Nerja Bridge Club
Shapely Bridge

What we want....

The "shape" of a bridge hand is important to us. Whether in no trumps or a suit contract, we want a long fit with partner and in suit contracts we want a short suit or a void to deal with the long enemy suits. In theory at least, we can make a small slam if we're missing the A and K of trumps provided we have 11 trumps and the opponents two split 1-1. Unfortunately, life is seldom like that in practice!

What we get....

In practice we feel we always get the "flattest" possible hands (4 – 3 – 3 – 3) whilst the enemy get all the "shapely" ones. We don't, of course, but it certainly can often feel like that. If we all usually received flat hands with 10 points (the average), we'd pass out every board and soon give up bridge altogether! It's actually the variety of distributions and hand strength which retain our interest, but if an eccentric pattern of hands appears, we should at least try to understand why....

What can we do about it?

For a start, we can learn the probabilities of how missing cards lie, always bearing in mind the bidding, but we can also consider what shapes of hands are most probable. The tables here show that our longest suit can be expected to have five cards a little less than half the time, while our shortest suit will be a doubleton about half the time, and so will the hands held by the opposition. They assume that the cards have been randomly shuffled (see below).

It can help to prepare for the play of each hand to gradually revise your expectations of the shapes of partner's and opponents' hands as the bidding proceeds, especially when dummy is spread and when considering what to discard, whether declarer or defender. But for this to be of real use, of course, the randomness of the shuffle is extremely important. Here is Zia Mahmood's description of what can happen when it's a goulash.

vs. What happened on Friday 4 February 2011....

The 27 boards played were all with very new cards. I am not certain how many times they have been shuffled, but I very much doubt it is the magic 7 referred to below. I strongly suspect that it was this the reason why the 108 hands dealt (see table at right) were substantially against the probabilities. Looking at the longest and shortest suits we can, perhaps, see this more clearly in the table below.

As can be seen readily, there were 11 hands with 7-card or longer suits rather than the expected 4, while more than double the expected number of hands had voids. Oddly, the numbers of hands with 6-card suits and singletons were almost exactly as expected, meaning that there were rather fewer "flattish" hands than could be predicted, yet there were two more completely "flat" hands than expected.

None of this suggests deliberate non-random dealing, and is what the opinion pollsters would call an outlier. My own suspicion is that the new decks, being much shinier than the "silk finish" cards we're used to, are actually marginally more difficult to shuffle. If this is the case, then we should consider....

Shuffling off....

The text below on shuffling is an extract from a 1990 New York Times article by Gina Kolata (their science correspondent who holds a Masters degree in Maths):

It takes just seven ordinary, imperfect shuffles to mix a deck of cards thoroughly, researchers have found. Fewer are not enough and more do not significantly improve the mixing.

The mathematical proof, discovered after studies of results from elaborate computer calculations and careful observation of card games, confirms the intuition of many gamblers, bridge enthusiasts and casual players that most shuffling is inadequate.

The full text is available here. I do think we need to put more effort into shuffling.