What is the size of our best fit?

[Cascade]

Roger asked me to do a simulation to determine the size of the best fit given we have a 4-4-4-1 hand.

 

Actually it turns out easy enough to enumerate all of the cases. Spreadsheets are a wonderful tool.

 

Given a specific 4-4-4-1 distribution there are 499 specific (ordered by suit) distributions that partner can have.

 

The probabilities of our best fits are:

 

7 cards . . . 0.169251734

8 cards . . . 0.490998116

9 cards . . . 0.267767366

10 cards . . . 0.063579522

11 cards . . . 0.007918909

12 cards . . . 0.000474227

13 cards . . . 1.01253E-05

 

These are wildly different than the a priori odds for each of these size fits which are:

 

7 cards . . . 0.157362521

8 cards . . . 0.45744659

9 cards . . . 0.280999069

10 cards . . . 0.086728774

11 cards . . . 0.015815833

12 cards . . . 0.001581699

13 cards . . . 6.55142E-05

[awm]

I've done something like this simulation before. It seems to validate my belief that mini-roman is a bad convention....

 

You'd think the right hands to preempt on would be ones where you are likely to have a good fit, whereas the dangerous hands to raise the level of the auction are the ones where your best fit is often seven cards or maybe eight. The 4441 shape provides less chance of a good fit than a randomly chosen hand, and is not substantially better than shapes like 4432...

[TimG]

Bring on the 2D openings which show 44 in the majors. Who says they are destructive?

[rogerclee]

Thanks a lot, Cascade.

 

One interesting point is that

 

Expectation of fit with 4441 hand = 8.251

Expectation of fit in general = 8.350

 

So it is interesting that these 4441 openers actually have a worse chance of finding a fit than any random sort of hand.

[Cascade]

I made a spreadsheet that will do this calculation for any distribution.

 

If you would like it let me know and I will send out copies.

 

It works on the brute force and ignorance approach so is quite a large beast ~ about 3MB. If I get lots of requests I will make it downloadable for a short-time.

 

Alternatively I suppose I could do the calculations for every distribution and post them here if people were interested. I think there are only 37 different distributions.

[benlessard]

So it is interesting that these 4441 openers actually have a worse chance of finding a fit than any random sort of hand.

 

Not really surprising, 4441 is so close to 4432 that its only getting an edge over the 4333 but it lose vs all the hand with 5 or 6 card suit.

[effervesce]

Nice calculation, but the in-quick out-quick nature of the mini-roman seems to make bidding decisions easier. Surely the bidding is greatly simplified for the 4414 hand with the 2D bid than having to open it as a nebulous 1C.

[rbforster]

Bring on the 2D openings which show 44 in the majors. Who says they are destructive?

All the cool kids know that 2♥ showing 44 in the majors is a better alternative :).

[han]

It's fun to see the numbers but I'm not sure if it adds something that we didn't already know. For example, we can all understand that the expected fit of a 4441 hand is a bit smaller than the expected fit of a 5431 hand and a bit larger than the expected fit of a 4432 hand. Also, I'm not sure if these numbers are really wildly different. If these are wildly different then I'd like to see the 4432 numbers to see if those are really not substantially worse.

 

The comment about mini-roman I don't get. For one thing, mini-roman is not only preemptive. For another, it maybe easier to get to your best fit at a low level after a mini-roman opening than after [insert favorite opening]. Or maybe partner can punish the opponents more easily after a mini-roman opening than after a weak 2. Or maybe it helps the rest of the system. It seems to me that there are so many factors that just these numbers do not validate anything.

 

BTW, Adam, didn't you post all these tables some years ago?

[Cascade]

           7           8           9           10          11          12          13          mean
4333  0.236016571 0.507602745 0.209421136 0.042103699 0.004605499 0.000245627 4.72359E-06 8.072434586
4432  0.208984611 0.501038957 0.232459375 0.051100329 0.00606     0.000349484 7.24439E-06 8.14528958
4441  0.169251734 0.490998116 0.267767366 0.063579522 0.007918909 0.000474227 1.01253E-05 8.251378939
5332  0.175228866 0.47995028  0.263107892 0.070383701 0.010519293 0.000788103 2.1865E-05  8.263466042
5422  0.155147423 0.469537256 0.283137927 0.079287379 0.01197367  0.000891959 2.43858E-05 8.326176038
5431  0.141903131 0.466521299 0.295489276 0.082770624 0.012378078 0.000912846 2.47459E-05 8.360036742
5440  0.107330368 0.448667954 0.332324662 0.096277225 0.014331093 0.001041031 2.76669E-05 8.46484448
5521  0.105323657 0.42785749  0.336568867 0.110463056 0.018289721 0.001455322 4.18874E-05 8.513071209
5530  0.089974366 0.421148495 0.353500078 0.115066765 0.018788359 0.00147965  4.22875E-05 8.556154354
6322  0.098149665 0.403730788 0.335226239 0.131712873 0.028129477 0.002938848 0.00011211  8.59720669
6331  0.08976448  0.398450673 0.345066135 0.135112738 0.028533769 0.002959735 0.00011247  8.623529724
6421  0.079465753 0.384840501 0.358893763 0.143635093 0.029986307 0.003063592 0.000114991 8.669486437
6430  0.067880069 0.376744625 0.373529828 0.148157339 0.030484829 0.003087919 0.000115391 8.706347555
6511  0.05392319  0.339572317 0.393382435 0.173076977 0.036285643 0.003626947 0.000132492 8.809640376
6520  0.050364349 0.33706611  0.398227287 0.174199461 0.036379872 0.003630388 0.000132532 8.820585691
6610  0.025767807 0.257246606 0.424831646 0.231849152 0.054279778 0.005801875 0.000223137 9.04992466
7222  0.03159034  0.268097167 0.384284779 0.233593147 0.071638996 0.010269475 0.000526097 9.078506103
7321  0.028887423 0.261990008 0.389585244 0.236678863 0.072041644 0.010290361 0.000526457 9.093974208
7330  0.024670697 0.253040286 0.398087648 0.240821402 0.07253842  0.010314689 0.000526857 9.116568057
7411  0.02338023  0.24424495  0.400366622 0.247180537 0.073883225 0.010415098 0.000529338 9.137304222
7420  0.021835706 0.24142868  0.403572984 0.248237359 0.073977353 0.010418539 0.000529378 9.144465102
7510  0.014808123 0.206312206 0.413957628 0.273208055 0.08018535  0.010981759 0.000546879 9.232783099
7600  0.007069414 0.149895481 0.410669576 0.320803925 0.09776882  0.01315526  0.000637524 9.394323129
8221  0           0.102739261 0.345222761 0.355767845 0.1617374   0.032297319 0.002235414 9.682336998
8311  0           0.099432283 0.345830661 0.358054404 0.162128678 0.032318199 0.002235775 9.688777173
8320  0           0.097649536 0.346677692 0.358893851 0.162221466 0.03232164  0.002235815 9.691595426
8410  0           0.089271006 0.345795064 0.366262883 0.163986102 0.03244625  0.002238695 9.711257613
8500  0           0.072909173 0.338471299 0.383428376 0.169923363 0.033011552 0.002256237 9.758425532
9211  0           0           0.18031333  0.412207322 0.308374727 0.090411664 0.008692957 10.3349636
9220  0           0           0.17982791  0.412604834 0.308459159 0.0904151   0.008692997 10.33554044
9310  0           0           0.178522951 0.41354676  0.30880106  0.090435872 0.008693357 10.33722992
9400  0           0           0.173749808 0.416613061 0.310378154 0.0905627   0.008696278 10.34384258
10111 0           0           0           0.28444445  0.462353428 0.221907659 0.031294462 11.00005213
10210 0           0           0           0.284386888 0.462407604 0.221911006 0.031294502 11.00011312
10300 0           0           0           0.284106927 0.462663972 0.221934199 0.031294902 11.00041708
11110 0           0           0           0           0.43859556  0.456141275 0.105263165 11.6666676
11200 0           0           0           0           0.438592853 0.456143942 0.105263205 11.66667035
12100 0           0           0           0           0           0.666666663 0.333333337 12.33333334
13000 0           0           0           0           0           0           1           13

 

Sorry it might be a bit hard to read on some screen resolutions. You should be able to cut and paste into a text editor.

[helene_t]

The comment about mini-roman I don't get. For one thing, mini-roman is not only preemptive. For another, it maybe easier to get to your best fit at a low level after a mini-roman opening than after [insert favorite opening].

There was an article in BW some three years ago about the "Jammer" 2m openings. http://forums.bridgebase.com/index.php?showtopic=8751 It was an interesting approach, computing for a number of alternative 2m openings the probability of finding a lawful partscore. In principle the same computations could be carried out for 1-level openings.

 

Still not the ultimate verdict of the usefulness of a convention, but closer.

[CSGibson]

My question is whether a mini-roman hand comes up frequently enough to be worth sacrificing my Flannery 2♦.

 

In all seriousness, this seems similar to the posting that Ben did a while ago on Flannery. I'm sure that mini-roman is a great tool to have when it comes up, and it allows a great exploration of the hand, because any bid that precisely defines your hand should give you an advantage. Whether it's worth giving up the other possible uses of 2♦ is the real question.

[rogerclee]

In all seriousness, this seems similar to the posting that Ben did a while ago on Flannery. I'm sure that mini-roman is a great tool to have when it comes up, and it allows a great exploration of the hand, because any bid that precisely defines your hand should give you an advantage. Whether it's worth giving up the other possible uses of 2♦ is the real question.

Not really. 2♦ mini-roman is horrible even when it does come up.

[PassedOut]

Not really. 2♦ mini-roman is horrible even when it does come up.

I have two partners who love mini-roman 2♦, and I think it is one of the worst conventions ever devised.

 

Sometimes you don't know whether your hand is worth a game try until it is too late. And with a weak or moderate 5332 responding hand, you risk playing in a 4-3 fit instead of your 5-4 fit.

 

This problem goes away if the singleton is known, of course, as with the Precision 2♦, but then the opening does not occur very often.

[zasanya]

Not really. 2♦ mini-roman is horrible even when it does come up.

I have two partners who love mini-roman 2♦, and I think it is one of the worst conventions ever devised.

 

Sometimes you don't know whether your hand is worth a game try until it is too late. And with a weak or moderate 5332 responding hand, you risk playing in a 4-3 fit instead of your 5-4 fit.

 

This problem goes away if the singleton is known, of course, as with the Precision 2♦, but then the opening does not occur very often.

Look up 'The Viking Precision Club' book by Glenn Groetheim and Alan Sontag.You may change your opinion."The opening has proven to be a very effective preventive bid" opines Glenn.

[benlessard]

The problem i have with 4441 hand is that when it lead to 7 card fit you are ruffing with the wrong hand.

 

A thing im curious is

3451 (12-14) vs 4324 (12-14)

 

I think the number of times 4H is making but 4S goes down is ridiculously low. My guess is that the difference between the wrong moysian and the right moysian is slightly under half a trick. Its a far guess so i can be wrong by a lot.

[kenrexford]

Not directly on point, but...

 

2♦ as Mini-Roman. To preserve the ability to play in 2M, you use 2NT to ask for the shortness. Even submarine (critical -- one under stiff) leaves you without knowledge of strength, just shape.

 

2♣ as Mini-Roman (the original Roman bid with weak hands). Same treatment was used (2NT asking). Dumb, IMO. Contrast with my structure over 2♣:

 

2♦ = asks for shape and strength. With a maximum, answer one below stiff (2NT for 4441, 3♣ 4414, 3♦ 4144, 3♥ 1444). With a minimum, bid 2♠ is 4144 or 2♥ with hearts and any other stiff. After 2♥, Responder can scramble or 3♦ demanding stiff (steps thru 3NT).

 

2NT = natural (minor-oriented)

 

3♣ = pass-or-correct

 

2M = pass-or-correct

 

3♦+ = special

 

Note also that you can compound this even further, allowing, for example, a 2♣ "Mini-Roman" with some very strong hands, where you skip-correct or respond 3♠/3NT to 2♦.