Some bridge questions and computer answers

[DavidKok]

I've been merrily formulating and collecting questions where the dealer software might help determine the answers. So far I'm really happy with the results. I figured I'd share the questions here, perhaps other people are interested as well, have other questions or answers to contribute or even just would like to have a copy of some of the scripts. For now I'll just share the list of questions. Any and all suggestions are very welcome!

 

I've already answered the following:

1. What is the opening frequency of 1NT, varied by range and style (include/exclude 5cM, include/exclude semibalanced hands)?
   
2. When including loads of semibalanced hands in a 1NT opening, what is the relative frequency of each of them?
   
3. What are the opening frequencies of all bids in Dutch Doubleton (including pass)?
   
4. What are the frequencies of responses to a Dutch Doubleton 1♣, including interference?
   
5. What are the shape probabilities of 1NT to a 1♣ Dutch Doubleton opening, including interference?
   
6. What are the opening frequencies of all bids in Standard Modern Precision?
   
7. What are the relative frequencies of the hand types in a nebulous Precision 1♦ opening?
   
8. What are the frequencies of the responses of several strong club systems to their 1♣ opening? I chose Standard Modern Precision, IMprecision and Revision. Includes interference.
   
9. What are the opening frequencies of (something that I hope is close to the actual description of) the Cottontail Club?
   
10. What are the frequencies of (natural) responses on the auction 1M-(X)-?
    
11. Conditional on having no fit with our own long suit on 1M-(X)-?, what is the point distribution?
    
12. Conditional on having no fit with our own long suit on 1♥-(1♠)-?, what is our point distribution (I'm trying to quantify playing NF versus F new suits here)?
    
13. On the Gazzilli auction 1♠-1NT; 2♣*-2♠* (7- HCP and no other good bid, may be a singleton in spades) what are responder's shape probabilities?
    
14. Partner opens a 14-16 NT - how much better/worse is making an invitational bid for 3NT, rather than pass-/blasting?
    
15. Partner opens a 14-16 NT and we find a 4-4 major suit fit - how much better/worse is making an invitational bid for 4M, rather than pass-/blasting?
    
16. Partner opens a 14-16 NT. Which hands are interested in a major suit fit, and which prefer 3NT even in the presence of a major suit?
    
17. We open an aggressive 5-card weak two bid. What is the chance that the opponents would do well by passing us out? By passing us out when we're making, and doubling us when we're not? Split by 2♦, 2♥ and 2♠.
    
18. We open a standard 6-card weak two bid. What is the chance that the opponents would do well by passing us out? By passing us out when we're making, and doubling us when we're not? Split by 2♦, 2♥ and 2♠.
    
19. We open 2NT (20-21). What is the probability that our best bet is running to 3M and playing it there?
    
20. We open 1NT (14-16). What is the probability that our best bet is running to 2♦ and playing it there?
    
21. We open 1NT (14-16). How much better is Crawling Stayman compared to Jacoby with a 54 hand?
    
22. We open 1NT (14-16). How much better is Garbage Stayman compared to Jacoby with a 54 hand?
    
23. We can (exactly) make a small slam in a suit. What is our combined hcp?
    
24. We can (exactly) make 6NT. What is our combined hcp?
    
25. We can (exactly) make a grand slam in a suit. What is our combined hcp?
    
26. We can (exactly) make 7NT. What is our combined hcp?
    
27. We open 1NT, natural. What is the chance that (double dummy!) it is important that we end up declaring the contract? That partner does? That it does not matter? How does this vary with NT range?
    

I've been playing around with a few more simulations (on the Wilkosz and some other assumed fit or two-suited preempts), but not in enough detail to add them to the list.

 

The questions I'm currently looking at are:

1. How accurate is the Law of Total Tricks?
   
2. As a function of HCP in one hand, how many tricks can we expect to obtain (i.e. is the old wisdom that 13 points means we're safe in 1NT opposite an average hand true, or by how much is it wrong)?
   
3. How accurate is the 'Rule of 15' for opening in fourth seat?
   
4. How accurate is the 'Rule of 17' for inviting opposite a weak two?
   

I've also got a few more questions that I've been keeping on the back burner for now:

1. After a 2+ 1♣ opening, what are responder's answering frequencies when playing T-Walsh? I would need to choose a set of methods for responding 1♠ and up for this question to make sense.
   
2. If the opponents bid (1♣ 2+)-P-(1♠* T-Walsh, denies a 4cM)-?, how often does fourth hand have both majors? I want to test how valuable playing double = both majors, rather than double = spades, is here.
   
3. Similar to my weak two questions, how often is a Rough 2♦ already over PAR?
   
4. Similar to my weak two questions, how often is a 2♥ 'Ekren-like' weak opening already over PAR?
   
5. With a 5M332 14-16 hand, can we quantify the gains and losses from opening 1NT rather than 1M?
   

[pescetom]

Good work, and I would be very grateful for a zip of the scripts plus a synthesis of the answers.

 

I used Dealer with trick-taking analysis intensively to evaluate the key choices of our NT subsystem a couple of years ago, and appreciate the potential.

It's a shame that BBO arbitrarily disabled the possibility for the BBO community at large to perform such analysis with just a browser and a script.

[thepossum]

Will follow all this work with interest :)

 

One I am considering ATM is when if ever Cappelletti pays

 

What we need is to hook ChatGPT up as a natural language interface (EDITED - useless predictive text or some weird dyslexic condition) to all David's scripts :)

[mikeh]

I second the commendation. I lack the skills needed to do this sort of thing, and the inclination to do it even if I could, but I expect there’s some useful information there

 

I do wonder, however, about the constraints.

 

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.

 

Also, and I may be betraying my ignorance here, knowing (say) the probabilities that the opps should pass us out in 2M after 3 passes doesn’t seem, to me, to have real world implications

 

After all, based on probabilities, it’s never right to open 7N but what if I held 13 winners, with the ace of every suit? I can just imagine the post game discussion. I didn’t open or later bid 7N because it’s almost impossible for me to hold this hand.

 

More difficult, I’d think, is to set minimum parameters for possible balancing actions in terms of shape and hcp, and then simulate those parameters. One might, I think, come up with something like….after 2S p p…if one holds 2=3=4=4 11 hcp one is slightly better off to pass than to double (or maybe the opposite) while with 1=6=3=3 8-9 hcp one is slightly better to bid 3H, or not..and so on.

 

I pick up QJ9xx Ax Jxxx xx, I don’t much care that ‘most of the time, ignoring what one holds, one should not pass out 2S’….because bridge decisions are based on hands, not relative likelihood of having the near infinite shapes one might hold. Knowing that passing is usually better than bidding, or vice versa, doesn’t tell us anything about what to do with many of the hands we may hold.

 

Where frequency of hand types really comes into its own, imo, is in system design, especially in the design of artificial methods. When I played relay, our system (which I most assuredly did not design) was explicitly designed to maximize the bidding space of frequent patterns rather than freaks. It meant showing a 1=5=6=1 hand after a 2C relay to 1D took up a huge amount of bidding space but 4432, 5422, 4333 etc were economical to show, which allowed for relays that could, on some hands, show the precise pattern and every card of Jack or higher.

 

Also, and it seems clear that you know this, this work will likely confirm that 14-16 is a far more common strength, in a balanced hand, than 15-17, thus encouraging the ongoing shift away from 15-17 1N.

 

I’m rambling. I have a nasty second bout of Covid and played 48 boards of KO today, so I’m excusing myself😀 I hope you will too. Despite my quibbles, I applaud your efforts.

[mikeh]

Will follow all this work with interest :)

 

One I am considering ATM is when if ever Cappelletti pays

 

What we need is to hook ChatGPT up as a natural language interference to all David's scripts :)

I know (I think) that the robots play cappelletti. I don’t think I’ve seen an expert play cappelletti in many years, if ever. It’s one of the worst possible methods, remaining popular (I guess) only because it was picked up by Ginsburg when he wrote GIB and it’s too much work to reprogram the robots to play anything else

 

In an ideal world, one could choose the conventions the robots use, to allow the player to learn conventions that real players use in real competition.

 

The big flaw is 2C as a one suiter. It’s not bad (except when one holds clubs) if the partner of the 1N bidder is sworn to silence. Should he bid..all advancer knows is that overcaller has a single suit somewhere. Good luck guessing when to compete.

 

Oh…and btw, in todays game everybody bids😀 that wasn’t as true when cappelletti was invented (by Hamilton as well as Cappelletti))

[DavidKok]

I’m rambling. I have a nasty second bout of Covid and played 48 boards of KO today, so I’m excusing myself�� I hope you will too. Despite my quibbles, I applaud your efforts.

I'm sorry to hear that, get well soon! You raised a lot of good points and I'll do my best to give some brief answers to each of them.

 

I second the commendation. I lack the skills needed to do this sort of thing, and the inclination to do it even if I could, but I expect there’s some useful information there

 

I do wonder, however, about the constraints.

Computer simulations are always going to have a number of unrealistic constraints. Personally I view this as two imperfect windows into bridge - one is our experience (maybe from playing in person, maybe from observing others). That part is obviously representative of actual play, on account of being actual play. But it suffers from biases due to imperfect memory, low sample size and even limited access to viable alternatives (most methods don't spread beyond a local circle). On the other hand computer simulations allow us to drastically increase the sample sizes on any question we may have (I typically simulate up to 100,000 relevant hands each for the frequency questions, or 1,000-10,000 relevant hands for the Double Dummy questions - this typically requires generating in the ballpark of 100,000,000 deals as any particular auction is very low frequency) and collect any form of statistics we like. In return there are issues with comparing simulations to actual play - humans don't play double dummy, their bidding decisions are not based on optimal criteria, judgement and hand evaluation are nigh impossible to program (and I haven't tried) and more.

I use these simulations as metrics of sorts to support or refute ideas based on personal experience. For example, if partner opens a 14-16 NT, we have a 3=4=3=3 with 10 to 15 points inclusive and opener has exactly 4 hearts (which responder doesn't know yet but can presumably find out through a Stayman auction), the simulation says that 3NT will make double dummy 66.8% of the time while 4♥ will make 63.2% of the time. My conclusion is that this is basically a wash, and you may as well blast 3NT and avoid the information leakage. That's not a particularly brilliant insight, but I think a simulation can definitely help gain more understanding of good choices and methods.

 

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've deliberately postponed the T-Walsh questions because there are so many different T-Walsh methods. Your point on 1♠ is well taken, I did mean a method where 1♠ may have a major and longer GF diamonds, I simply failed to specify this in the question statement. My intent was to assume 1♣ on any balanced hand out of 1NT range without a 5-card suit outside clubs, e.g. including 3=4=4=2 hands. I also think that any weak hand with long hearts (in fact, most 0-point 5-card hands) are clear 1♦ responses - as you say you can handle any response. One of the important preliminaries to answering T-Walsh questions is specifying an exact T-Walsh method(/system), and I haven't gotten around to that yet. But my intent is to include:

• Open 1♣ on (almost) all balanced hands outside 1NT range - i.e. only excluding 5332 hands with the 5-card not being clubs (personally I wouldn't mind including 5♦332 as well).
  
• Respond even on very weak hands with a long major, protected by the knowledge that partner will accept the transfer with weak balanced hands and will bid 1NT with strong balanced hands, and won't jump around very often.
  

My main concern are the 1♠ through, say, 2♠ responses. Nearly every partnership seems to have their own set of rules for them.

 

Also, and I may be betraying my ignorance here, knowing (say) the probabilities that the opps should pass us out in 2M after 3 passes doesn’t seem, to me, to have real world implications

 

After all, based on probabilities, it’s never right to open 7N but what if I held 13 winners, with the ace of every suit? I can just imagine the post game discussion. I didn’t open or later bid 7N because it’s almost impossible for me to hold this hand.

 

More difficult, I’d think, is to set minimum parameters for possible balancing actions in terms of shape and hcp, and then simulate those parameters. One might, I think, come up with something like….after 2S p p…if one holds 2=3=4=4 11 hcp one is slightly better off to pass than to double (or maybe the opposite) while with 1=6=3=3 8-9 hcp one is slightly better to bid 3H, or not..and so on.

 

I pick up QJ9xx Ax Jxxx xx, I don’t much care that ‘most of the time, ignoring what one holds, one should not pass out 2S’….because bridge decisions are based on hands, not relative likelihood of having the near infinite shapes one might hold. Knowing that passing is usually better than bidding, or vice versa, doesn’t tell us anything about what to do with many of the hands we may hold.

 

Where frequency of hand types really comes into its own, imo, is in system design, especially in the design of artificial methods. When I played relay, our system (which I most assuredly did not design) was explicitly designed to maximize the bidding space of frequent patterns rather than freaks. It meant showing a 1=5=6=1 hand after a 2C relay to 1D took up a huge amount of bidding space but 4432, 5422, 4333 etc were economical to show, which allowed for relays that could, on some hands, show the precise pattern and every card of Jack or higher.

The "how often should they pass us out" metric is not useful at the table. The purpose of that question is to aid in system design. For example, even over my aggressive 2♠ opening (which is a 5-card suit more often than not) it seems the opponents can theoretically get a good score by passing me out while nonvul only 2.40% of the time, while they can get a good score by passing me doubled and vulnerable (if I would not change my suit requirements under those conditions) 26.0% of the time. I use these figures as an imprecise metric to determine how aggressive my weak twos should be, based on position and vulnerability. At some point I intend to write a followup specifying what direct and balancing doubles look like, what penalty passes look like, what runout sequences look like and verify how frequently I might actually get passed out (un)doubled - but it helps to know at least in theory how often they could catch me speeding, given perfect information.

Frequency information on relay auctions is really useful (and, ironically, usually inaccurate - conditioning on the opponents not having an overcall and the partnership having enough combined strength for a GF auction has a noticeable impact on the hand frequencies, so most textbook/a priori frequencies are actually wrong). This is part of why I looked into, among other things, the IMprecision auctions.

 

Also, and it seems clear that you know this, this work will likely confirm that 14-16 is a far more common strength, in a balanced hand, than 15-17, thus encouraging the ongoing shift away from 15-17 1N.

A traditional 14-16 NT covers approximately 6.40% of all hands, which increases to approximately 8.02% if we include a host of semibalanced hand types. For 15-17 NT the figures are 4.84% and 6.23% respectively. This represents an increase of approximately 30% for the lower range, although there is a slight adjustment when we consider seating. The other three players will more frequently have an opening conditional on us holding 14-16 compared to 15-17, so a slightly smaller fraction of the times you do hold a strong NT you won't get to open it with the weaker range.

[pilowsky]

Get well soon Mike.

 

Useful though Bird and Anthias are, one thing they lack is taking into account vulnerability - they do compare IMP's vs MP's.

Some people play different NT ranges depending on vulnerability. Is it important?

Preempts vary in required length - does it matter?

 

Is it possible that entirely different systems would work better depending on vulnerability?

[DavidKok]

Rather than just 'possible', I personally think this is 'beyond probable', perhaps even 'a near certainty'. The relative value of the main goals in bidding (e.g. bidding good partscores, scoring game and slam bonuses, finding profitable sacrifices and preventing our opponents from doing all of the above) change and with it the probabilities that we should investigate them. I think if we really want to split hairs we should play 16 different 'systems' - one for each combination of seat and vulnerability.

Of course this is much too complex, and thankfully we don't have to resort to these extremes to get competitively viable bidding systems. But keep in mind for a second that many players already do play this to a certain degree - 4cM openings in third seat, no weak preemptive bids for fourth seat openings, 2/1 not GF by a passed hand, chicken NT (weak or kamikaze when NV, strong when V), different competitive agreements and preemptive requirements based on seat and vulnerability, different defences to 1NT in direct and balancing seat, balancing doubles and fourth seat NT are all mild examples. Most of these are of the form "retain basically the same meaning but shift the requirements by a certain amount", but in some cases these are entire systems that only apply in specific positions.

 

As for a more innocent example: my simulations imply that, when partner opens a strong 1NT, it is foolish to make a game try while NV. However, when vulnerable, it is winning bridge to make an invitational bid with some very specific hand types.

[mikeh]

Rather than just 'possible', I personally think this is 'beyond probable', perhaps even 'a near certainty'. The relative value of the main goals in bidding (e.g. bidding good partscores, scoring game and slam bonuses, finding profitable sacrifices and preventing our opponents from doing all of the above) change and with it the probabilities that we should investigate them. I think if we really want to split hairs we should play 16 different 'systems' - one for each combination of seat and vulnerability.

Of course this is much too complex, and thankfully we don't have to resort to these extremes to get competitively viable bidding systems. But keep in mind for a second that many players already do play this to a certain degree - 4cM openings in third seat, no weak preemptive bids for fourth seat openings, 2/1 not GF by a passed hand, chicken NT (weak or kamikaze when NV, strong when V), different competitive agreements and preemptive requirements based on seat and vulnerability, different defences to 1NT in direct and balancing seat, balancing doubles and fourth seat NT are all mild examples. Most of these are of the form "retain basically the same meaning but shift the requirements by a certain amount", but in some cases these are entire systems that only apply in specific positions.

 

As for a more innocent example: my simulations imply that, when partner opens a strong 1NT, it is foolish to make a game try while NV. However, when vulnerable, it is winning bridge to make an invitational bid with some very specific hand types.

Some strong pairs play either no game tries or very few game tries.

 

One of the more challenging things to simulate is the cost of the information leak caused by game tries, especially vulnerable at imps.

[pescetom]

my simulations imply that, when partner opens a strong 1NT, it is foolish to make a game try while NV. However, when vulnerable, it is winning bridge to make an invitational bid with some very specific hand types.

 

Either I'm having a bad day or there is a typo here.

[DavidKok]

Some strong pairs play either no game tries or very few game tries.

 

One of the more challenging things to simulate is the cost of the information leak caused by game tries, especially vulnerable at imps.

My simulations do not include information leakage at all, since they are based on double dummy analysis. In my opinion this point is incredibly important, nearly impossible to capture in a computer simulation, and should be kept in mind whenever we are discussing game tries of any sort. The surprising result of my earlier simulations is that, even with double dummy play, game tries over 1NT don't really make sense. My interpretation is that there is not enough room for the partnership to evaluate the degree to which the hands are fitting, and "15-16 go, 14 pass" is not really more accurate than "always go" - the fraction of 15-16 hands opposite which game will make is not much better than the fraction of 14-counts opposite which game will make, so you don't gain much by distinguishing them. The downside of playing 2NT (or 3M) rather than 1NT costs about as much as you gain from splitting opener's hands by strength.

 

Either I'm having a bad day or there is a typo here.

There is no typo. My simulations claim that, facing a 14-16 NT and with a balanced hand:

• With 10HCP bid game.
  
• With 8HCP passing is best by a wide margin.
  
• With 9HCP not vulnerable inviting is slightly better than passing (2.0 points per deal on average, where a vulnerable game is 400 points and 1NT making is 90 points), and both are a lot better than blasting game.
  
• With 9HCP vulnerable inviting is better than passing (+17.2 points per deal average) and blasting game (+20.8 points per deal average).
  

My tentative conclusion is that reserving an invitational sequence for balanced hands over a 14-16 NT only really makes sense with exactly 9 HCP and while vulnerable. That being said I am not eager to play different systems over NV and V 1NT (then again, the chicken NT is quite popular here), so I'd either always or never reserve room for a balanced invitational sequence. I also expect blasting to do better than a simulation indicates for the reasons mikeh specified above.

As an aside, if we do have a(t least a) 4cM the situation is a lot worse all around and inviting becomes significantly worse. Not only will inviting take us to the 3-level*, we will also leak lots of information by using a Stayman sequence (especially if we have spades). I now think playing 1NT-2♣; 2M-3M as invitational is really wasteful.

That being said the standard wisdom is to invite with 9HCP even NV, and many of these games do come home. It is very plausible that on average the defenders will slip up often enough to skew the odds in favour of bidding more games. I don't know how to properly adjust for this in the simulation - perhaps I can give declarer a small random chance of taking an extra trick, and see how that changes the odds.

 

*If you play Spademan, where 1NT-2♣; 2X-2♠ shows 5S and inv NF, you can recover some of these losses.

[pescetom]

My simulations do not include information leakage at all, since they are based on double dummy analysis. In my opinion this point is incredibly important, nearly impossible to capture in a computer simulation, and should be kept in mind whenever we are discussing game tries of any sort. The surprising result of my earlier simulations is that, even with double dummy play, game tries over 1NT don't really make sense. My interpretation is that there is not enough room for the partnership to evaluate the degree to which the hands are fitting, and "15-16 go, 14 pass" is not really more accurate than "always go" - the fraction of 15-16 hands opposite which game will make is not much better than the fraction of 14-counts opposite which game will make, so you don't gain much by distinguishing them. The downside of playing 2NT (or 3M) rather than 1NT costs about as much as you gain from splitting opener's hands by strength.

 

There is no typo. My simulations claim that, facing a 14-16 NT and with a balanced hand:

• With 10HCP bid game.
  
• With 8HCP passing is best by a wide margin.
  
• With 9HCP not vulnerable inviting is slightly better than passing (2.0 points per deal on average, where a vulnerable game is 400 points and 1NT making is 90 points), and both are a lot better than blasting game.
  
• With 9HCP vulnerable inviting is better than passing (+17.2 points per deal average) and blasting game (+20.8 points per deal average).
  

My tentative conclusion is that reserving an invitational sequence for balanced hands over a 14-16 NT only really makes sense with exactly 9 HCP and while vulnerable. That being said I am not eager to play different systems over NV and V 1NT (then again, the chicken NT is quite popular here), so I'd either always or never reserve room for a balanced invitational sequence. I also expect blasting to do better than a simulation indicates for the reasons mikeh specified above.

As an aside, if we do have a(t least a) 4cM the situation is a lot worse all around and inviting becomes significantly worse. Not only will inviting take us to the 3-level*, we will also leak lots of information by using a Stayman sequence (especially if we have spades). I now think playing 1NT-2♣; 2M-3M as invitational is really wasteful.

That being said the standard wisdom is to invite with 9HCP even NV, and many of these games do come home. It is very plausible that on average the defenders will slip up often enough to skew the odds in favour of bidding more games. I don't know how to properly adjust for this in the simulation - perhaps I can give declarer a small random chance of taking an extra trick, and see how that changes the odds.

 

*If you play Spademan, where 1NT-2♣; 2X-2♠ shows 5S and inv NF, you can recover some of these losses.

 

OK, I follow you now: you were thinking about responder with a balanced hand, not any hand (surely it is far from foolish to make a game try NV with many unbalanced or semi-balanced hands, where the capacity of opener to evaluate fit and combined strength is vital).

Your conclusions about quantitative game/pass/invite thresholds exactly match those I reached when simulating for 15-17 (with you requiring 1 point more for responder).

I agree with most of the rest too, although our Stayman leaks less than most (often only "has no 5cM" as far as Opener is concerned) and our spades invite can stop in 2♠.

[DavidKok]

I think there is some irony here. If I were to rank the hand types from 'most important to have an invitational sequence facing a strong notrump' to 'least important to have an invitational sequence facing strong notrump', I think it would be something like:

 

1. Unbalanced hands with a 4cM (so also including a long minor, perhaps this should include 4441 hands).
   
2. Unbalanced hands with a 5(+)cM (so also including a 4cm - 5-5 hands should just blast).
   
3. Hands with a 6(+)cm (asking for the degree of fit).
   
4. Balanced hands without a 4cM.
   
5. (semi)balanced hands with a 4cM.
   

The irony is, of course, that the most common methods only include 3 through 5, with most beginners omitting 3 as well. Typically the hand types 1 and 2 can only be shown with at least GF strength.

For what it's worth I have only simulated hand types 4 and 5 so far, I might add the rest at some later point.

 

As for information leakage, I still think my 'mini-Heeman' solves all problems with little to no downside. I hope that one day I will get to play it. It doesn't even require changing methods substantially, it just swaps two bidding sequences compared to Stayman.

[mycroft]

Interesting. You seem to agree with Ron Klinger. I have:

1. a sequence for "10-11, 4 or 5 card M" (opposite 12-14)
   
2. see above (and yes, the problem is that we can't tell the difference)
   
3. a sequence for "invitational, 6cm" (again, nominally 10-11, but primarily interested in fit)
   
4. a straight range ask (that has some rare slam hands hijacked into it).

in Keri.

 

Of course we don't have "want to play in something that resembles a fit, tell me where it is" unless we're doubled. Which is a large drawback, especially when it's 0-10, not 0-7.

[pilowsky]

 

As for information leakage, I still think my 'mini-Heeman' solves all problems with little to no downside. I hope that one day I will get to play it. It doesn't even require changing methods substantially, it just swaps two bidding sequences compared to Stayman.

 

I searched for mini-Heeman and found this.

Is there something on the mini version?

 

It looked impressive.

[thepossum]

I know (I think) that the robots play cappelletti. I don’t think I’ve seen an expert play cappelletti in many years, if ever. It’s one of the worst possible methods, remaining popular (I guess) only because it was picked up by Ginsburg when he wrote GIB and it’s too much work to reprogram the robots to play anything else

 

In an ideal world, one could choose the conventions the robots use, to allow the player to learn conventions that real players use in real competition.

 

The big flaw is 2C as a one suiter. It’s not bad (except when one holds clubs) if the partner of the 1N bidder is sworn to silence. Should he bid..all advancer knows is that overcaller has a single suit somewhere. Good luck guessing when to compete.

 

Oh…and btw, in todays game everybody bids😀 that wasn’t as true when cappelletti was invented (by Hamilton as well as Cappelletti))

 

It would be good to be able to select robot bids

 

Failing that play real Bridge with a half decent human

 

Regarding Cappelletti my evidence suggests it may be better for Rubber than Duplicate

[thepossum]

Can I offer an observation or question regarding the only one of David's analyses I have really looked at, including even replicating the script - NT invite or blast one

 

Its a broader observation or question about many more specific or possibly over fitted sims

 

There did not appear to be very much of a distribution - in the sense of the scores being highly dominated by one score - sorry difference (eg zero from memory)

- what can be truly concerning though is when the confidence intervals do not include 0 or other likely numbers

 

 

If you look at cumulative distributions and quantiles they may be more instructive than basing everything on means

 

That's a question or consideration I have about all DD sims actually

 

We happily go around working out means which even have confidence intervals including many(infinite) impossible scores - eg 95% chance of -0.003 +/- 0.12 etc :)

 

How many hands would we have to play to get a real and genuinely significant effect too

 

Maybe its more about looking for the best upsides or avoiding the worst downsides

 

One thing I have noticed though is how often obviously good leads score best in lead sims :)

[DavidKok]

I searched for mini-Heeman and found this.

Is there something on the mini version?

 

It looked impressive.

That's the 'full version'. I found some of the sequences unwieldy, and some others unnecessary (most of the CONFIT stuff, the immediate responses of 2♠ and up, and a few more sequences). So I've cut and modified it to keep some core principles but minimise it. The results are in mini Heeman and some bonus topics.

[DavidKok]

Can I offer an observation or question regarding the only one of David's analyses I have really looked at, including even replicating the script - NT invite or blast one

 

Its a broader observation or question about many more specific or possibly over fitted sims

 

There did not appear to be very much of a distribution - in the sense of the scores being highly dominated by one score - sorry difference (eg zero from memory)

- what can be truly concerning though is when the confidence intervals do not include 0 or other likely numbers

 

 

If you look at cumulative distributions and quantiles they may be more instructive than basing everything on means

 

That's a question or consideration I have about all DD sims actually

 

We happily go around working out means which even have confidence intervals including many(infinite) impossible scores - eg 95% chance of -0.003 +/- 0.12 etc :)

 

How many hands would we have to play to get a real and genuinely significant effect too

 

Maybe its more about looking for the best upsides or avoiding the worst downsides

 

One thing I have noticed though is how often obviously good leads score best in lead sims :)

From my perspective I think this completely misses the point, in multiple ways.

 

1. The goal of my simulations is not to provide a (scientifically) rigorous underpinning for system design. In fact, I think any such attempt is doomed from the start. The out-of-model errors dominate the in-model confidence margins - there's no point giving a 95% confidence interval when at least one in every 10 scripts makes unrealistic assumptions or simplifications. These include more nuanced hand evaluation (I've just been using HCP!), interference (not all my simulations include this yet), inferences from passed hands, the difference between real play and double dummy play and more. I think at best these simulations should be thought of as limited insights or clues - your local expert says A, the simulation says B, those are two pieces of limited information on how you might wish to design your bidding system.
   
2. As a brief aside, using the 'average' function in the dealer software gives the variance and standard deviation of the sample. Just keep in mind that this is total sample st. dev., which is not the uncertainty in the mean. When comparing blast and invite, for example, we'll have many deals where blast is in 3NT while invite is in 2NT. No matter how many tricks the solver will take those two contracts will lead to different scores, so the variance in the sample is huge. That does not mean that the uncertainty in the average is huge. But as I said above I don't think this is very important either way - rather than the sign of the mean, I think the quantity is most important. If it is small the simulation has no real insight to offer either way. If it is large (and now the sign matters) that is an indication that it might be worth trying at the table. That being said if you really want confidence intervals it is not a big challenge to include them (the sim gives the sample st. dev. and the sample size, perfect for classical statistical analysis). I just think they'll be worthless.
   
3. Lastly, in my opinion, I think this is at least somewhat an isolated demand for rigour. When someone (perhaps your partner, perhaps a bridge book or pamphlet or some other source) suggests "Using bid X in situation Y to show hand type Z is a good idea" we don't retaliate with "show me your spread of results over the last 5,000 times it came up, I will believe that only after statistical analysis". I think it borders on the foolish to demand this from a flawed simulation but not from other sources. You might not trust the results of the computer over your source at the table (I know I don't), but it is equally wrong to disregard it entirely because it didn't meet some bar you set (but if you insist, I will share my code once I have the time and have cleaned it up a bit more, so feel free to improve it to match your requests). In particular, I selected these questions precisely because I already had reason to question some common treatments or wisdom, and they are relatively suitable for cramming into a simulation. The only claim I'm making is that this is a big step up from not having a simulation - any and all suggestions of rigour or confidence are your own.
   

[hrothgar]

High level comment

 

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

[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]

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]

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.