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RPGshop.com sells "precision" dice; but are they Gamescience brand?
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<blockquote data-quote="resistor" data-source="post: 4729523" data-attributes="member: 9142"><p>To start, I don't accept you definition of random. What you're talking about is determinism vs. non-determinism.</p><p></p><p>From an information theoretic perspective, a string of bits is random if the string is shorter than the shortest possible Turing machine that can produce those bits. In short, a random bit string is one for which no compression is possible.</p><p></p><p><em>Any</em> sufficiently long string with non-uniform distribution of the bits is non-random under this definition. <a href="http://en.wikipedia.org/wiki/Arithmetic_coding" target="_blank">Arithmetic coding</a> is a fairly standard technique that exploits exactly this property to compress bit strings.</p><p></p><p>The obvious extension from bit strings to integer strings applies.</p><p></p><p>-----</p><p></p><p>Continuing with determinism vs. non-determinism, your claim still isn't really true. Rolling a die is the product of fairly straightforward mechanical process, which we could model in detail to predict the results. It only appears non-determinic because some parts of the process are 'hidden': we don't know the exact starting state of the die, or the exact shape of your hands when you throw it.</p><p></p><p>So, in a sense, it's no less determnistic than a PRNG: the non-determinism comes from some initial seed state, which is itself assumed to be non-deterministc. (Queue debate over deterministic vs. nondeterministic universe.)</p><p></p><p>In terms of the actual rolling process being <em>practically</em> predictable, I'd argue that it's not materially different from provably strong PRNGs. Reasonably robust Newtonian physics modellers are pretty easy to write, while the difficulty of integer factorization underlies a decent percentage of modern cryptography.</p></blockquote><p></p>
[QUOTE="resistor, post: 4729523, member: 9142"] To start, I don't accept you definition of random. What you're talking about is determinism vs. non-determinism. From an information theoretic perspective, a string of bits is random if the string is shorter than the shortest possible Turing machine that can produce those bits. In short, a random bit string is one for which no compression is possible. [I]Any[/I] sufficiently long string with non-uniform distribution of the bits is non-random under this definition. [URL="http://en.wikipedia.org/wiki/Arithmetic_coding"]Arithmetic coding[/URL] is a fairly standard technique that exploits exactly this property to compress bit strings. The obvious extension from bit strings to integer strings applies. ----- Continuing with determinism vs. non-determinism, your claim still isn't really true. Rolling a die is the product of fairly straightforward mechanical process, which we could model in detail to predict the results. It only appears non-determinic because some parts of the process are 'hidden': we don't know the exact starting state of the die, or the exact shape of your hands when you throw it. So, in a sense, it's no less determnistic than a PRNG: the non-determinism comes from some initial seed state, which is itself assumed to be non-deterministc. (Queue debate over deterministic vs. nondeterministic universe.) In terms of the actual rolling process being [I]practically[/I] predictable, I'd argue that it's not materially different from provably strong PRNGs. Reasonably robust Newtonian physics modellers are pretty easy to write, while the difficulty of integer factorization underlies a decent percentage of modern cryptography. [/QUOTE]
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RPGshop.com sells "precision" dice; but are they Gamescience brand?
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