First, my short survey into sleep is still active and it would be great if you could take part. The link is here. Thank you.
On Friday I posted this puzzle…I want to play a game with you. We have three unbiased dice, and each of the two of us have a target number. My target number is 9 and your number is 10. On each round of the game we throw all three dice and add up the numbers. If I get my target number I get 1 point, and if you get your number you get a point. The winner is the person with the most number of points after 20 rounds. There are 6 ways of getting 9 (1,2,6: 1,3, 5: 1,4,4: 2,2,5: 2,3, 4: 3,3,3) and 6 ways of getting 10 (1,3,6: 1,4,5: 2,2,6: 2,3,5: 2,4,4,: 3,3,4) and so it seems to me that it is a fair game. Want to play?
If you have not tried to solve it, have a go now. For everyone else, the answer is after the break.
No, it is not at all fair because there are many more ways for the number 10 to come up. For example, the combination 3, 3, 3 can only come up one way (with all three of the dice showing a 3), whereas 2,4, 4 can come up three ways. As a result, a total of 10 is far more likely than a total of 9. So yes, you should have taken the bet.
Any other answers or ways of explaining it?
I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for theKindle (UK here and USA here) and on the iBookstore (UK here in the USAhere). You can try 101 of the puzzles for free here.