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It doesn't have to be a random number from any particular distribution - you can roll 1d20, or use your age, or anything else you like. The point of the parado
by fenomas 11y ago
It doesn't have to be a random number from any particular distribution - you can roll 1d20, or use your age, or anything else you like.
The point of the paradox is that picking a value and trading anything below it is always a non-losing strategy, and may also be a winning strategy, depending on factors that are not defined in the puzzle (i.e. whether your opponent's choices are anywhere close to the number you chose).
- JackFr 11y agoThere is no paradox, because under the conditions of the problem, the advantageous solution cannot be shown to occur with a probability greater than 0.
- fenomas 11y agoWhether a solution is actually advantageous depends on whether your chosen number lies between your opponents choices, which are not defined. The author notes that if you select from an unbounded distribution, you can in principle have a nonzero (though in practice very small) advantage regardless of the opponent's choice.
- mjd 11y agoRolling 1d20 doesn't work, because if the first player always chooses numbers bigger than 20 or smaller than 1, the second player wins with only probability ½. To get a winning probability greater than ½ the second player needs to choose from a distribution that is everywhere positive, which means that a discrete distribution won't do.
- deleted 11y ago[deleted]
- fenomas 11y agoAh, I see what you mean - I meant that any old number will suffice for having a non-losing strategy, assuming that the opponent's strategy is unknown and undefined.