Author Topic: The Gambling Tyrant  (Read 5817 times)

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Offline Tailchaser

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The Gambling Tyrant
« on: February 21, 2007, 05:57:50 pm »
This is a paraphrase of a logic puzzle I heard in an undergrad philosophy course. It's designed as a challenge to the principles of anthropic reasoning. It's one of those "no right answer" things, and is probably only interesting to people who like discussing the nature of logic, etc. But anyway.

There is a country with an infinite number of people in it ruled by an evil dictator. One day, the dictator decides to play a cruel game. He will call nine people into a room. He will then roll a pair of dice. If he rolls double 6's, he will shoot all nine people. If, however, he rolls anything OTHER than double 6's, he will let those people go, bring in 90 new people, and roll again. He will continue bringing in new groups of people, each ten times bigger than the last, until he's killed someone.

The upshot of this is that about 90% of the people called to his room will die (unless he rolls double 6's the very first time, in which case 100% will die).

On the other hand, there's only a 1/36 chance that he'll get double 6's on any given roll - a bit under 3%.

Now, let's say you are a citizen in this country, called up by the evil dictator, and he's about to roll the dice. What is your chance of survival, over 97% (the chance that he won't roll double 6's) or under 10% (the percentage of people overall who survive this process)?

This is not my puzzle, I quoted in its entirety from a different place I found it.


Offline Scrimno

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The Gambling Tyrant
« Reply #1 on: June 26, 2007, 10:00:57 am »
There are 6 sides on a die. The chances to roll any given number is 1/6. For each die you add, that number is squared. Hence to roll any given number on 2 dice is 1/36.
The way I see it, your chances of survival are 35/36 on any given roll.
The fact he brings in ten times more people every time means that there are 90% more people in the room each time. True, if he rolls double 6s, 90% of all people die, but the chances that'll happen are still 1/36.
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