The game starts with 6 empty glasses in a row numbered 1 to 6. You roll a standard die. If the number for the glass is empty, then the glass is filled up. If the number for the glass is full, then you drink that glass. There is a special rule when 5 glasses are full. If you roll the number for the lone empty glass, then the final glass gets filled and you have to drink all 6 glasses. At this point the game ends.

From the start of the game, what is the average number of rolls until the game ends?

Blog post (text explanation): http://wp.me/p6aMk-4tu

I read about this game on Reddit Math: https://www.reddit.com/r/math/....comments/408a45/how_

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"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1523231467/

"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/1517421624/

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