[DavidKok]

This WeTransfer link leads to a .zip file containing most of the scripts and analysis that I wrote in an effort to simulate the above questions. It will expire in a week, I might pick a more long term solution if there's further interest in the topic. Most of the scripts were used to answer multiple questions at once, usually by changing variables slightly (e.g. the range of a NT opening or conditioning on which opening bid partner made).

[DavidKok]

 hrothgar, on 2023-April-05, 05:10, said:

High level comment

Its a lot more useful to post your code that your findings

My findings resulted in 20 comments in 3 days, including new ideas, constructive criticism and open questions. It's been 9 days since I posted my code. Could you expand on this?

[DavidKok]

After that riveting discussion on my code I've returned to my list of questions and added a few more.

I've since answered the questions I was looking at last time, along with one new one:

If we have a minimum (say, 10-15 HCP) 5-5 or longer hand, how often is the par at the 2-level or lower? If one or both of the suits are a major suit, how often is our best contract in a different suit (e.g. one of our short suits, or partner's long minor if that is our shortage)?

I've still got the old set of 5 open questions remaining, but I can probably make good progress on them (or even just find satisfactory answers to them) with a bit of effort. I've been spending more time on the 4cM canapé system lately and ran lots of numbers on that as well (e.g. how often do we have a 4-4(+) fit versus a 5-3(+) fit, some conditional probabilities on hand distributions and more) but I don't think those are very useful for other systems.

It has come to my attention that it is almost never right to play 2m, based both on actual play and on simulations. This isn't much of a surprise (especially not to LAWful bidders), but it does raise some questions about bidding theory. For example, why should 1M-1NT; 2♦ be natural NF, if we 'never' want to play there?

[DavidKok]

 mikeh, on 2023-April-02, 23:29, said:

For example I play T-Walsh with two partners, but with very different methods beyond the 1C 1R start.

When you look at frequencies, what parameters do you use for the opening bid? 2+ or 3+…my two partners prefer different styles

Do you assume 1D on 3343 or 4243 etc? In one we open all balanced hands out of range for 1N with 1C…not with a five card major but 3=3=5=2 is definitely included. In the other, we open 1C with 4=3 minors only if 3=3=4=3.

How light do you assume for a response? Today I held xxx Jxxxxx xxx x. Partner opened 1C, 2+. To us, this is an obvious 1D, showing hearts. We don’t play 1C as forcing and it’s often 11 hcp, but we virtually never pass it without club length. We’re sort of protected from most disasters because he bids 1N with 17-19, 2-3 hearts and never bids 4H unless 5=6, where I’d be delighted. We use 2N as a gf raise, and I can transfer and pass 3H should I choose.

You say you are working on frequencies of opponent hand types after 1C P 1S, assuming that 1S denies a major. I don’t play that in either of my partnerships.

1S denies a major unless responder has longer diamonds and a game force hand…while the ‘no major’ holdings are far more common than the ‘longer diamonds, gf’ hands, I think you’d be overestimating the frequency of 4th seat holding both majors if you didn’t recognize that. Maybe there are people who use 1S to deny a major, but I think that is an unnecessary complication, making relative major-minor length more difficult to assess when we own the hand.

I have ran some simulations on my T-Walsh questions now. I noticed that the 2-level responses (and higher) to a 1♣ opening were very low frequency, with almost all hands responding 1♦ through 2♣ in most schemes. Therefore I chose a scheme that I've personally been interested in, although it does chip into some of the system a bit.

It opens 1♣ on hands with primary clubs, three-suiters with a red suit shortage, 12-13 balanced without a 5cM and 17-19 balanced without a 5cM. This includes 5♦332 in both balanced ranges.
The responses are as follows:

• Pass - no other good bid
  
• 1♦ - 4(+) hearts, 0(+) hcp
  
• 1♥ - 4(+) spades, 0(+) hcp
  
• 1♠ - 3(-) in both majors, 5(+) hcp
  
• 1NT - Art. GF, may have one or both 4cM (but no 5(+)cM, no 6(+)cm).
  
• 2♣ - 5(+) clubs, 10(+) hcp
  
• 2♦ - 6(+) diamonds, 9-11 hcp (INV NF facing 12-13)
  
• 2♥ - 6(+) hearts, 9-11 hcp (INV NF facing 12-13)
  
• 2♠ - 6(+) hearts, 9-11 hcp (INV NF facing 12-13)
  
• 2NT - 5(+) clubs (usually 6(+)), 0-5 hcp
  
• 3♣ - 5(+) clubs, 6-9 hcp
  
• 3♦ - 7(+) diamonds, 0-4 hcp
  
• 3♥ - 7(+) hearts, 0-4 hcp
  
• 3♠ - 7(+) spades, 0-4 hcp

There are lots of overlapping options, I split those in the directions I pleased (e.g. 12+ with 5 clubs bids 1NT, but with 6(+) I'd bid 2♣). Also in writing this I realised that I messed up some of these overlaps and I will have to fix my code a bit. As I said though all responses of 2♦ and up are very rare and don't have a significant impact on the system. If you want you could slap a multi, or reverse flannery, or something else in here without significantly impacting the probabilities.
I think the 6♦4M GF hands should probably respond 1♠ and then complete a reverse next round, while the GF 5♦4M hands are better served bidding the 1NT relay. This is something I need to fix.