Pete, being the highly logical, calculating person he is, rejects all of that as superstitious nonsense. He instead applies the scientific approach. Over the years, he's collected somewhere around a thousand twenty-sided dice. Every so often, he gathers them all together. He sits down at a table and carefully and individually rolls each of the thousand dice, once. Of course, roughly a twentieth of them will roll a one. He takes those fifty-odd dice and rolls them a second time. After about an hour of concentrated dice rolling, he'll end up with around two or three dice that have rolled two ones in a row. He takes those primed dice and places them in special custom-made padded containers where they can't roll around, and carries them to all the games he plays.
Then, when in the most dire circumstances, where a roll of one would be absolutely disastrous, he pulls out the prepared dice. He now has in his hand a die that has rolled two ones in a row. Pete knows the odds of a d20 rolling three ones in a row is a puny one in 8,000. He has effectively pre-rolled the ones out of the die, and can make his crucial roll with confidence. Furthermore, being scientific about it means he knows that it doesn't matter who rolls the die for the third time, so he has no qualms about sharing his primed dice with other players, if that's what it takes to avoid disaster.
[It might seem] that the discovery by the Culture's Minds that some humans were actually capable of matching and occasionally beating their record for accurately assessing a given set of facts would lead to machine indignation and blown circuits, but this was not the case. It fascinated those Minds that such a puny and chaotic collection of mental facilities could by sleight of neuron produce an answer to a problem which was as good as theirs. There was an explanation, of course, and it perhaps had something to do with patterns of cause and effect which even the almost god-like power of the Minds had difficulty trying to fathom; it also had quite a lot to do with sheer weight of numbers.
There were in excess of eighteen trillion people in the Culture, just about every one of them well nourished, extensively educated and mentally alert, and only thirty or forty of them had this unusual ability to forecast and assess on a par with a well-informed Mind (of which there were already many hundreds of thousands). It was not impossible that this was pure luck; toss eighteen trillion coins in the air for a while and a few of them are going to keep landing the same side up for a long, long time.
-Consider Phlebas, Iain M. Banks
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