Dubious Logic

Good, Better, Best

Computer analysis continues to affect – some might say 'interfere' – with bridge. The latest contribution is a new book, Good, Better, Best by Jan Eric Larsson (Master Point Press). I cannot precis better than its subtitle; 'A Comparison of Bridge Bidding Systems and Conventions by Computer Simulation'.

In a similar vein to the books on leads by Taf Anthias and David Bird (Winning Notrump Leads, 2011 & Winning Suit Contract Leads, 2012), Larsson uses double-dummy analysis of deals as an objective measure. He codifies systems used by the computer to bid random deals in matches where the play is perfect on the lie of the cards, seeking answers to such questions as,

• Are four-card majors better than five-card?
• … Weak or strong no-trump?
• … Constructive six-card weak two openings, or wild and obstructive five-carders?
• … Natural or strong club systems

And many more. Naturally, to system geeks, Good, Better, Best is catnip and I checked every prejudice I hold – finding support, but far from unanimous. My penchant for 4-card majors with a strong no-trump is confirmed, as is the 'majors first' approach in that context (hearts-spades-clubs-diamonds) but – spoiler – five-card majors outperform four-card. Larsson discovers the best variant before the system deciders and presents his findings thus:

'System' is shorthand for the minimum suit-lengths for one-level openings and the above compares 'five-card majors longer minor' (top row), with four-card suits, preferred in the indicated order. 'Mean' is the average level of opening (Pass = 0, 1 = 1 etc.), obviously higher for the system that is able to open four-card hearts and spades. IMPs is the number won or lost over 300 matches of 24 boards (7200 deals).

The remaining columns restate the raw IMP totals; 'Match' is IMPs divided by the number of matches, here 300 head-to-head. 'Board' the per-board average, i.e. IMPs/(300 x 24). The large divisors partially explain why the number are so small, but even so, if you start a 24-board match playing the better system, you enjoy advantage of only 0.7 IMP.

Naturally, there are examples of why these differences occur:

Played by East, five hearts makes 11 tricks, EW +450.

But with West as declarer, a club leads holds declarer to 10 tricks, EW -50 and 11 IMPs to Team 4444.

There are relatively few examples and, I would say, not always well chosen. Above, many users of '4444 HSCD' (even with strong NT) open East with One Diamond anyway, to preserve the ability to show five hearts in the unopposed auction, 1 – 1; 2-minor (that diamonds may not be five after 1 – 1; 2 is less worrying). And note that if North leads the spade king, West's five hearts makes – and that in any case declarer must play diamonds perfectly to make from either side.

I found Good, Better, Best genuinely fascinating. It will certainly provoke discussion: on bidding systems themselves; their relative importance; the author's methods and more. I somehow think this is the start of this approach rather than the last word. If you want to know how your pet methods fare and what is 'Best', buy the book, there's much else inside.

Afterword

Many other 'matches' in the book are multi-way. Below, three versions of five-card majors compete against each other:

As there are two simultaneous matches (computers can be trusted to play the same board more than once!) the divisor to give a per-match margin is 2 x 300 = 600 and per-board, 600 x 24 = 14400. The tiny differences in mean-opening-level reflect the frequency of preferring 1 to 1.

I was surprised the data were not provided in a cross-table: it would have been interesting to see where the IMPs arose. Whilst it is likely 5533 beat both opponents, the margins are less convincing between 5542 and 5551 – perhaps the latter narrowly defeated 5542, the shared disadvantage of opening One Club with fewer than three cards offset by the advantages of knowing diamonds to be five-plus.

More critically I couldn't find if '5542' entailed 1 on any 4-4-3-2 out of range for 1NT (currently much in vogue) or only on 4=4=3=2 (where 5533 opens 1). It is possible that these are addressed – as mentioned, I did read it quickly (and on-screen). Larsson answers some of these questions online, see https://bridgewinners.com/article/view/good-better-best-by-jan-eric-larsson-sweden/.

Back to the example above: my experience of playing '1 is 4-4-3-2 unsuitable for 1NT' in a club setting is that opponents are inconvenienced when denied their club overcall. That is the thin end of why artificial methods enjoy disproportionate advantages against the less-experienced. On one hand therefore, the simulations reflect sound practise where opponents are not fazed by unusual bids and are well-equipped to deal with them.

However, on the other is that unusual and highly-active systems leak information to the opponents. As the play is perfect, that declarer may be assisted is not relevant. Moreover, weak overcalls and openings are baled out when partner always leads the best suit for the defence, not habitually, the one you bid.

The program defines each system up to a certain point and then has a 'natural bidding module' to take over. That seems a very sensible way of proceeding but why not take it a step further and equip each system with an opening lead module? That would not eliminate the subsequent double-dummy bias, but it would help offset it.

I was going to mention that in the book, by chance the example deal I selected was labelled, "Deal 20 West EW" but North opened and the EW scores at both tables are NV. That misprint provides an accidental insight into the sheer amount of data marshalled for the 190-odd pages. It took Larsson four years to code, test and appraise the results, it was clearly a labour of love and I can't help thinking it won't be the first edition.

Published Saturday 24.Jul.2021