3 ms·

If you use 32 cards, it maps cleanly to 5-bits of entropy. You can keep the others in there to keep shuffling randomness of 52 cards. Just ignore them when ente

If you use 32 cards, it maps cleanly to 5-bits of entropy. You can keep the others in there to keep shuffling randomness of 52 cards. Just ignore them when entering numbers.

klodolph 8y ago
Using 32 cards to get 5 bits of entropy only works if you are randomly selecting a single card at a time. If you shuffle a deck of 32 cards, you get ~117 bits, a fair bit less that the 160 bits you would get for 5 bits/card, and there's extra math.
- nickpsecurity 8y ago
  I shuffled a full deck multiple times, no less than five, before using cards in order ignoring any but the 32. I know shuffling all the cards adds randomness vs just shuffling 32. I do want to know why you say two things: 1. 32 = 117 bits of entropy, not 150, after lots of shuffling. 2. It works if I randomly select a single card at a time but not in order from a randomized deck. In order from a randomized deck should give the entropy amount or close to it. I'm not a probability expert. Just doing what I could with good, shuffling skills. Good enough that people refused to play Spades with decks I shuffled. So, I thought I had good entropy. I'm always up for improvements.
  - klodolph 8y ago
    The first card you draw can be any one of 32 cards. This gives you 5 bits of entropy. The second card can be any one of 31 cards, because it can't be the same as the first card. This gives you log2 31 = ~4.95 bits of entropy. If this argument isn’t convincing, think of it this way. If you draw two cards, then there are 32 choose 2 cards you can draw, and 32 choose 2 is 496, giving log2(496) = ~8.95 bits. You can draw them in two different orders, giving 1 extra bit, total of ~9.95. If you could draw a pair of the same card, there are 32 different pairs to draw, giving (496 * 2) + 32 possibilities, which is 1024, and log2 1024 = 10. But you can't draw a pair of the same card. Or for another argument, consider that there are 32! different ways to shuffle the deck with 32 cards. log2 32! = ~117.

If you use 32 cards, it maps cleanly to 5-bits of entropy. You can keep the others in there to keep shuffling randomness of 52 cards. Just ignore them when entering numbers.

klodolph 8y ago

Using 32 cards to get 5 bits of entropy only works if you are randomly selecting a single card at a time. If you shuffle a deck of 32 cards, you get ~117 bits, a fair bit less that the 160 bits you would get for 5 bits/card, and there's extra math.

nickpsecurity 8y ago
I shuffled a full deck multiple times, no less than five, before using cards in order ignoring any but the 32. I know shuffling all the cards adds randomness vs just shuffling 32. I do want to know why you say two things: 1. 32 = 117 bits of entropy, not 150, after lots of shuffling. 2. It works if I randomly select a single card at a time but not in order from a randomized deck. In order from a randomized deck should give the entropy amount or close to it. I'm not a probability expert. Just doing what I could with good, shuffling skills. Good enough that people refused to play Spades with decks I shuffled. So, I thought I had good entropy. I'm always up for improvements.
- klodolph 8y ago
  The first card you draw can be any one of 32 cards. This gives you 5 bits of entropy. The second card can be any one of 31 cards, because it can't be the same as the first card. This gives you log2 31 = ~4.95 bits of entropy. If this argument isn’t convincing, think of it this way. If you draw two cards, then there are 32 choose 2 cards you can draw, and 32 choose 2 is 496, giving log2(496) = ~8.95 bits. You can draw them in two different orders, giving 1 extra bit, total of ~9.95. If you could draw a pair of the same card, there are 32 different pairs to draw, giving (496 * 2) + 32 possibilities, which is 1024, and log2 1024 = 10. But you can't draw a pair of the same card. Or for another argument, consider that there are 32! different ways to shuffle the deck with 32 cards. log2 32! = ~117.