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 sA, s2, cA and c2. The legal calls are 1c, 1s, 1NT (contracting for one trick) together with pass, double and redouble. The scoring system ignored redoubles:

To make a contract undoubled: +100
To make a contract doubled: +130
To go one off undoubled: -90
To go one off doubled: -180

Two questions were set:

(a) What are the best defensive methods against a `Natural' system, where 1s shows sA, 1c shows cA 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 1s, showing sA, they both recommend passing if we hold c2, otherwise bidding the `Gambling 1NT'. 1NT makes 50% of the time, when LHO holds c2, 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 c2. If then we hold c2 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 c2, as he knows our defensive methods will transfer to 1NT. He therefore does best to bid 1NT holding c2, 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 1c, showing cA, our winners differ slightly. Ross overcalls 1s on all hands! (Will the EBU license this?) This will make unless LHO has s A. If LHO holds s2 he should try 1NT. Our expected score is -180/3+100/3+(180-100)/6=-40/3.

Chris prefers passing with s2, bidding 1s with sA and 1NT with c2. 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 s2. If partner holds sA he bids 1s; if he holds cA 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.