Comments on: The Dice Brain Teaser: A Technical Interview Question that Can Help You Solve Problems Better

By: Faisal

Faisal — Fri, 16 Dec 2011 23:27:06 +0000

Here is how I solved the problem:

Probability I win in any given round – 1/6

Probability that my opponent wins in any given round – (5/6)*(1/6) = 5/36

Since we keep playing till we have a winner, we just need to normalize the above two probabilities.

So the probability I win the game is –
(1/6)/[(1/6)+(5/36)] = (6/36)/(11/36) = 6/11

So I do get the same answer, with slightly different logic.

By: A Day in the Life of a Game Theorist: A Tribute to One Year of Game Theory Tuesdays - Mind Your Decisions

Sat, 20 Aug 2011 06:14:08 +0000

[...] Darn you, Presh. You make infinite series seem so conventional. Aside from that, I absolutely adore the third solution. Erik in The Dice Brain Teaser (link) [...]

By: Puzzle: how often does it rain? - Mind Your Decisions

Puzzle: how often does it rain? - Mind Your Decisions — Mon, 20 Jun 2011 21:06:37 +0000

[...] Hint 1 You can solve this by using the law of total probability (as an example, this is used in solution method 3 of the dice brain teaser) [...]

By: Quick puzzle: how long to get to heaven? - Mind Your Decisions

Quick puzzle: how long to get to heaven? - Mind Your Decisions — Mon, 20 Jun 2011 20:19:26 +0000

[...] Hint: see method 3 of the dice brain teaser [...]

By: Janus

Janus — Sun, 06 Feb 2011 20:18:30 +0000

@Rob:

Here is the first line in the description of the problem: “You and I play a game where we take turns rolling a die. I win if I roll a 4. You win if you roll a 5.” Note, it stipulates that the players take turns. Plural “turns.” Not each take one turn. The clarifying notes make clear that this game continues until one wins. Since player 1 winning and player 2 winning are mutually exclusive events, you are essentially making the claim that the probability of player 2 winning is 5/6, since the probability of player 1 winning is 1/6.

I’m not sure why you think that when we all answer 6/11 we are referring to odds.

And if you still think that the probability of player 1 winning is 1/6, I will happily play this game (as player 1) over and over with you according to the rules set out in the post. I can almost guarantee that I will come out way ahead of you.