Summer is in full swing! Time to get those brains as warmed up as the rest of you.
Note: If you could all please input your answers using the previously noted html code it will allow others to answer without having a spoiler. Also, in your answer, do not include any ' or " or it will not work properly. Also, if you are having trouble getting the code to work, please do not be the first person to answer.
Question
I am thinking of a number between 1 and 100. You can guess a number and I will tell you if it is high or low. If you get it right on the first guess I will pay you $5, on the second guess $4, and so on. If you get it right on the sixth guess I will pay you nothing, on the seventh guess you owe me $1, on the eight you owe me $2, and so forth.
Q1) Should you play the game with me?
Q2) What is your expected return?
Good Luck!
EV of $-.417 to -$.361 is what I got. Thats assuming the optimal strategy is to just guess the middle number each time and go from there. The range exists because if theres an even number of numbers left to guess you cant chose the exact midpoint so one side is going to have one fewer options than the other if you guess wrong that turn")" />
Other people's buttons aren't working for me for some reason, so I hope I'm not writing more of the same. Hopefully I did the code right...
@3green - It looks like your code is missing some parantheses. Lets see if I can fix it. You're not the first person to have trouble with the code suggesting that I may be giving bad advice. Oddly, the buttons in the initial post I reference all work fine.
your original answer with the parantheses added:
and, another test with your same answer:
Let's see how this works...
cooldurg's answer: EV of $-.417 to -$.361 is what I got. Thats assuming the optimal strategy is to just guess the middle number each time and go from there. The range exists because if theres an even number of numbers left to guess you cant chose the exact midpoint so one side is going to have one fewer options than the other if you guess wrong that turn")" />
smeethu's answer:
My code looks right. Let me know if it doesn't work.
Del.
Additionally log base 2 of 100 = 6.6438 giving the average guesses needed. While this may make it appear as if your average would be a negative value you need to account for the fact that this distribution terminates at 7 (the maximum number of guesses needed) but the lower extreme is 1 guess. I don't have a calculator on me, so I can't find the standard deviation (it would allow for the output of the average expected value of $.20). This is abridged/statistical method of finding the same answer as mikeswimn and I found through a manual method.
Veritatis repellat ut aliquam velit dolorem laborum eum. Nobis et quidem eius. Sit odio omnis dolore expedita.
Officiis ducimus a esse nobis et praesentium. Velit consequatur esse ea quas aut error. Autem odio beatae enim nam.
Ea ab ex ipsum aliquam tenetur optio. Sit quia doloremque qui blanditiis. Deleniti doloribus nihil aspernatur officiis exercitationem aspernatur placeat. Omnis sunt sint maiores.
See All Comments - 100% Free
WSO depends on everyone being able to pitch in when they know something. Unlock with your email and get bonus: 6 financial modeling lessons free ($199 value)
or Unlock with your social account...