>Suppose that as we run the
>experiment, every person in the room turns to their neighbor and makes
>this bet. One person in each pair bets that the dice will come up
>double sixes, while the other bets that they will not. (We make sure
>there are an even number of people in the room each time.)
>At the end of the experiment, 90% of the people who bet that the dice
>will come up double sixes will have won, while only 10% who bet the way
>David and Richard advise will have won. Their advice is a loser for 90%
>of the people who follow it.
>Does everyone agree on this?
This is a variant of an old gambler's fallacy. Make a nearly even bet. If
you lose, double your bet and do it again. Repeat until you win, at which
point you have gained your original bet.
This fails because there is a chance of losing everything you have, and that
chance outweighs the likely small gain.
To put this in context, there's about a 75% chance that you'd have the entire
population of planet earth in the room and still no double sixes.