(Page of 3)

First a specific example. Problem, I already polled our users. With a non-satisfactory result, while a discussion was interesting. Here the problem will be more specific.

I started the poll with a phrase that first leader wants to play against the field to obtain a good result - position "asks" for the routine spades lead that surely will give a result, which will be close to average.

Here I'll try to to proof that there exists generally the best - statistically speaking - lead. Or that a specific "crazy" lead is optimal.

South

♠

xx

♥

865432

♦

K10x

♣

9x

W

N

E

S

1♣

2♠

3NT

P

P

P

How one can prove this optimality.

1. We choose the hand of N randomly but with the following restrictions:

A. Must have 6 spades with probability 90% or 7 spades with probability 10%.

B. Must not have any of the cards that are specified in the holding of S

C. Has 9-11 HCPs. It may be added an additional restriction that N can not have 2 aces. Many experts say that hand with 2 aces is too strong for a block.

2. The N's hand must be secure in this vulnerability. For a specific hand chosen in point 1. we generate a sample of , say 10 000 of three other hands. In this case the restriction is that W has 11+ HCPs, no 5 in mayors and clubs better than diamonds. We reject the hand chosen in point 1 if the average number of tricks (in the sample of 10 000) played double-dummy will be less than 6, when spades is the trump suit. I.e. we don't want the N's hands that will result -2 or worse in contract 2♠x.

3. Now we produce say 50 000 deals with the following restrictions

A. N passed the tests described in 1. & 2.

B. S is our original hand, from we have to choose the first lead on the 3N contract played by E.

C. W has the same restrictions as specified in 2.

D. E is the hand with 13-16 HCPs and double spades stopper. It can not have clubs stopper more frequently than diamonds and hearts stopper. This is because W has in average 4-5 clubs.

We calculate averages in 50 000 deals of setting (double-dummy) 3N contract after the S's leads:** ♠x, ♥6, ♦x, ♣9.**

Lead with the highest average is the optimal.

Computer program that realizes the above algorithm should run some minutes. Of course it is worth to run such program several times to be sure that one of the four first leads is really the best.

I feel that A CLUBS LEAD will be the optimal. But first someone must write such program. It is not very difficult. But if one wants to improve the algorithm to the certain professional level it might be not that easy! I mean professional not only in the computer programming sense. It also should be improved from the probabilistic point of view, too.

For really decisive and not obvious positions in bridge such type programs BUT SUBSTANTIALLY DIFFERENT NOT ONLY IN ALGORITHM BUT ALSO IN SCIENTIFIC APPROACH can or should be written, to establish the optimal moves. I do not want to discuss here the strict definition of optimality in bridge, because it requires quite complicated mathematical methodology.

I can assure you that in many positions such programs will find moves that are better than those made by experts. You will be surprised how many times those programs will be better than the bests of us.

What it means?

It means that bridge is far more scientifically complex than chess. It does not mean that the** running time** of bridge programs that look for optimal moves, are larger than time of the analogical chess ones. But the bridge programs - when they will be written as the universal ones - will need many, many times more scientists than the number of those who helped writing the chess playing programs.

67 Comments

.

OR

Benefits include:

- Create and share convention cards
- Create/answer bridge problems
- Connect with other bridge players
- Write and comment on articles

Plus... it's free!