4 ms·

Shuffling can be done in linear time, e.g. with https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_s

• gamegoblin 11y ago
  I believe user thomasthomas was referring to this problem: https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle#Pseudorandom_generators:_problems_involving_state_space.2C_seeding.2C_and_usage https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle#P... That is, is there enough entropy in your typical PRNG to actually generate all of those shuffles with equal probability.
  • sltkr 11y ago
    You can easily seed your PRNG with a cryptographic entropy source which can certainly provide enough entropy. But in reality you don't care. You could seed the PRNG with the current system time in nanoseconds or something, and every game you'll ever play is different. Even if the PRNG has limited state, you'll never notice it as a human player.
    • dietrichepp 11y ago
      I'd like to elaborate. The cryptographic PRNG has lots of entropy, and it probably happens to be enough entropy. You need ~226 bits, and most cryptographic PRNGs will be more than that—but not all! Information-theoretic entropy is actually a stronger requirement, and it's why we use /dev/urandom (which is secure and fast) instead of /dev/random (which is information-theoretic secure, but slow). So it might be possible that your secure PRNG still cannot generate all permutations.
      • schoen 11y ago
        Paging tptacek to quarrel with the account of RNG entropy presented here (?)
        • dietrichepp 11y ago
          Quarrel? Here, let me clarify. A PRNG has state with a certain amount of potential entropy, call this X. Uniformly shuffling a deck of cards requires a certain amount of entropy, Y. If X > Y then theoretically you can generate all possible shufflings with your PRNG, assuming it's seeded properly. If X < Y, then you can't. The key difference is that your PRNG could be cryptographically secure even though X < Y. It turns out that Y ≈ 226 bits, and so it's plausible that your cryptographically secure RNG would have X = 128 bits, for example, even though I'd typically expect a larger number. People often conflate entropy with security. A random number source could have high amounts of entropy and be insecure, while a random number source with less entropy could be very secure. Or let me put it this way: entropy is necessary but not sufficient for security.
          • schoen 11y ago
            I agree with your argument on a pigeonhole-principle level (if you only observe fewer than 128 bits of state and then shuffle cards in a deterministic way based on a summary of your observations, you can't get all possible shuffles out), and I think that's a nice observation. 52! is surprisingly huge, and determinism is deterministic. :-) The issue is just about what /dev/urandom and /dev/random do.
            • dietrichepp 11y ago
              There's a lot of misinformation and cargo cult crypto programming, but the basic summary is that /dev/random information-theoretic security is unnecessary for most applications, but necessary for being able to know that you can produce every possible permutation of a deck of cards. http://www.2uo.de/myths-about-urandom/ http://www.2uo.de/myths-about-urandom/
              • tptacek 11y ago
                /dev/random and /dev/urandom are the same CSPRNG construction; /dev/random just provides some extra (almost always counterproductive) checks on the rate at which it's rekeyed. It is not the case that using /dev/random somehow gets you an information-theoretic security level that /dev/urandom doesn't.
    • xigency 11y ago
      Well, beyond what a human player would notice, to be able to be dealt any possible hand in solitaire, a random or pseudo-random number generator would need log 2 (52!) bits of state or > 226 bits, which is the point I think the commenter was making, compared to the 32- or 64-bits of information a built-in function would take. Something like a properly seeded 256 bit xorshift might satisfy this as a random number generator. But even that setup may not be sufficent.
  • cobaltblue 11y ago
    You can always use https://www.fourmilab.ch/hotbits/ https://www.fourmilab.ch/hotbits/ as well.