Hackix - a Quick and Dirty Bridge Dealer

Here is a short Perl program:

$boards = shift;               # how many boards for the session?
srand( time );                 # seed based on wall clock
@c = split( '', '0123' x 13 ); # init: 52 tokens, 13 of each
while( $boards-- ) {
  for $i ( reverse 1..52 ) {
    push( @c, splice( @c, int(rand($i)), 1) ); # shuffle tokens
  }
  print @c, "\n"; # output the deal for one board
}

And here is an example of its output, given the input 10:

3200201213233210330013110103122203301200312121303221
1302111323022021303011210213220201132330001102032333
2221321210033133123202020100012333031110201203201313
3030322102101213013332321001233211211013202022310030
1223012130323213213000201122010200110133220101332333
0103321120320132130210003223102313100310021212231332
2313131001233222200011233111032032200301303112201023
1122023231020003303120130203333203120122131012132101
3100121023103320122122000323302120103111312212030333
1323320131330220303210310322011203110212332021120001

The program generates series of a random strings, each containing 13 zeroes, 13 ones, 13 twos, and 13 threes. Each of the possible D (D = 52!/13!/13!/13!/13!) sequences are equally probable, assuming sufficient statistical soundness of the rand function.

We will associate the directions North, East, South and West to the numbers 0, 1, 2, and 3, respectively. We will also associate each of the 52 positions in a string with a card in the bridge deck: A, K, ..., 2. In this way, each string represents a bridge deal.

In essence, we have a dealing program. Of course, the output needs to be massaged in order to represent the deals in a relevant format, but we can leave that to other hackers for the time being.

How good is the Hackix program?

Statistics (strong). The random number generator provided with Perl 5 is well behaved for short runs like this (52 calls per board), and the dealing algorithm used does formally shuffle 52 tokens in such a way that each permutation is equally likely. Tests made on 4000 runs of 40 boards have shown that Hackix's output is indeed statistically indistinguishable from random boards.
Non-repeating (medium). A sequence of boards generated for one event must not be observably related to the boards generated for some other event. Hackix is in reasonable shape here, because the algorithm uses chaining (the previous board is input to the next board), so if a different run gets into an old rut in the rand function, the shuffle of the tokens might be identical to some previous run, but the tokens would be extremely unlikely to be in the same place. However, if two runs are done within the same second of wall clock time, the boards will be identical..
Clerically robust (none). Hackix does not in any way support clerical procedures that help prevent inadvertent use of generated deals in an event that they were not intended for.
Unpredictable (weak). If you can guess the time when the run is made with an accuracy of one second, you have the boards. If you know the date that the boards were dealt, a brute-force enumeration requires 86400 tries - which is just a matter of minutes of computer time.
No discernable pattern (weak). It is not possible for an honest but knowledgeable player to predict the rest of the deals to be played during a session, given the deals already played. Hackix is much too complicated to analyse its behavior without dishonest use of computer assistance.
Users (weak). Hackix is suited only for use by a few users who know and trust each other. It cannot be released to the general public and still be used in serious tournaments.
Auditable (none). It is not at all possible to ascertain after the event that the deals were not intentionally modified after dealing.
All boards possible as output (weak). This is a very popular requirement, although it is somewhat irrational from a statistical point of view. Anyway, Hackix does not fulfill this requirement at all. The seed determines the boards deterministically. The seed is (I think) a 31-bit number in the Perl rand function, and that limits the number of different sessions possible. There will be up to 40 boards in each session. D is slightly less than 96 bits, so only a tiny fraction (2**(-60)) of the D boards are actually represented in the possible output.

updated 2000-02-06 / jbc