All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Games
Coin Toss (Posted on 2013-06-13) Difficulty: 3 of 5
Two persons engage in a game of chance. The game is to nominate a sequence of three consecutive coin tosses [H or T].

Player one firstly nominates a sequence and then player two makes a nomination. The game finishes when the last three tosses match either one of the players' nominations.

How can player two be assured of winning most of the time?

Given the choices that can be made by player one, what are the odds of player two winning?

Oh, it doesn't matter who tosses the coin.

See The Solution Submitted by brianjn    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Player 2 strategy Comment 4 of 4 |

Based on Charlie's table, here is a set of rules for player 2 to follow to optimize his/her results based on player 1's choice of a pattern:
If player 1 chooses "xyz" then player 2's best choice is  "wxy". 
If x = y     then w is the opposite.   (so "not x", x, x)
If x <> y   then w is the same as x. (so x, x, y).


It makes sense that the last 2 of player 2's pattern would be xy, since in a series of coin flips, for player 1 to win, there has to be a wxyz (unless he wins right from the beginning), so if player 2 has some wxy pattern, he wins before player 1 has the chance.

But I can't explain why the 'w' should be either heads or tails except by looking at Charlie's table

  Posted by Larry on 2013-06-21 16:34:35
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information