Problem: The Montenegrin Dice Game

It is said that the inhabitants of Montenegro have a little dice game that is both ingenious and well worth investigation. The two players first select two different pairs of odd numbers (always higher than $3)$ and then alternately toss three dice. Whichever first throws the dice so that they add up to one of his selected numbers wins. If they are both successful in two successive throws it is a draw and they try again. For example, one player may select $7$ and $15$ and the other $5$ and $13.$ Then if the first player throws so that the three dice add up $7$ or $15$ he wins unless the second man gets either $5$ or $13$ on his throw.

The puzzle is to discover which two pairs of numbers should be selected in order to give both players an exactly even chance.

Solutions: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:
@H-Dudeney

References

Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

This eBook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this edition or online at http://www.gutenberg.org. If you are not located in the United States, you'll have to check the laws of the country where you are located before using this ebook.