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Those #@%$& Bot Leads
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I don’t play much on BBO, so have little personal knowledge of bot leads, but I infer from BW posters that the double-dummy leads against notrump contacts lean considerably conservative, and might charitably be called unconventional.

There has also been recent BW chatter about ‘I hate leading from kings’ and ‘oh yeah well that beats leading from jacks’.

So I thought I might try to kill two birds with one stone. My plan is to use a double dummy engine to catalogue leads defending a large number of notrump contracts. My theory (hope, expectation) is that these results will reasonably proxy bot leads, which are also double dummy. Declarer has 15-17 balanced, responder has 8-10 balanced. Bot on lead is 8-12, no 6-card or longer suit, not 5332 or 4333 (obviousness of lead?), usually 4432 or 5422 or 5431. Changes to the overall mix, or strengths of hands, would have little effect on project results.

I want to emphasize I am merely reporting from bot world, and not commenting on the validity of how bot ''strategies' translate to human play.

I dealt 100K suitably-framed hands. The solver reported the ‘best’ leads from a total of 400K suits. There are many ties. Average number of 'bests' per hand was 2.7. A typical hand on lead might be K864 J982 KQ2 86, with best results obtained from leads of the spade spots and all the minor-suit cards.

I collapsed all leads into 24 categories. From the hand above, Kxxx and Jxxx and HHx and xx are examples of categories, with Kxxx and HHx and xx each gaining a ‘best’. As a practical matter I disregarded spot quality, which evens out over thousands of deals.

Sample sizes for all holdings are more than sufficient. The most frequent bracket turns out to be xx (includes occasional singleton), of which there were 67K instances. Even the least-frequent 5-card holdings appear in the 4K range.

How to measure large-scale results? To determine lead ‘value’, I chose 2 metrics. ‘Average tricks won’ looks obvious, and a second you might call 'win frequency' --- category Kxxx arises X times and 'wins' Y of those.

Below is a copy of a spreadsheet which summarizes results for the 24 classes of leads. Left side of the spreadsheet ranks by ‘# of bests/frequency’, right side by ‘average number of tricks’. Of course the two metrics are strongly positively correlated ( > 0.8).

I consolidated SSx ('SS' for split honors AQ AJ KJ), because they were all major losers.

I consolidated TTx ('TT' for touching AK KQ QJ), because they were all major winners. Interestingly, from these holdings the bots preferred leading an honor to leading a spot, strongly so for AKxx(x), substantially for KQxx(x), mildly for QJxx(x).

Now take a look at the Kxxx vs Jxxx 'controversy'.  In the 100K sample, Kxxx arises 20.7K times and is a ‘best lead’ 13.4K times, so Kxxx ‘wins’ (or ties for the win) 65% of the time it is played. Jxxx comes along 18.3K times, and is a best lead also 13.4K of those, or 74%. By that metric, the win frequency for bot on lead with Jxxx is some 13-14% higher than for Kxxx. so 'lead from jack' haters take note.

The margin when measured by average tricks won, is 0.14 tricks. Haters might say big deal. On the other hand 0.14 tricks represents one full trick every seven or so deals, and that trick is worth masterpoints! Might be the setting trick against 3NT! That trick difference is fully equivalent to the margin for win frequency.

A questioning mind might now ask ‘how do bot leads from Kxxx and Jxxx (and all other matchups) fare when head-to-head’?

Well, they fare like the study predicts. Given a large sample of hands with a choice of leads from specifically Kxxx or Jxxx (typical hand is Kxxx Axx Jxxx Qx, say), leads from Jxxx win more tricks. Even with much better spots, say K987 vs J432, the bot still gets better results leading from the jack.

‘Winners’ of the head-to-head ‘confrontations’ generally adhere to the rankings up and down the line, provided the ranking spread is material. I'll pick two at random. From the table, a lead from xxxxx scores marginally higher than a lead from Axxx (4.18 tricks versus 4.11 tricks). When I put those holdings head-to-head, xxxxx does maintain about the same trick margin, typical hand perhaps xxxxx Axxx Kx Qx.

There are some eye-openers. Evidence of bot conservatism --- leads from xxx and particularly xxxx came off surprisingly strongly. For example, from Kxxx Qxxx xxx Ax, top lead is xxx, with both 4-suiters being under-performers. Bots dislike leading from Kxxx(x) and Qxxx(x) and even KJxx(x).

Generally leads from 5-suits fare well, but bots get better results leading from a quality 4-suiter than a weak 5-suiter. Bots will choose AKxx holding both AKxx and Qxxxx, say.

Bots avoid leads from Hxx, even if the alternatives are ‘bad’ 4-suiters --- bots prefer a heart from Kxxx Qxxx Kxx xx. Hxx and Hx are usually bottom-of-barrel choices,

These bot preferences might (or not) be confirmed by knowledgeable BBO users. If the rankings do actually reflect bot-lead tendencies, then when a bot leads some spot and neither the J nor the K is in your hand or dummy, there is a larger chance bot has the J, than the K. And an even larger chance the bot has neither, having led from xxx(x)!

A confounding contributor to bot lead 'peculiarity' would be the number of the sample deals the BBO bot analyzes, and how effective are the bot's auction-specific deals. If the bot is sifting through just a couple dozen badly-conforming deals, that might go a long way to explaining some of the goofiness of the leads, especially if the choice of leads is close, and it often is. Still, this post lays out the underlying lead 'preference' base for double dummy leads.

(Note I had to estimate ‘tricks won’ for all holdings that were not ‘best leads’. This was not reported by the double dummy engine. Let’s say the best leads produced 5 defensive tricks, how many defensive tricks on average would a losing lead produce? 4? 3? I ended up using an informed proxy which I applied equally to all cases, and any variation between my guess and the real world results, would have negligible impacts on the summaries.)

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