Results of the Four Card Bridge competition

by Jonathan Mestel

Last newsletter, I set a competition to find the best bidding system for four card bridge. This uses a 4-card deck, containing the A, 2, A and 2. The legal calls are 1, 1, 1NT (contracting for one trick) together with pass, double and redouble. The scoring system ignored redoubles:

Two questions were set:

(a) What are the best defensive methods against a `Natural' system, where 1 shows A, 1 shows A and pass denies an ace?

(b) What is the best system of opening bids?

This game gets more confusing the more you think about it. Exchanging information helps the opponents, and to assess even the simplest methods, you have to consider the best countermeasures. Perhaps for this reason, I received no sufficiently detailed answers for part (b). As everyone soon found, part (a) is quite complicated enough.

The best two answers received were from Chris Chambers and Ross Midgley, who draw similar conclusions. Chris hails from Suffolk, and so should perhaps be disqualified, but I don't want to be accused of Countyism, so I'll award them both a prize. Ross sent a particularly detailed and lucid analysis, which I could forward to anyone interested.

If RHO opens 1, showing A, they both recommend passing if we hold 2, otherwise bidding the `Gambling 1NT'. 1NT makes 50% of the time, when LHO holds 2, but otherwise it goes one off doubled. The expected score for this strategy is (-100)/3+(+100)/3+(-180)/3=-60. However, perhaps a better strategy is for second hand to pass, and fourth hand to reopen with a double provided he doesn't hold 2. If then we hold 2 we pass for -130, but otherwise we bid the laydown 1NT. So this would expect to score -100/3+100/3-130/3=-130/3.

But responder can do better than passing meekly if he holds 2, as he knows our defensive methods will transfer to 1NT. He therefore does best to bid 1NT holding 2, which makes half the time. We would then score -100/3+(180-100)/6-130/3=-190/3. But if we know he will do this, then partner doesn't have to reopen with a double! We then score 23(-100)+16(180-100)=-160/3. Who has to declare their methods first? I think responder's bid must be defined first - we begin to see the need for probabilistic strategies...

If RHO opens 1, showing A, our winners differ slightly. Ross overcalls 1 on all hands! (Will the EBU license this?) This will make unless LHO has A. If LHO holds 2 he should try 1NT. Our expected score is -180/3+100/3+(180-100)/6=-40/3.

Chris prefers passing with 2, bidding 1 with A and 1NT with 2. This give LHO perfect information, and so the expected score is 16(+100-100+100-100+100-180)=-30 and Ross's method is preferable.

Over an opening pass (showing a two), both our winners bid naturally, showing their ace or passing. I am not convinced this is optimal. Curiously, the best card to hold over a pass is the 2. If partner holds A he bids 1; if he holds A he gets to bid 1NT before opener can.

It's a difficult game! Thanks to all who entered, and I apologise for any suffering caused.