How random is random?
Suppose we're using a computer program to deal boards for a bridge event. In order to ensure that the boards are being dealt randomly, the computer needs to use an external source of randomness (such as a hardware random number generator), but those are quite frequently included with computers nowadays (yours probably has one).
There are two sorts of hardware random number generators commonly available today:
- Some generators ensure that every single bit of data they generate comes from an external source of randomness. These generators are very slow (by modern computer standards), and not intended to be used for large amounts of data, but it would be possible to use one to deal boards for a bridge tournament as long as you didn't do so too often. Dealing boards using this sort of generator would generate every possible sequence of n boards with equal probability.
- Most generators, however, use the hardware random number generator as input to a cryptographic algorithm, which then outputs a series of random numbers. In this case, after the sequence reaches a certain point, not all possible sequences have equal probability, but (assuming there are no major discoveries in cryptography) there's no way to know which sequences are the more or less likely ones. As a consequence, if you deal boards using this sort of generator, then looking at individual boards, each possible deal will have the same probability; but some sequences of boards will be more or less likely to occur together within the same tournament. However, nobody knows or can know which sequences those are, and so there's no information available that could allow anyone to predict boards before they are played.
Obviously, the former sort of generator is sufficient for generating deals for a tournament (assuming that it's programmed correctly). However, the cryptographic community normally considers the latter sort of random number generator to be sufficient for all practical purposes – it guarantees that all the information generated will be unpredictable and unknowable to anyone in advance of actually seeing the output (and is a lot more random than hand-shuffling!).
My question is: is this latter sort of generator sufficient for bridge? (More concretely: would a dealing machine that used this sort of generator be compliant with Law 6E4?) There are a number of practical advantages (e.g. this sort of generator is cheaper and more readily available than the former kind, and runs much more quickly), so it would be preferable to use it if it's acceptable.
(In practice, I suspect that many dealing machine programs in use today are "less random" than either of the above techniques – the introduction of hardware random number generators as standard components in ordinary computers is a fairly recent development compared to the history of dealing programs and dealing machines – but this is a guess, and I don't know the actual situation.)
Comments
Oooh random numbers - one of my favourtie topics!
A couple of initial observations:
1) There is no such thing as random in the real world (unless you go down to the quantum level). Pseudo random is the best that can be obtained, and even that is difficult. Pseudo random being defined as indistinguishable from theoretical random for practical purposes.
2) Shuffling by hand (and then dealing) is a long way from pseudo random, as the results are too dependent on the inital conditions (order of the pack). That's why hand shuffling and dealing leads to flatter hands than computer dealing.
Now let's look at Law 6A and B - essentially saying you should shuffle and deal manually.
But we're not doing that (with computer dealing), so how do we justify it?
As ais523 suggests, we use Law 6E4: "The Director may require a different method of dealing or pre-dealing to produce the same wholly random expectations as from A and B above."
But but but...
We know that computer dealing does NOT produce hands to the same "randomness" as hand dealing, so we can't use 6E4. All our computer deals are illegal!
I note that 6E4 uses the phrase "wholly random". Whatever that means in cannot suggest that hand dealing produces truly random resuts, because it does not.
It's interesting that ais523 is questioning whether computer dealt hands are random enough, whereas I submit they are too random.
[Yes I know this doesn't really matter - like many discussions on here it's about a very very fine point of the law.]
My understanding is that modern processors' hardware random number generators do in fact go down to to the quantum level in order to generate their randomness. Components on modern processors are small enough that they're naturally susceptible to quantum effects; much of modern processor design is about trying to reduce that problem, so it isn't much additional cost to include a few additional components where you go the other way and try to read the quantum-mechanical noise rather than trying to get rid of it.
The point of "computer deals may be illegal because they don't introduce the same bias towards flatter hands that hand-dealt deals do" is an interesting one (and IIRC some players are able to tell the difference, and prefer one dealing mechanism or the other). It would probably be possible to program a computer to simulate a hand-shuffle, although working out the appropriate initial order of the deck could be quite difficult.
I am sure the contributors above know that 'wholly random' and 'less random' are tautologies. Something is either random or it is not. In practice computer-generated hands will be pseudo-random. The question is how good they are at making all possible bridge hands equally likely and not having the possibilities of Hand 2 constrained by Hand 1. Infamously this latter problem affected the pseudo-random hand generator used by the ACBL where by inputting details of the first three deals and throwing a lot of processing power at it you could derive the rest of the hands. The ACBL has now changed its pseudo-random generator, I believe, to 'Big Deal'. I believe the EBU uses 'Big Deal' certainly my County does and all the clubs I know do. Duplimate who many years used another pseudo-random hand generator now appear to supply 'Big Deal' as their default hand generator. You can find out about the origins of 'Big Deal' at https://sater.home.xs4all.nl/doc.html .
"Big Deal" is very close to the second sort of generator I listed above – it extracts randomness from an external source (in this case, a human typing), and expands it to a set of boards in a way that's cryptographically secure (so that each board is equally likely to generate on its own, and some sequences of boards are possible and some are impossible, but there's no known way to figure out which is which).
The shipping of hardware random number generators with ordinary computers is a relatively new development – Big Deal was written at a time when such things didn't exist. I was wondering if there might therefore be a benefit from creating/using a new dealing mechanism that takes advantage of that fact, which is what inspired me to create the thread (and specifically, I was interested in what the "correct" mode for using them would be when it came to preparing a bridge tournament).