Can anybody calculate this?

[gwnn]

Many of those 13 tricks I think are 3NT+4 where defenders would have beaten 7NT but didn't care about overtricks, or just fell asleep/gave up/whatever, during the play of the 3NT.

[Mr. Dodgy]

yeah, but that should be adequately compensated for by the fact that that it myself who is declarer reasonably often in these figures and should probably make 13 tricks far more often than I do :)

[ArcLight]

I can't believe that grand slams are as frequent as 2%

 

It might change the defense if the defenders are defending 7 instead of 6.

 

You would lead an ace against 7, you might not against 6.

In a 7 level contract you might be forced to take a certain line, where in 6 you would take another, guaranteeing the contract for the certain loss of 1 trick.

 

 

As for 33 HCP slams, those are not that common in my experience, usually shape contributes some points.

 

 

 

>I guess my (anecdotal) experience is that there are a fair number of boards where I don't bid slam and slam is lousy looking at my hand and partner's, but things lie very favorably and slam ends up making. It feels like there are probably more of these than hands where slam is actually good in fact! But these are basically "unbiddable" slams because if you bid them you will also end up bidding a much larger number of slams which are equally lousy and where the cards don't like favorably...

 

I agree.

You make 6 or 7 because of working jacks and 3-3 splits, adn 2 finesses being right.

Pard made 12 on 3NT becaus eopps lead a suit other than Diamonds allowing a finesse, and then later a squeeze. No way to bid that

[barmar]

But generally I agree with you. Sometimes you have a double fit and only one of the two denominations makes game, sometimes game needs to be rightsided, sometimes 3NT is the only game with a 8- or 9-card major fit etc. All this makes for a lot of DD games that would never be bid in practice.

Don't forget all the contracts that require dropping a singleton king or taking a deep finesse that would never be found in practice.

 

There are some cancellations, though. DD won't bid 75% contracts that require either of 2 finesses, but they're both off, while it *will* bid 25% contracts when both finesses are on.

[Finch]

It seems pretty obvious (to me, anyway) that the % of DD slams will be much higher than the % of hands on which you want to be in slam.

 

There's a basic asymmetry

 

It's very common to be able to make 2 or 3 overtricks in game, EVEN ON BEST DEFENCE, but not want to be in slam.

 

It's much less common to find a hand where you want to be in slam single dummy but it is off double dummy.

 

The "10%" figure feels roughly right on my empirical experience, although if anything very slightly too low.

[BebopKid]

Okay there are 4.95919E+14 unique 26 card layouts for 1 pair. Combination (52,26) I ignored which hand specific high cards were in.

 

I have the percent that between the 2 hands there are a fixed number of HCP.

 

I agree on the concept that HCP aren't the only determinant, but here are the HCP layouts that I came up with.

 

HCP Percent % Cummulative (those HCP or higher)

 

0 0.0000513% 100.0000000%

1 0.0004846% 99.9999487%

2 0.0019990% 99.9994641%

3 0.0063868% 99.9974652%

4 0.0179859% 99.9910784%

5 0.0426910% 99.9730925%

6 0.0927186% 99.9304015%

7 0.1856480% 99.8376830%

8 0.3411376% 99.6520350%

9 0.5877062% 99.3108974%

10 0.9546726% 98.7231912%

11 1.4634633% 97.7685186%

12 2.1239452% 96.3050553%

13 2.9433742% 94.1811101%

14 3.8833877% 91.2377359%

15 4.8918758% 87.3543482%

16 5.9072842% 82.4624724%

17 6.8310913% 76.5551882%

18 7.5662308% 69.7240969%

19 8.0467824% 62.1578661%

20 8.2221673% 54.1110837%

21 8.0467824% 45.8889163%

22 7.5662308% 37.8421339%

23 6.8310913% 30.2759031%

24 5.9072842% 23.4448118%

25 4.8918758% 17.5375276%

26 3.8833877% 12.6456518%

27 2.9433742% 8.7622641%

28 2.1239452% 5.8188899%

29 1.4634633% 3.6949447%

30 0.9546726% 2.2314814%

31 0.5877062% 1.2768088%

32 0.3411376% 0.6891026%

33 0.1856480% 0.3479650%

34 0.0927186% 0.1623170%

35 0.0426910% 0.0695985%

36 0.0179859% 0.0269075%

37 0.0063868% 0.0089216%

38 0.0019990% 0.0025348%

39 0.0004846% 0.0005359%

40 0.0000513% 0.0000513%

 

Algorithm used:

 

I cycled through every possible combination of A's, K's, Q's, and J's using "for" loops. I added their HCP and determined how many cards where left to fill in the other cards. Multiplying the number of combinations of the remaining cards times the number of combinations that could made.

Then add up each of these for all layouts with those HCP's.

 

Ex.

For 9 HCP, using four cards, there are 304 possible combinations.

For the other 22 cards out of 36 with no point value, there are 3796297200 possible combinations.

So for 9 HCP using 4 cards, there are 1.154074E12