Skip to main content

Flipping Quarters

Here's an interesting puzzle involving chance:

A man in a park asks you to play a game with him. It's a form of gambling. To play, you must pay the man $5, then flip a coin repeatedly until you get heads. As soon as you get heads, you stop flipping. If you only flipped the quarter once, he'll give you $1. If you flipped it twice, you get $2. Three times, $4. Four times, $8. Each extra flip gets you twice as much money, so the longer it takes before you get tails, the more money you get.

Should you play, if you have a lot of time and the man will play as many games as you want? How much money, on average, would you gain (subtracting the $5 fee)?

I will give the solution in a later post.
Labels:

Comments

  1. Dave ShanklinDecember 31, 2015 at 7:28 PM

    1. As long as you can quit and he can't.
    2. Have a substantial bankrole (assets to risk).
    3. -5 + (1/2)(0) + (1/4)(1) + .(1/8)(2) + (1/16)(4) + 1/32(8) + 1/64(16) + .....=
    = -5 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 .... = -5 + (n-1)*(1/4) -> which goes to infinity as the n approaches infinity.
    4. Reasons to quit.
    a. (bankroll is exhausted or there is a small risk of flipping tails a large number of times); Check the coin, if this seems to be the case.
    b. Can make a better ROI doing another activity either in dollars or personal satisfaction.
    c. Moral compulsion of not taking advantage of someone else.

    Note: There are limits to betting on tables in vegas (this is generally to protect the house) :)

    ReplyDelete

Post a Comment

Popular posts from this blog

Should Tau Replace Pi?

The digits of π, organized in a very new way Happy π-day! And happy π-month! Today's month and day - that is, March 14 or 3.14 - includes the first 3 digits of π. And today's month and year - March 2014 or 3.14 - also includes the first 3 digits of π. We won't have another double-day for π for the next 100 years, so enjoy this one! For the special occasion, I'm posting two π-related posts - one for π-month, and the other for π-day. In both posts, I'm setting the font size to approximately π * π + π + π. This is the first post, for π-month; to see the second, go to http://greatmst.blogspot.com/2014/03/pi-month-pi-day-post-2-5-common-pi-myths.html . In this post, I am including an essay I wrote about whether π or τ is the more superior constant. This was written for people who know very little about math, so the basic idea should be easy to understand even for people who are not mathematically inclined. Should Tau Replace Pi? A constant is any number or value that ne...
Post a Comment
Read more

The Geminids

The Geminid meteor shower is coming up! At 2:00 AM, on December 14 (that's Thursday night, or Friday morning), you can see anywhere from 100 to 150 meteors per hour - depending on the sky and weather conditions. That's more than 1 meteor per minute! This particular meteor shower comes from a 5.1 km wide asteroid called 3200 Phaethon. Flecks of debris fall off this asteroid in a trail around the sun. These bits are called meteoroids . Every year, in December, Earth passes through this stream of meteoroids; when one of them enters Earth's atmosphere, it burns up and we see a meteor. If the meteor is brighter than Venus, it's called a fireball. Fireballs are much less common than meteors. This year, viewing conditions will be especially good; the peak occurs only 1 day past new moon. If you live in an area with lots of light pollution, you will definitely want to drive into the country. If you think the weather will be bad, go out a day or two before or after the peak. Kee...
Post a Comment
Read more

Which Hurts More?

212° F Let's play a little game. I'll list a bunch of possible actions. Each action will have 2 variations, (a) and (b). You choose either (a) or (b), depending on which would be safer (or less painful). Each of the questions will involve an oven hot enough to bake a cake (350° F), and a pot of boiling water (assume we're at sea level). So... would you rather: 1.     (a) Stick your hand in the oven     (b) Stick your hand in the boiling water   ... for a period of 10 seconds 2.     (a) Leave a fork in the oven     (b) Leave a fork in boiling water   ... for a period of 15 minutes. Then hold the fork tight with your bare hand. 3. Fill a jar to the top with cool tap water. Then:    (a) Place the jar in the oven    (b) Place the jar in the boiling water   ... for a specific, but unknown, period of time. Then remove the jar and put your hand in it. First see if you can figure these out yourself. They shouldn't be too...
Post a Comment
Read more