**From:** Kevin Peterson (*kevinpet@gmail.com*)

**Date:** Mon Nov 05 2007 - 17:56:36 MST

**Next message:**Rolf Nelson: "Re: how to do something with really small probability?"**Previous message:**Wei Dai: "Re: how to do something with really small probability?"**In reply to:**Wei Dai: "how to do something with really small probability?"**Next in thread:**Lee Corbin: "Re: how to do something with really small probability?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

On 11/1/07, Wei Dai <weidai@weidai.com> wrote:

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*> Suppose an SI wants to do something with a very small, but non-zero
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*> probability, say 0 < p <= 1/3^^^3 (in Knuth's up-arrow notation). How
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*> would
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*> it go about doing this? The answer seems to be "it can't", because
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*> algorithmic information theory says there is no way that it can generate a
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*> sufficiently long random number that it can know is truly random. Can
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*> anyone
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*> see a way around this limitation?
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There is no situation that would call for taking an action based on such a

low probability.

Suppose someone, call him Tim, is evaluating what course of action he should

take. Tim calculates that the correct action is to play a mixed strategy of

A with probability p, and B with probability 1 - p. But wait! p is so small

that Tim cannot randomly choose a number with sufficient precision to

properly play this strategy. Tim's head explodes from thinking about this.

So why isn't this a problem? Because the ability to determine that the best

strategy is to perform some action with probability p guarantees that Tim is

able to calculate with numbers of the same order of magnitude as p.

I don't think the subtleties of randomness come into play at all here,

although they could in different similar situations -- rock-paper-scissors

is not completely random, but it's generally good enough for children who do

not have access to better methods of settling trivial disputes. The analogy

here would be that Tim might determine that the correct probability to play

some portion of a mixed strategy is very low, so low that the cost of not

playing that strategy was lower than the cost of accurately calculating that

cost.

**Next message:**Rolf Nelson: "Re: how to do something with really small probability?"**Previous message:**Wei Dai: "Re: how to do something with really small probability?"**In reply to:**Wei Dai: "how to do something with really small probability?"**Next in thread:**Lee Corbin: "Re: how to do something with really small probability?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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