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

Home > Probability
Tic-Tac-Toe Toss Tactics? (Posted on 2004-10-04) Difficulty: 3 of 5
Two expert and jaded tic-tac-toe players, after drawing for the n-th time, decided to add some randomness to their favorite game.

First, they used a coin to decide who would start. Then, that player would pick his initial move randomly. Next, the other player would also pick his answer randomly. Finally, from then on the game went on as usual, with each player playing in the best possible way.

For each player, what are the odds of winning, losing, or drawing?

See The Solution Submitted by Old Original Oskar!    
Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: Here's a try | Comment 2 of 10 |
(In reply to Here's a try by Rajal)

By symmetry, you just have to consider X going first. As you calculated, there are 72 cases:


X on corner, O on corner -- Win (12)
X on corner, O on edge -- Win (16)
X on corner, O on center -- Draw (4)

X on edge, O on center -- Draw (4)
X on edge, O on adjacent edge -- Win (8)
X on edge, O on opposite edge -- Draw (4)
X on edge, O on adjacent corner -- Draw (8)
X on edge, O on other corners -- Win (8)

X on center, O on corner -- Draw (4)
X on center, O on edge -- Win (4)

Out of the 72 cases, I get 48 Wins (not 40) and 24 draws. So, the player who goes first has 2/3 odds of a win, and 1/3 tie -- adding the initial toss, you get 1/3 equal chances for win, draw, or loss.
  Posted by Federico Kereki on 2004-10-04 12:41:13
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information