[jschafer]

No single card gives away more tricks than the opening lead, and none gets less feedback because you only ever see the one layout that was dealt. Killer Bridge Leads is a browser tool for exactly that question: which card should I have led? It deals the hidden hands thousands of times randomly, keeps only the layouts a bidding engine would actually have bid the way you heard, solves each one double-dummy, and ranks every lead with its margin of error. Then it trains you on the answers. The analyzer is free, no account needed.

What it does

Practice deals you a hand and an auction from a bank of 100,000+ lead problems, each chosen because the lead matters. Tap a card; the verdict says whether it was right and by how much. Five right in a row moves you up the ladder, and a rating tracks the climb from beginner to expert.

Analyze takes a hand you led from (typed in, from a BBO screenshot, or from a BBO Handviewer link) and tells you which lead was right and by how much: every card ranked by beat rate and average tricks, with the layouts behind the numbers one tap away. Change a call, edit a seat's constraints, run more, browse every deal.


Why it's different

• Auction-verified, not range-dealt. Typical lead simulation tools deal to a written range (e.g., 11–17 HCPs with 5+♠), and the verdicts drift with the range. Here we only keep layouts a real bidding engine bids exactly the way you heard: call for call, bids made and bids not made. It's what a defender actually knows at the table, and as far as I can tell no other lead tool does it.

• Dealt until it means something. Every result carries a margin of error, and a winner is only called when the gap to the runner-up is statistically solid. No more 100-deal sims settling arguments they can't settle.

• Calibrated. A bot leading purely from these verified layouts scores 80 on the double-dummy lead-accuracy scale the online cheating investigations used (95% CI 77–84): indistinguishable from world-class experts at about 81, and below the 85 that flags a cheat.

• Private. Dealing, bidding and solving all run in your browser; your hands never leave your device. Nothing to install.


Why bother

• Experience the table can't give. A session offers a dozen leads and no way to check one. Here it's thousands of comparable problems each with ground truth, the best lead across every layout the auction allows.

• How close it really was. When you are torn between leads, you can quantify the gap and hone your intuition.

• Why, not just what. Every winning layout is a tap away, seeing the hands where your lead lost teaches faster than any rule.

• At your level. The ladder adapts, so you spend your time on hands that challenge you appropriately.


Example Deal



What do you lead? The doubleton in the unbid suit, a trump from Qxxx to cut the ruffs, or one of the bid majors?


The Verdict

Spoiler

A trump. The small club beats 2♣ 35.4% of the time (±7%) across 240 engine-verified layouts, clear on the paired test (both leads scored on the same deals). The doubleton ♦4 (which I led) manages 28.8%; the ♠A 27.1%; the ♥Q trails at 23.3%.

The Layouts

All 240 layouts are there to browse, sorted by whichever lead you pick; and every one is a deal on which the engine would have opened 1♥, responded 1♠, rebid 2♣ and passed. Bids not made are evidence too. The usual double-dummy caveat applies, the one every lead book carries: perfect play after the lead slightly flatters attacking honour leads and undervalues passive or deceptive ones.

Spoiler

Free, and what's paid

Free, no account: the entire analyzer including manual entry, BBO import, auction-driven constraints, the full ranked table, the deal browser. Once you unlock ratings, 30 intermediate-to-expert hands are on the house.

The subscription unlocks every level up to expert, the practice filters (contract, level, scoring, auction type) and your misses list: $5.99 a month or $49.99 a year, with a 7-day free trial.

Who built it

I built it because leads were the part of the game where it felt like I was going in blind. I played junior international bridge for Belgium from 2008, including three European Youth Championships, and captained Imperial College London to the Portland Bowl in 2013. By profession I work in advanced analytics. It also uses Edward Piwowar's EPBot/BBA bidding engine provided with his kind permission and Bo Haglund's double-dummy solver. My thanks to both.


Please give it a try at killerbridgeleads.com. I would be grateful for any feedback as I am always looking to improve it further.

[mike777]

Please comment on the numerous criticisms of double dummy lead solvers.
Michael Rosenberg among others have written extensively on this subject.

[awm]

There are some known biases created by double-dummy, which I've already seen in running a small number of hands. Two prominent ones:

1. Leading unsupported aces looks good double-dummy, because of the assumption that you will always find the best switch at trick two. In practice this is not so easy.
2. Leading a singleton king looks good double-dummy, because it might establish a ruff and doesn't give declarer anything as he would never lose to your singleton king if he has (for example) AQJx in hand. But in practice this gives a trick fairly often against real declarers.

I'm not sure if there's an efficient way to correct for these issues, but it might be worth at least a note in the results.