[fast lane]

When your partner opens a NT and you do a transfer (♥+♠)

What are the percentages that he has either a 2 or a 3 card support.
Same for 4 or 5 card, though this will be less frequent.

Thx in advance,

fast lane

[TylerE]

Impossible to answer without knowing the rest of your system.

Upgrade good 14s? Good 17s out of one NT?
Open 1NT with 5 card major.... never/sometimes/always?
etc

[helene_t]

Hi Fast Lane, welcome to the forum!

There's a software called "dealer" which you can use to simulate this.

A crude calculation can be done using any standard statistical software, for example the R package (or you can look up the hyper-geometrical distribution on wikipedia and do the calculations on a calculator or spreadsheet):

> dhyper(2:4,8,31,13)/sum(dhyper(2:4,8,31,13))
[1] 0.3783784 0.3963964 0.2252252

This means there's 38% chance of 2-card support, 40% chance of 3-card support and 22% chance of 4-card support.

The assumption is that responder has 5 trumps and 8 non-trumps (the arguments 8, 31 and 13 refer to the number of trumps outside responder's hands, the number of non-trumps outside responder's hand, and the number of card in opener's hand). Opener's cards are randomly selected among the 39 cards not held by responder.

In reality, the fact that opener's hand is bound to be balanced makes the chance that he has a doubleton a bigger, because 4441 and 5431 shapes are excluded. On the other hand, if you also exclude 6322 and 5422 shape (a matter of style), the percentages presented here may be fairly close to realistic.

Also the fact that opponent's didn't bid, and that responder might have more than 5 trumps, make the chance of a doubleton larger.

So probably the chance of a doubleton will be about 50% in practice.

[TylerE]

helene_t, on 2018-July-19, 17:26, said:

So probably the chance of a doubleton will be about 50% in practice.

I don't think that can possibly be right.

Let's say transferer has a 6 card suit. Then the other 3 players have on average 2.3333 cards in the transfer suit. Given that we know opener has at least, we can rule our all the cases where opener as a singleton or void, that can only shift partners expectation higher.

[steve2005]

TylerE, on 2018-July-19, 19:49, said:

I don't think that can possibly be right.

Let's say transferer has a 6 card suit. Then the other 3 players have on average 2.3333 cards in the transfer suit. Given that we know opener has at least, we can rule our all the cases where opener as a singleton or void, that can only shift partners expectation higher.

Yes tyler is correct length of responder matters.
The simulation example assumed responder had 5.
Which is what fast lane was looking for, I think.

[smerriman]

Over 10000 hands where one player has any 5332, 4333, or 4432, and the other has exactly 5 spades, I get:

2 cards: 28.05%
3 cards: 47.83%
4 cards: 20.37%
5 cards: 3.75%

So considerably smaller than Helene's numbers.

[helene_t]

Thanks Smerriman, I suppose the clue is that a balanced hand often has two or three trippletons, and always at least one. While it has either one or zero doubletons. That makes the doubleton less likely then the trippleton.

[pescetom]

smerriman, on 2018-July-19, 20:27, said:

Over 10000 hands where one player has any 5332, 4333, or 4432, and the other has exactly 5 spades, I get:

2 cards: 28.05%
3 cards: 47.83%
4 cards: 20.37%
5 cards: 3.75%

So considerably smaller than Helene's numbers.

I may be wrong but it doesn't seem like I get 4-card super-accepts 24% of the time.
Did your weighting of the probabilities of 5332 vs 4333 vs 4432 take account of the fact that another hand had 5 spades?

[Stephen Tu]

pescetom, on 2018-July-20, 07:18, said:

I may be wrong but it doesn't seem like I get 4-card super-accepts 24% of the time.
Did your weighting of the probabilities of 5332 vs 4333 vs 4432 take account of the fact that another hand had 5 spades?

- Most people aren't super-accepting every time they have 4+ support, only 4+ support AND maximum NT.

I get similar results to smerriman when restricting to balanced hands only. I ran another sim with including semi-balanced 5m422 and some 6m322, to reflect the way I open, and get up to 36.x% doubletons under those conditions.

[ggwhiz]

I am curious as to the reason for the question.

My partnership uses a whole range of super accepts such that a simple 2M response to a xfer is usually 2 or less often, a really sketchy minimum (full of Q's and J's). We don't care about these percentages at first but care greatly about finding out immediately through openers response.

[pescetom]

Stephen Tu, on 2018-July-20, 10:25, said:

- Most people aren't super-accepting every time they have 4+ support, only 4+ support AND maximum NT.

I get similar results to smerriman when restricting to balanced hands only. I ran another sim with including semi-balanced 5m422 and some 6m322, to reflect the way I open, and get up to 36.x% doubletons under those conditions.

Thanks. We do super-accept every time we have 4+ support, differentiating between maximum NT and not.
But my impression of less than 24% is only that, could easily be wrong.

[smerriman]

pescetom, on 2018-July-20, 07:18, said:

I may be wrong but it doesn't seem like I get 4-card super-accepts 24% of the time.
Did your weighting of the probabilities of 5332 vs 4333 vs 4432 take account of the fact that another hand had 5 spades?

Yep - the only thing I didn't take into account were eg responder hands with 54 in the majors that would sometimes bid Stayman instead of transfer.

Note however that this is from responder's perspective when he is transferring with a 5 card suit - from opener's perspective, you will be superaccepting less as partner will sometimes have more than 5.

Though from responder's perspective, you also know your full shape, and eg transferring with 5530 is likely to give different results. So I'm not really sure what the point of any of this is.

[apollo1201]

Stephen Tu, on 2018-July-20, 10:25, said:

I ran another sim with including semi-balanced 5m422 and some 6m322, to reflect the way I open, and get up to 36.x% doubletons under those conditions.

With current NT openings, it could even be interesting to know how often the transfer will face a singleton K or A🤣

[fast lane]

helene_t, on 2018-July-19, 17:26, said:

Hi Fast Lane, welcome to the forum!

There's a software called "dealer" which you can use to simulate this.

A crude calculation can be done using any standard statistical software, for example the R package (or you can look up the hyper-geometrical distribution on wikipedia and do the calculations on a calculator or spreadsheet):

> dhyper(2:4,8,31,13)/sum(dhyper(2:4,8,31,13))
[1] 0.3783784 0.3963964 0.2252252

This means there's 38% chance of 2-card support, 40% chance of 3-card support and 22% chance of 4-card support.

The assumption is that responder has 5 trumps and 8 non-trumps (the arguments 8, 31 and 13 refer to the number of trumps outside responder's hands, the number of non-trumps outside responder's hand, and the number of card in opener's hand). Opener's cards are randomly selected among the 39 cards not held by responder.

In reality, the fact that opener's hand is bound to be balanced makes the chance that he has a doubleton a bigger, because 4441 and 5431 shapes are excluded. On the other hand, if you also exclude 6322 and 5422 shape (a matter of style), the percentages presented here may be fairly close to realistic.

Also the fact that opponent's didn't bid, and that responder might have more than 5 trumps, make the chance of a doubleton larger.

So probably the chance of a doubleton will be about 50% in practice.

Thx all for your input, very enlightening.

[pescetom]

Stephen Tu, on 2018-July-20, 10:25, said:

- Most people aren't super-accepting every time they have 4+ support, only 4+ support AND maximum NT.

I get similar results to smerriman when restricting to balanced hands only. I ran another sim with including semi-balanced 5m422 and some 6m322, to reflect the way I open, and get up to 36.x% doubletons under those conditions.

Re-reading the topic I realise that I missed the significance of your second point.
We too open NT with some semi-balanced 5422 and some 6m322, and if you are getting more % of doubletons then I guess you are getting less % of 4+, which would be consistent with my perception of < 24%.