The shuffling algorithm used to ensure a truly random deck is of extreme importance. This section deals with the technology used by 32Red to make sure you get a fair game. Excuse us in advance for using boffin's language to explain further the random number science!
The 32Red Multi-Player Poker software employs a sort shuffle using a random number generator that generates 232 different values pulled from a 4096 bit entropy pool. This is different than the Knuth Shuffle used by some other systems, and it has some advantages.
Here is an example of how the shuffling algorithm works.
A random value is assigned to each card, as follows:
Ace Clubs
= 289384521
2 Clubs
= 1543421228
3 Clubs
= 410684245
Jack Spades
= 306557875
Queen Spades
= 1382797013
King Spades
= 1886740576
The cards are then sorted by their unique index value. This results in an ordering like so:
Ace Clubs
= 289384521
Jack Spades
= 306557875
3 Clubs
= 410684245
Queen Spades
= 1382797013
2 Clubs
= 1543421228
King Spades
= 1886740576
This is for all you mathematicians:
A deck of cards can have 52 (roughly 8x1067) permutations. How this number has been arrived at can be determined fairly easily.
The first card dealt can be any one of 52 cards. The second card can be one of any of the remaining 51 cards. At this point there are 51x52 different permutations. The third card can be any of the remaining 50.
Therefore, to find the number of possible shuffled decks, the number to be calculated is 52x51x50x49... 3x3x1, resulting in approximately 8x1067 different combinations.
Given a true random data source, the initial permutation available using the shuffle method is (232)52. This is roughly 8x10500.
Due to the fact that a 4096 bit entropy pool is used, the numbers are pulled from any one of 24096 different combinations. As a result, there are 10433 different ways that data can be generated to produce random decks.
To state this fact a little more clearly, it is 10382 times as likely that one could randomly choose the same molecule of water from the ocean twice in a row, than the same set of values being generated in a shuffled deck.
