Simulation Question

[awm]

I'd like to ask if someone with access to a double dummy solver and dealer program could run the following simulation.

 

Opener has 5♠-4♥-2♦-2♣ and 12-13 hcp.

 

Responder has 2♠-3♥-4♦-4♣ and 10-11 hcp.

 

What is the frequency (double dummy) of making various numbers of tricks in each of:

 

(1) The 5-2 spade fit

(2) The 4-3 heart fit

(3) Notrump

 

Thanks in advance.

[fromageGB]

Good question. My instinct is that the best contract is spades (in terms of the score obtained), then NT then hearts, in that sequence.

[awm]

The best contract obviously depends on level as well as strain. My guess for partials would be:

 

1♠ > 1♥ > 1NT > 2♠ > 2♥ > 2NT > 3♠ > 3♥

 

Game is probably bad but it wouldn't surprise me if 3NT outscored three of a major at IMPs.

 

In any case, I'm having this long argument with Dan Romm (see other thread) and I'd like to inject some actual facts into the discussion. He claims that 3♥ will outscore 2NT consistently on these hand types and I don't believe him.

[TimG]

Frequency Tricks at notrump:
Low            1
   5          3
   6         28
   7        133
   8        202
   9        112
  10         21
  11          0
  12          0
  13          0
Frequency Tricks at spades:
   5          0
   6         10
   7         74
   8        192
   9        173
  10         48
  11          3
  12          0
  13          0
Frequency Tricks at hearts:
   5          1
   6         10
   7         78
   8        184
   9        176
  10         48
  11          3
  12          0
  13          0
Average tricks at NT: 7.904
Average tricks at spades: 8.368
Average tricks at hearts: 8.36

Generated 66691533 hands
Produced 500 hands
Initial random seed 1254176028
Time needed 880.00 sec
_____________________________________________________
# south 5=4=2=2 12-13 HCP
# north 2=3=4=4 10-11 HCP
# Compare tricks in NT, Spades and Hearts

# South (opener)

 s_shape = shape(south, 5422)
 s_hcp = hcp(south)==12 || hcp(south)==13
 s_ok = s_shape && s_hcp
 
# North (repsonder)

 n_shape = shape(north, 2344)
 n_hcp = hcp(north)==10 || hcp(north)==11
 n_ok = n_shape && n_hcp

# double dummy results
 
 th=tricks(south,hearts)
 ts=tricks(south,spades)
 tn=tricks(south,notrump)
   
# Condition
     
 match = s_ok && n_ok
 condition match

 generate 100000000
 produce 500

# Output  
 
 action
   frequency "Tricks at notrump"(tn, 5, 13),
   frequency "Tricks at spades"(ts, 5, 13),
   frequency "Tricks at hearts"(th, 5, 13),
   average "Average tricks at NT"(tn),
   average "Average tricks at spades"(ts),
   average "Average tricks at hearts"(th),

[awm]

Thanks Tim. This data indicates roughly what I expected. It seems that:

 

(1) Hearts and spades are roughly equivalent strains.

(2) At IMP scoring, 2M > 2NT > 3M.

(3) At MP scoring, you want to play in notrump.

[jdonn]

(3) At MP scoring, you want to play in notrump.

I agree with you on 1 and 2, but on 3 I fail to see how you reach that conclusion from the results Tim presented. Is it that notrump and suits both average around 8 tricks, and that many tricks score better at notrump? But the suits also average nearly half a trick more than notrump, which is huge. There is also the giant problem that you don't know how strong the correlation is between hands that do well in notrump and well in a suit, or vice versa. I think your conclusion is hovering somewhere between unsupported and completely wrong.

[awm]

There are several things leading to my MP conclusion; they are not based on the average number of tricks but rather the charts Tim generated. Two things:

 

(1) If the number of tricks were independent from the distributions given, notrump would win.

(2) If we assume maximum correlation in that the hands which make the most tricks in the trump contract also make the most tricks in notrump, then notrump wins.

 

The reality is somewhere in between. Of course, we could have Tim figure out which is better at MP on a hand by hand basis, but I'll bet notrump wins more than it loses.

[nigel_k]

Based on a sample of 5852 hands and assuming the 5422 hand is declarer in spades or hearts and the 2344 hand is declarer in NT, I get the following percentage chances of making each contract:

 

1H 97.64

1S 97.47

1N 93.68

2H 82.57

2S 82.38

2N 69.51

3H 45.27

3S 44.84

3N 28.52

4S 11.12

4H 11.06

 

The expected tricks as a % are:

 

Notrump

4 0.05

5 0.65

6 5.62

7 24.16

8 40.99

9 22.76

10 5.52

11 0.22

12 0.02

 

Spades

5 0.14

6 2.39

7 15.09

8 37.54

9 33.71

10 10.51

11 0.60

12 0.02

 

Hearts

5 0.26

6 2.10

7 15.07

8 37.30

9 34.21

10 9.98

11 1.03

12 0.05

 

An overall average of 7.970 tricks in NT, 8.363 in spades and 8.374 in hearts.

 

If you have a teams match where one side always plays 2NT and the other always plays 3H, the side playing 2NT will average a gain of 1.28 IMPS per board which is a lot on a partscore hand.

 

At pairs it is closer though. The percentage of each denomination being the highest scoring is:

 

NT 44.69

S 42.02

H 42.26

 

It adds up to more than 100% because hearts and spades may tie or they all make an equal number of undertricks. This does assume you always stop at a makeable level though. The real best denomination will probably be the lowest one your system enables you to actually play in.

 

The usual caveats abut double dummy analysis apply. Declarer'a advantage is greater in NT than in a suit. I suspect DD favours a 4-3 over a 5-2 as well because you can draw trumps when they break and not when they don't.

 

The following is the raw data. The columns are:

#tricks in NT

#tricks in spades

#tricks in hearts

#frequency

 

So you can load this into a spreadsheet and play with it if you want.

 

8,8,8,595

8,9,9,590

7,8,8,494

9,9,9,426

8,9,8,264

8,8,9,242

7,7,7,195

9,10,10,152

8,7,8,151

9,8,9,147

7,8,7,144

9,9,8,137

7,9,9,136

9,8,8,131

8,7,7,130

8,8,7,121

10,10,10,116

7,7,8,115

7,8,9,110

9,10,9,110

6,8,8,93

8,9,10,87

6,7,7,85

9,9,10,83

7,9,8,74

8,10,10,59

8,10,9,51

10,10,9,50

10,9,9,47

7,6,7,36

6,8,7,32

6,7,8,29

9,7,8,28

7,7,6,26

10,9,10,26

9,7,7,22

9,8,7,22

8,6,7,21

7,9,10,20

9,10,11,19

10,9,8,18

7,6,6,17

5,7,7,16

6,7,6,16

6,9,9,16

8,10,11,16

9,7,9,16

6,6,6,13

8,7,6,13

6,8,9,12

8,9,7,12

10,8,9,12

6,6,7,10

6,9,8,10

8,6,6,10

9,9,7,10

8,7,9,9

10,10,11,9

7,10,9,8

9,11,10,8

10,8,8,8

7,9,7,7

7,10,10,7

8,6,8,7

7,7,9,6

10,11,10,6

5,6,6,5

5,8,7,5

7,8,6,5

8,8,10,5

8,10,8,5

10,10,8,5

10,11,11,5

7,8,10,4

8,8,6,4

10,7,9,4

11,11,11,4

5,7,6,3

6,7,5,3

9,6,7,3

9,6,8,3

9,9,11,3

9,11,11,3

10,7,8,3

10,8,10,3

11,10,10,3

5,6,5,2

5,7,8,2

5,8,8,2

6,6,5,2

6,6,8,2

6,8,6,2

7,5,7,2

7,6,8,2

7,7,5,2

7,10,8,2

9,7,6,2

10,7,7,2

10,8,7,2

10,11,9,2

10,11,12,2

11,9,9,2

11,11,10,2

4,6,5,1

4,7,7,1

4,7,8,1

5,5,5,1

5,8,6,1

5,9,10,1

6,5,5,1

6,7,9,1

6,9,7,1

6,9,10,1

7,5,6,1

7,6,5,1

8,5,6,1

8,5,7,1

8,6,5,1

8,6,9,1

8,7,5,1

8,9,11,1

8,11,9,1

9,5,6,1

9,6,6,1

9,7,10,1

9,8,6,1

9,10,7,1

9,10,8,1

9,11,9,1

10,6,6,1

10,6,8,1

10,9,7,1

11,11,9,1

11,12,12,1

12,10,9,1

[jdonn]

Of course, we could have Tim figure out which is better at MP on a hand by hand basis, but I'll bet notrump wins more than it loses.

Maybe, but what happened to interjecting actual facts into the discussion? :) You just backed up your conclusion with three statements. The first started with "if", the second started with "if", and the third ended with "I'll bet".

 

One more factor against notrump at matchpoints. It clearly goes down more often than the suit does. Going down when the suit contract makes creates a wide range between the scores into which other scores may fall. In other words, 140 vs 120 or 120 vs 110 is a win vs that pair. But -100 vs 110 is not only a loss vs that pair, but vs all the pairs that scored +50 or +100. Those pairs aren't relevant when both contracts make.

 

Oddly, I think it also works against notrump that notrump makes game more often than the suit does. This is because there may be some pairs stretching to bid game on their balanced hands totalling 24, and those pairs will definitely be in notrump. So you are in 2NT and make 9 or more tricks, you (let's say) beat the pair in the suit but lose to the pair that bid game. The same consideration doesn't hold if the suit makes game because there is probably no one in a suit game, so it only holds to the extent that tricks in notrump and the suit contract are positively correlated, which must be < 100%.

 

What my last two points mean to me is that the winning cases for notrump are worse than the winning cases for suits, and also the losing cases for notrump are worse than the losing cases for suits. However, according to Nigel's numbers, notrump beats the suit more often than the suit beats notrump. So combining all that, it's entirely possible notrump is better at BAM scoring (it beats the suit contract more often than not) yet worse at matchpoint scoring (it is prone to being beaten by other pairs more often than the suit contract is).

 

All in all it seems very close to me. I don't think a reasonable conclusion can be drawn based on what we have seen.

[awm]

Nigel's stats need to be read carefully.

 

The issue is that there are a fairly large number of ties between spades and hearts. This causes some double-counting when you compare all three contracts to determine winners.

 

Suppose that we try to compare just spades versus notrump (ignoring hearts completely). We have:

 

Spades makes more tricks 2749 times

Notrump makes more tricks 918 times

Same number of tricks, and at least 7 tricks 2157 times

Same number of tricks, and less than 7 tricks 28 times

 

Thus at MP, notrump wins 3075 times to spades winning 2749 times and a push 28 times.

 

This is 52.54% to 46.97% in favor of notrump, which is not insignificant.

[TimG]

the 2344 hand is declarer in NT

Making responder declarer in my sample made little difference:

Frequency Tricks at notrump (responder):
Low            2
   5          2
   6         28
   7        132
   8        195
   9        118
  10         23
  11          0
  12          0
  13          0

Average tricks at NT (responder): 7.924

Frequency Tricks in Spades (6-11) v Tricks in NT (4-10):
       Low      4      5      6      7      8      9     10   High    Sum
Low      0      0      0      0      0      0      0      0      0      0
  6      0      1      0      1      2      3      3      0      0     10
  7      0      1      1     14     26     23      8      1      0     74
  8      0      0      1     13     78     78     21      1      0    192
  9      0      0      0      0     25     83     55     10      0    173
 10      0      0      0      0      1      8     31      8      0     48
 11      0      0      0      0      0      0      0      3      0      3
High     0      0      0      0      0      0      0      0      0      0
Sum      0      2      2     28    132    195    118     23      0    500

[nigel_k]

Spades makes more tricks 2749 times

Notrump makes more tricks 918 times

Same number of tricks, and at least 7 tricks 2157 times

Same number of tricks, and less than 7 tricks 28 times

 

Thus at MP, notrump wins 3075 times to spades winning 2749 times and a push 28 times.

 

This is 52.54% to 46.97% in favor of notrump, which is not insignificant.

How you use the analysis depends on the real-life problem you are trying to solve. The 'at least 7 tricks' condition assumes the decision is whether to play 1NT or 2S, but this requires a system where you can discover the lack of an eight card fit and less than game values without going past 1NT.

 

If the decision is whether to play 2NT or 2S, then:

 

Spades makes more tricks 2749 times

Notrump makes more tricks 918 times

Same number of tricks, and at least 8 tricks 1813 times

Same number of tricks, and less than 8 tricks 372 times

 

Notrump wins 2731 times to spades winning 2749 times and a push 372 times.

 

The advantage of 2S is that you have a plus more often which has many more ways to gain as jdonn pointed out. 20% of the sample makes 2S and not 2NT. However a big advantage of NT at matchpoints is that you go with the field. This kind of hand will swing tricks in the play and i expect the field to mostly bid 2NT over 2H. So I would be concerned about taking a view to go against them.

[jdonn]

Nigel's stats need to be read carefully.

 

The issue is that there are a fairly large number of ties between spades and hearts. This causes some double-counting when you compare all three contracts to determine winners.

 

Suppose that we try to compare just spades versus notrump (ignoring hearts completely). We have:

 

Spades makes more tricks 2749 times

Notrump makes more tricks 918 times

Same number of tricks, and at least 7 tricks 2157 times

Same number of tricks, and less than 7 tricks 28 times

 

Thus at MP, notrump wins 3075 times to spades winning 2749 times and a push 28 times.

 

This is 52.54% to 46.97% in favor of notrump, which is not insignificant.

At least 7 and fewer than 7?? You are stopping in 1♠ or 1NT???

 

According to the last post, spades wins very slightly (essentially a tie). I think that makes it the winner based on the factors I have already mentioned.

[fromageGB]

Very interesting. What really surprised me, borne out by both analyses, is that hearts is just as good as spades. A 4-3 fit with a singleton in the short hand - yes, I would anticipate that. But with only a doubleton ! I suppose the big benefit is that by ruffing just once you are setting up a couple of tricks in the other hand. Nigel's double dummy comment may come into play here.

[goodwintr]

Richard Pavlicek has some relevant material (in fact, lots of relevant material) at rpbridge.com. (Look under "matches.") He is looking at real deals, not simulations. And he is concerned exclusively with IMPs, not matchpoints. I haven't looked at this in detail, but it seems from a quick once-over that when the contest is between 1NT and two of a suit, and between 3NT and four of a major, the odds favor the suit contract if there is a real fit, and notrump if there is only a seven-card fit. But you can look at the details yourself. (Warning: small sample size. This is always a problem with at-the-table statistical analysis.)

[benlessard]

ATB 43 fits are a lot tougher for declarer to play than 52 fit. The DD knows the bad H/S break so he will pull exactly the good number of trumps.

 

Also this exact hand shapes only allow for S and H to develop. So unless you have really bad trumps and good S, Hearts will rarely make less tricks than 2Nt.

 

But for a 4432 VS 3244. At NT you can setup tricks everywhere. Here NT might easily score better (Imps) than 2S in Moys.

 

My Nt structure allow me to play often in 43 fits at 2M and often its very difficult to make the correct decision between 2M and 2NT.

 

In all case its a very interesting thread.