Since the club has been using Duplimate to prepare the hands for use on Wednesday nights many members have complained that the deals are "fixed" or "biased" to give extreme distributions. The reason that the hands are more varied than those we are used to seeing is that shuffling by any method will not truly randomise the distribution of the cards within a pack.
After seven "riffle" shuffles the pack is close to being random. In contrast, shuffling overhand is ridiculously ineffective - it can take over 20 minutes for a pack to be close to being random. Bizarrely, the switch to randomness can be abrupt. After six riffle shuffles, a pack is still visibly ordered - it is only after the seventh that it suddenly becomes random. If a pack is not shuffled effectively then it can retain information from its previous play.
The laws of bridge clearly state that the pack should be thoroughly shuffled. Unfortunately, Bridge players often do not shuffle hands enough to ensure random distributional patterns. They either make insufficient riffle shuffles or use sub-standard methods like overhanded shuffles. It has been shown that poor shuffling results in flatter hands.
The Duplimate uses a random number generator to sort the pack into the four hands for each board. The statistical tables in the The Bridge Players Encyclopedia published by Hamlyn provides the following statistically expected distributions, grouped by longest suit in balanced/semi-balanced hands to the more extreme distributions.
Balanced Hands:
4-4-3-2 = 21.6%, 4-3-3-3 = 10.5%, 5-3-3-2 = 15.5% >>> Total = 47.6%
Other 5-card Hands:
5-4-3-2 = 10.6%, 5-4-3-1 = 12.9%, Any 5-5 = 4.0%, 5-4-4-0 = 1.2% >>> Total = 28.7%
6-card Hands:
Any 6-3 = 5.6%, 6-4 = 4.7%, 6-5 = 1.2%, Other 6-card hands = 4.6% >>> Total = 16.1%
Other Common Hands:
4-4-4-1 = 3.0%, 7-card suits = 2.5%, 8-card suits = 0.4% >>> Total = 5.9%
It can be seen that this gives 98.3% of possible combinations leaving 1.7% of hands that may have really odd hands. This means, from about 100 hands on a Wednesday night session, that there will be 1 or 2 odd hands being dealt. As a player, when you only play about 25 hands in a session, you should expect to encounter a really odd hand every 2 or 3 sessions.
It has also been said that there are an unusually high number of singletons and voids, again this is due to the non-randomisation of the cards during a manual shufle. The odds against any hand holding a singleton are approximately 4:1 which means that we should expect one hand in five to contain a singleton. This means that for a normal club evening using approximately 100 hands that there should be 20 hands containing a singleton. The odds against any hand holding a void are approximately 19:1 - thus on a normal club night the expectation is that 5 hands should contain a void. As a player, playing 25 hands in a session, you should expect to have a singleton in 5 of these hands and a void in 1 of them.
On the handout available at the end of the session, there is a recap section at the end of the hands that gives the number of balanced hands; hands with voids and singletons; and hands with suits of 7+ cards - this can be used to check how close to the odds that the session has been. For example, on 25th June 2008, there was 3 voids and 23 singletons from 120 hands - this means that we had 3 voids and 1 singleton less than expected.
As with all statistical predictions they only hold true over a very large number of hands but if anyone were to check the deals over a 6 month period then the figures would be expected to be very close. I hope that these explanations allay some worries that members have about the use of Duplimate for preparing hands on Wednesday nights. It is clear that if bridge players complain about poor hands resulting from computer generated hands then this indicates that these people are used to inadequate shuffling.
Based on an article from West Sussex Bridge Club |