[JmBrPotter]

 Davekapiti, on 2019-August-04, 23:58, said:

. . . I have been playing Bridge competitively for over 40 years and I have never experienced this type of trump distribution over such a continuous period of time. Occasionally bad distribution as mentioned above can be a challenge, but the current situation is becoming quite boring t the point of expecting it each time a game in a suit has been bid correctly. . . .

Dave,

If the powers behind Big Deal say that BBO has a good hand generator, I strongly trust that BBO has a good hand generator. The authors behind that generator have excellent knowledge of both the math behind good generators and the statistics to validate them. That theory knowledge has excellent backing by good computer programming to turn the theory into practice.

I have a very minor philosophical quibble with Big Deal. It samples the population of all possible bridge hands without replacement (Big Deal would deal every possible bridge hand exactly once before it repeated a hand (perhaps, a desirable property if you want to be certain that the hands for your tournament will have no duplicates). Philosophically, I feel that the sampling should be conducted with replacement (There is a tiny chance {several orders of magnitude larger than Planck's constant but still quite small} that a set of a few thousand hands for a large tournament would contain one or more duplicates.) The practical difference is that once in several human lifetimes we are very unlikely to see a headline about two identical hands at the same tournament versus never seeing two identical hands at the same tournament. That is, no practical difference.

You may have built a "feel" for what "random" bridge hands should resemble from playing shuffle and play events (e.g., local club games, KO teams, and Swiss teams). To get genuinely random hands via shuffle and play, every hand would need to be shuffled seven or more times. How likely is that? What proportion of the hands will be shuffled one or two (at best three) times before dealing? Inadequate shuffling will skew the hand distribution towards deals with four balanced hands each with 8-12 HCP (e.g., lots of 3-2, 2-2, and 3-1 trump splits and way to few 4-0, 4-1, and 5-0 trump splits). Players who encounter randomly distributed hands when they leave the sheltered waters of their local shuffle and play club for the first time will have their instincts for how the cards should break thoroughly battered.

[JmBrPotter]

 thepossum, on 2019-August-06, 04:05, said:

. . . Suffice to say I trust that the hands are suitably random, whatever randomness means :)

Possum,

To a statistician, "randomness" means something like, "The statistical properties of an observation are indistinguishable from the statistical properties of a random sampling (e.g., tosses of fair coins, rolls of fair dice, or clicks from a Geiger counter) with a distribution matching the claimed distribution of the afore mentioned observation."

That definition probably sounds very precise and quite sensible. Yet, a statistics professor could probably speed a full semester long advanced graduate level course on the topic (and wish for a second semester). Donald E. Knuth devotes Chapter 3 (nearly 180 pages) of his The Art of Computer Programming to the topic of generating pseudo random variants and validating their "randomness" by that definition. It is a suitable text for a one semester undergraduate class on the topic and barely scratches the surface.

[tomkron]

 barmar, on 2019-August-06, 08:59, said:

We also use the Linux rand() function, which is admittedly not the best random number generator.

Actually, it's a terrible random number generator, even if you are using excellent seeding. (How are you seeding it?) The version of rand() on my Linux box has a period of at most 34,359,738,352 (~2**35) per the man page which means it can produce only an infinitesimal fraction of the 53,644,737,765,488,792,839,237,440,000 (~2**96) possible bridge deals. That tiny fraction might be representative of deals in general, but maybe the people doing the complaining are in fact observing patterns which weren't checked for by your statistical analysis.

Why can't you use a better random number generator, perhaps Mersenne Twister? It has a period of roughly 2**19937. Or get 96 bits of entropy from a hardware RNG or /dev/random or a cryptographically-secure RNG and use them to select a deal from the space of all possible deals? Several web sites (I believe Thomas Andrew's and separately Richard Pavlicek's) contain descriptions of how to do this.

[pescetom]

 smerriman, on 2019-August-07, 14:24, said:

This can't make a single bit of difference. The probability a given deal occurs is identical whether you rotate or swap.

I'm no statistician and would be happy to hear from someone who is, but your argument doesn't convince me: the probability of a given deal is identical to that of any other deal, but that does not mean that any set of deals is equally random however the hands were generated.

[barmar]

 Lorneg, on 2019-August-07, 19:13, said:

It's not as random as you think. Just keep track of the leads for a while. It is probably
less than 2 or 3% of the time that the opening lead is away from a King. Now later on
in the play you get the Bots leading from Kings.
When I play in the club you just learn who leads form Kings and who doesn't There it
is at least 30 or 40% leading from a missing king.

I don't think that's because the deals are less random, it's because of GIB's algorithm for selecting opening leads. It tends to avoid leading away from kings much more than humans do.

[barmar]

 pescetom, on 2019-August-08, 06:38, said:

I'm no statistician and would be happy to hear from someone who is, but your argument doesn't convince me: the probability of a given deal is identical to that of any other deal, but that does not mean that any set of deals is equally random however the hands were generated.

If the deals are generated independently, I don't think there should be any difference between the randomness of an individual deal and that of the set of deals.

The only question here is whether, when creating Best Hand deals, and the original random deal has the best hand in West, for instance, it makes a difference whether you swap West with South or rotate W->S, S->E, E->N, N->W. I don't think it should matter, because any permutation of the other 3 hands is equally likely.

[barmar]

 JmBrPotter, on 2019-August-07, 21:15, said:

The ACBL began using Big Deal for the Winter NABC in 2016. Nicolas Hammond (author of the recent Detecting Cheating in Bridge) proved that feeding a suitable program boards 1, 2, & 3 of an ACBL generated board set would yield boards 4-36 in a short enough time for the result to be useful for cheating on most of the "solved" boards. He also delivered statistics indicating that some pairs might be using this "crack" (or one like it) to cheat at NABCs and Regionals. The ACBL (and EBU, and USBF, and WBF) finished switching to Big Deal by January 2017.

We're less concerned about this kind of problem on BBO. The above crack depended on the fact that all the deals in a particular session were generated sequentially starting from the same seed. But the BBO dealer is generating hands concurrently for tournaments and regular bridge tables, so it's hard to discern the sequence of hands.