One of my specialties is investigating close bidding decisions with the help of computer simulations. Suppose my partner opens 1NT (15-17), and I have ♠Q32 ♥987 ♦JT9432 ♣2. Is it better to leave partner in 1NT, transfer to 3♦, or use Stayman, dropping partner in a 4-3 major fit? You'll never face this decision enough times to be sure what's best. But a computer can hold your cards fixed, deal your partner a bunch of notrump openings, and deal your opponents random hands, and tell you what the outcome each possible final contract would be on each deal. (As shown below, the answer is using Stayman. Bidding 3♦ is better than passing 1NT, but Stayman is even better.)

Starting in 2010, I produced a series of short articles describing the outcome of some of these simulations. Those articles are reproduced below (as-yet unedited, still in their 2010 format.)

I have several more articles in the works, but they take time to write up nicely. Feel free to write me if there's one you'd like me to hurry up and finish.

I've also done a number of simulations in response to requests from posters on internet forums. For example:

• Is ♠Kxx ♥xx ♦QTxxx ♣Kxx worth an invite opposite a 15-17 notrump? (No.) Comments on a BridgeWinners thread
• BBO forum question:: choose a lead from ♠6 ♥J97632 ♦J85 ♣962 against 1NT-2♥-2♠-3NT. (A club is best.)
• BBO forum question: is ♠A73 ♥98652 ♦93 ♣T62 worth continuing on to game after 2NT-3♦-3♥?

Index of articles with simulation results

Older material, reformatted for delivery on the new web page:

Choosing an opening bid when partner is barred

Specific advice for every hand pattern and strength, for what to do after you bid out of turn and shut your partner out of the auction.

2010-era articles related to 1NT and 2NT openings:

Responding to 1NT with an 8-count

The experts are not unanimous in their opinions as to when it's right to drop partner in 1NT, when it's right to use Stayman with a marginal hand, and whether 1NT-2NT should be an invitation to 3NT.

Dropping partner after using Stayman

Closely related to the previous article: with what hand patterns and strengths is it more profitable to drop partner in 2\d, 2\h, or 2\s than to play 1NT?

Responding to 1NT with 3-3-6-1 distribution

The right response is obvious once you think about it, but the field hasn't ever thought about it.

Raising 2NT to 3NT

Are all 5-counts created equal, or is AJ significantly better than QJJJ for putting partner in game?

How much does it matter how declarer's and dummy's high cards are divided?

Everyone knows it's easier to make 3NT with 25 HCP than with 24 HCP. Sharp-eyed players also know that it's better to have 25 HCP divided 15-and-10 than 20-and-5. How much better?

Topics I've investigated but not had time to write up yet:

Why I don't use Puppet Stayman

At least at matchpoints, it doesn't turn a profit even when it uncovers a 5-3 fit, unless you use it extremely judiciously.

Game tries after 1♠-2♠

A detailed study of when game tries show a profit, of how best to tune acceptance critera for short- and help-suit game tries, and how different types of game tries interact with each other. (The results of this study will lead to a new article on my conventions page, too.)

The cost of the blind opening lead

Comparing double-dummy results with the outcome of choosing a blind opening lead based on the auction, then playing the other 51 cards double-dummy, for several different auctions. (Against 1NT-2NT, it is as much as one-third of a trick; against a very precise auction like 1NT-2♣-2♥-2NT-4♠, it can be less than one-tenth of a trick.)

How is double-dummy simulation done?

A new approach to studying bridge emerged starting in the late 1990s: dealing out large numbers of hands satisfying a set of constraints, then determining how many tricks can be taken with perfect play and defense if everyone can see everyone else's cards. There are some limitations to this method. For a start, it doesn't quantify the value of leaving your opponents in the dark about how best to defend, and this article by Thomas Andrews discusses some others -- but it remains a useful tool to estimate how often a given auction gets you to the right contract.

I use Thomas Andrews's Deal 3.1.9 package, which uses scripts written in TCL to specify hand types and is integrated with Bo Haglund's free double-dummy solver. (If you like spiffy graphical interfaces, you'll want to use something different. If you already speak Python and don't want to learn any TCL, you can try ReDeal, a translation of the Andrews package into Python by Antony Lee.)