Random Number Generator
TrueMoneyGames uses a random number generator that is based on a hardware diode, produced by the Swedish company Protego. Therefore, nobody can predict the rolls in advance since it is not based on a pseudo random number generator's seed. The dice are generated only on our server and are then sent to the client software in an encrypted way. This method offers our customers the most truly random dice in existence; even precision dice could not come close to this. To find out more information about the hardware diode and to learn about the statistical tests that have been performed please have a look at the web page of Protego.
Shuffling
The shuffling algorithm used to ensure a truly random deck is very important. We use a sort shuffle using a random number generator that generates 2^32 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 exactly how the shuffling algorithm works:
We assign a random value to each card, as follows.
Ace clubs = 289384521
2 clubs = 1543421228
3 clubs = 410684245
...
Jack spades = 306557875
Queen spades = 1382797013
King spades = 1886740576
Then we sort the cards by their unique index value. This results in an ordering like this:
Ace clubs = 289384521
Jack spades = 306557875
3 clubs = 410684245
Queen spades = 1382797013
2 clubs = 1543421228
King spades = 1886740576
Our method of shuffling eliminates the problem that a single pass Knuth shuffle has involving the modulo bias. It's possible to mitigate the effects of this by using a multi-pass Knuth shuffle, but there's no reason to do that when you can use a superior algorithm.
Some other interesting numbers....
A deck of cards can have 52!(Roughly 8x10^67)permutations. This number can be determined simply 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, so to find the number of possible shuffled decks you calculate 52x51x50x49 .. 3x2x1 which results in approximately 8x10^67 different combinations.
Given a true random data source, the initial permutation available using our shuffle method is (2^32)^52. This is roughly 8x10^500. Since we use a 4096 bit entropy pool, this means we are pulling our numbers from any one 2^4096 different possibilities which is significantly larger than the possible number of combinations we use. This means that there are 10^433 different ways that we can generate data to get any given random deck. For comparison, it is 10^382 times as likely that one could randomly choose the same molecule of water from the ocean twice in a row than it is that we would ever generate the same set of values to create a shuffled deck from.
