CTK Exchange
Front Page
Movie shortcuts
Personal info
Awards
Reciprocal links
Privacy Policy

Interactive Activities

Cut The Knot!
MSET99 Talk
Games & Puzzles
Arithmetic/Algebra
Geometry
Probability
Eye Opener
Analog Gadgets
Inventor's Paradox
Did you know?...
Proofs
Math as Language
Things Impossible
My Logo
Math Poll
Other Math sit's
Guest book
News sit's

Manifesto: what CTK is about |Store| Search CTK Buying a book is a commitment to learning Table of content Things you can find on CTK Chronology of updates Email to Cut The Knot

CTK Exchange

Subject: "Three Dices "Paradox""     Previous Topic | Next Topic
Printer-friendly copy     Email this topic to a friend    
Conferences The CTK Exchange This and that Topic #131
Reading Topic #131
activeco
Charter Member
2 posts
Jul-08-01, 08:18 AM (EST)
Click to EMail activeco Click to send private message to activeco Click to add this user to your buddy list  
"Three Dices "Paradox""
 
  
Three dices are thrown simultaneously.
You can bet $1 on a single number, 1 to 6.
The odds are rightly 1/2 so you get $1 for every occurrence
of your number. Of course you get $2 or $3 for double or triple
occurrence.

After 1000 throws you won $500 betting always on the same number. Even game?
Wrong! You lost money, considerably.

Here is what happened:

There was 355 throws with only one of your numbers shown.
68 throws with doubles.
3 times you got triples.

This makes $500 in total, but made in 426 throws.
The rest of 574 you lost $1 for each throw, which makes -$74.

This is a regular pattern, proved in many simulations.

Nice one, isn't it?


  Alert | IP Printer-friendly page | Edit | Reply | Reply With Quote | Top

Conferences | Forums | Topics | Previous Topic | Next Topic

You may be curious to visit the old CTK Exchange archive.

|Front page| |Contents|

Copyright © 1996-2018 Alexander Bogomolny

[an error occurred while processing this directive]
 Advertise

New Books
Second editions of J. Conway's classic On Numbers And Games and the inimitable Winning Ways for Your Mathematical Plays