Quote:Gialmere

Book Bore

Next to the exhibits is a coffee shop which (evidently keeping with the museum theme) has a bookcase stocked with old gambling titles for customers to peruse. Placed in order on one shelf is a ten-volume gambling encyclopedia set. Each volume is two inches thick. You idly grab #5 and flip through the pages.

What the...? There's a hole drilled all the way through the tome. You check the other volumes and find that a bookworm type insect has bored a straight, horizontal hole through the books. It starts at the front cover of volume-1 and ends at the back cover of volume-10. Quite a feast.

How far did the "bookworm" travel?

16 inches. As books sit, reading L to R on a single shelf, front cover is to the right of Vol 1, and back cover is to the left of Vol 10. So the worm only hit the 8 volumes in the middle.

Hey, Gialmere. Were you a dungeon-master in college? You're awfully good at running games. Thanks again for doing it!

Quote:beachbumbabs16 inches. As books sit, reading L to R on a single shelf, front cover is to the right of Vol 1, and back cover is to the left of Vol 10. So the worm only hit the 8 volumes in the middle.

Winner! Winner! Chicken Dinner!!

Quote:beachbumbabsHey, Gialmere. Were you a dungeon-master in college? You're awfully good at running games. Thanks again for doing it!

Thanks babs. It's funny you should say that since I was just thinking that writing in the second person makes me feel like I'm running a role-playing game.

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Battle Bones

You leave the coffee bar and head back to your booth. This late in the day most of the crowd has filtered out. You see that three people are checking out the game next to yours and, with a twinge of jealousy, note that they are casino reps. The reps smile, shake hands with the designer and walk off so you decide to check out the competition.

The game is called "Battle Bones" and is played with three colored dice each with unusual numbers. The red one has two 3's, two 4's and two 8's. The yellow one has two 1's. two 5's and two 9's. Finally, the blue one has two 2's, two 6's and two 7's. It seems simple enough. The player places a bet and selects any of the three dice. The dealer matches the player's wager then selects one of the remaining two. The dice are rolled simultaneously and the highest roll wins the money.

Which of the dice gives the player the best chance of winning?

The technical term for the above is non-transitive dice and it is very interesting that you can be a loser if you have to pick first. I have heard about them before (333333 222255 114444). Here's a link which I found today about them http://weberprobability.blogspot.com/2014/02/nontransitive-dice.html and a photo from a shop ( www.mathsgear.co.uk ) where you can buy them.

Quote:GialmereQuote:beachbumbabs16 inches. As books sit, reading L to R on a single shelf, front cover is to the right of Vol 1, and back cover is to the left of Vol 10. So the worm only hit the 8 volumes in the middle.

Winner! Winner! Chicken Dinner!!This one you either get quick or you never do.

Thanks babs. It's funny you should say that since I was just thinking that writing in the second person makes me feel like I'm running a role-playing game.

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Quote:

Battle Bones

You leave the coffee bar and head back to your booth. This late in the day most of the crowd has filtered out. You see that three people are checking out the game next to yours and, with a twinge of jealousy, note that they are casino reps. The reps smile, shake hands with the designer and walk off so you decide to check out the competition.

The game is called "Battle Bones" and is played with three colored dice each with unusual numbers. The red one has two 3's, two 4's and two 8's. The yellow one has two 1's. two 5's and two 9's. Finally, the blue one has two 2's, two 6's and two 7's. It seems simple enough. The player places a bet and selects any of the three dice. The dealer matches the player's wager then selects one of the remaining two. The dice are rolled simultaneously and the highest roll wins the money.

Which of the dice gives the player the best chance of winning?

The dice values, when considered collectively against the other two, each win 9 times and lose 9 times. However, choosing first guarantees a house edge.

If you select the red die, dealer should select yellow. This guarantees the house 5 wins out of 9 results.

If you select yellow, dealer should select blue. 5 wins out of 9 again.

If you select blue, dealer should select red. 5 of 9 results win again.

Quote:charliepatrickWhat is nice about your problem is the probabilities of B>A C>B A>C are all 5/9.

Quote:beachbumbabs

The dice values, when considered collectively against the other two, each win 9 times and lose 9 times. However, choosing first guarantees a house edge.

If you select the red die, dealer should select yellow. This guarantees the house 5 wins out of 9 results.

If you select yellow, dealer should select blue. 5 wins out of 9 again.

If you select blue, dealer should select red. 5 of 9 results win again.

Two Winner Winners!! Two Chicken Dinners!!

To be continued...