fivethirtyeight.com/features/can ... ench-coat/

If your first guess is 744, then whenever the actual number is that or more, you're guaranteed to win via the obvious strategy. You've still got a chance when the number is lower. That would be my first thought. --Bob

Bob78164 wrote:

Bob78164 wrote:

silverscreenselect wrote:It's somewhat similar to the one a couple of weeks ago that sparked a lot of interest here:

Aman in a trench coat approaches you and pulls an envelope from his pocket. He tells you that it contains a sum of money in bills, anywhere from $1 up to $1,000. He says that if you can guess the exact amount, you can keep the money. After each of your guesses he will tell you if your guess is too high, or too low. But! You only get nine tries. What should your first guess be to maximize your expected winnings

As with the one two weeks ago, the obvious answer would appear to be $500, but I'm almost positive that's wrong. There's no prize other than getting a shoutout on the site next week if you get it right and they pick your entry. Here's the link:

http://fivethirtyeight.com/features/can ... ench-coat/

If your first guess is 744, then whenever the actual number is that or more, you're guaranteed to win via the obvious strategy. You've still got a chance when the number is lower. That would be my first thought. --Bob

Repeating this strategy (decreasing the power of two by one at each step) means that you'll win whenever the number is 489 or higher, and never otherwise. This gives you an expectation value of $381.184. --Bob

TheCalvinator24 wrote:When I ran a simulation, starting at 745 didn't get me a guarantee win in 9 tries. It took 10 tries.

Of course, I did it manually, so I may have screwed it up somewhere.

TheCalvinator24 wrote:"That does guarantee a win when the number is 490 or higher."

Maybe I'm misreading this line, or like I said, maybe I screwed up my simulation, but this is the result I can't replicate.

Bob78164 wrote:

TheCalvinator24 wrote:"That does guarantee a win when the number is 490 or higher."

Maybe I'm misreading this line, or like I said, maybe I screwed up my simulation, but this is the result I can't replicate.

When the number is lower than 745, your next choice will be 617. If it continues to be lower, you choose, in order, 553, 521, 505, 497, 493, 491, and 490. Any time the number is higher than your previous choice, you choose the midpoint of the two endpoints that you know about. --Bob