6NT

We missed a slam the other day.

          S: KJT2
          H: K42
          D: AKQ6
          C: K7


          S: Q95
          H: AQ83
          D: 73
          C: AJ64

The auction would bore you but North showed spades and diamonds with invitational values and South saw there was no fit and that the partnership had fewer than the traditionally required 33 points and so stopped in game. As you can see, though, slam is very good. It requires hearts 3-3 or a club finesse or one of several possible squeezes. Why is it so good? Undoubtedly, that 10 is valuable, but even if you take it away, the slam is still a decent spot.

So I endeavoured to find out. My plan was to delve into the details of what makes these hands worth 12 tricks and try to come up with a better evaluation method for 6NT contracts than pure high-card points. However, I didn't need to — points work fine. Over 2,000 tests where the partnership had 32 combined points, slam made a whopping 69% of the time! Since when did this change? We've always been told that you need 33 points to make 6NT and I've never heard anyone say anything to the contrary. Or is this common knowledge that all experts use but which has mysteriously remained a gap in my bridge learning? Post a comment calling me a naïve idiot if you like.

And don't give me any crap about double-dummy results being completely different from real life. I don't buy it. Yes, our solver will pick up any two-way guesses for a Queen or know which squeeze to play for, but in the real world the defence might underlead a Queen at trick one, obviating a guess, or they might have trouble knowing which four-card suit to discard from. And besides, I'm not saying that 69% of slams will make — only that 69% of slams are makeable and I for one would be very happy to bid them on this basis.

It doesn't stop there. With 31 points between the hands, over 2,000 deals, almost exactly 50% of them make 6NT. Who here is surprised by this? This means that you can bid slam more freely knowing that, at worst, it will be makeable 50% of the time.

Of course, if you're bidding these slams with lower point counts you're in more danger of having two cashing aces against you. If only there was some kind of convention which can be used to check for aces after a 1NT opening...

More gambling in third seat

Oops, I'm an idiot. When I did the gambling 3NT test before, I was actually giving North (our partner) 9-11 balanced. That was something which interested me too, but I had forgotten to take the condition out when I did the main test. So, as bad as those stats made it look to open a gambling 3NT in third seat, it's actually an awful lot worse! These are correct (hopefully):

Tricks   Num
0        355
1        482
2        680
3       1080
4       1307
5       1324
6       1323
7       1356
8       1554
9        510
10        29
11         0
12         0
13         0

That figure of 11% making 3NT goes down to 5.4%!

The reason I took a second look at the figures is because Steve asked:

What is recommended for a 3rd seat 3NT? I guess we could increase the hand strength until we reach a certain threshold. But what would that threshold be?

So I ran another 10,000 hands, giving South AKQJxxx but with no restriction on the rest of his hand apart from having no five card major. The following stats emerged:

Tricks   Num
 0        77
 1       136
 2       249
 3       398
 4       605
 5       785
 6      1073
 7      1254
 8      1955
 9      1359
10      1054
11       625
12       322
13       108

HCP      +        -        % 
 0       26      442      5.6
 1       34      355      8.7
 2       67      604     10.0
 3      137      805     14.5
 4      289      998     22.5
 5      282      833     25.3
 6      370      741     33.3
 7      478      659     42.0
 8      501      437     53.4
 9      385      309     55.5
10      324      169     65.7
11      262      109     70.6
12      144       37     79.6
13       79       26     75.2
14       56        6     90.3
15       23        1     95.8
16        5        1     83.3
17        4        0    100.0
18        2        0    100.0

Cont     +        -        % 
 0      244     2043     10.7
 1      361     1695     17.6
 2     1032     1720     37.5
 3      837      764     52.3
 4      650      250     72.2
 5      275       56     83.1
 6       55        4     93.2
 7       14        0    100.0

The first table shows the number of times we made a certain number of tricks. It tells us that, with no restriction on side values, we'll make 3NT only 35% of the time.

The second table shows us the number of side HCPs we hold and how often we make 3NT (+) or go off in it (-). This shows that with 0-7 points on the side we're a fair underdog in our contract, with 8-9 it's pretty close and we need 10+ before we're favourite to make. That's a 20 count, folks. HCPs aren't perhaps a very useful measure so the third table breaks it down by controls (A=2, K=1). This says that with 2 controls (an Ace or two Kings) we're unlikely to make 3NT, with 3 controls it's close and with 4 controls we're a solid favourite.

In other words, we need a pretty massive hand before we can hope to actually make 3NT and if we do get this, we're hardly crippling ourselves by opening at the one level, or 2. My advice is to find another use for your 3NT opening entirely. Over 1 million hands, with North and East passing, I found myself holding the following hands:

7 solid clubs with 3 or more controls on the side:   162 *
6-5 in the minors or longer and 0-12 points:         932
6-5 or 7-4 in the minors or longer and 0-12 points: 1382
7+ minor/4 major and 0-12 points:                    892

These are just suggestions but as you can see they are vastly more frequent than a gambling 3NT opening which you can actually expect to make. The 6-5 hand seems quite enticing, especially if you can lower this to 5-5 when non-vulnerable. Just 932 per million amounts to about once every 1000 hands where you're in third seat — maybe once a year if you play a lot. Better than never, anyway.

* Of course, we should double this figure as solid diamond suits count too.

Defence to 3♠, part III

One of the negative points of using 3NT as a takeout double shape is that when partner passes it (with a few values, no long heart suit and a decent spade stopper) you will often wrong-side the contract. The preemptor's partner is now on lead and can play a spade through the stopper at trick one. This could be expensive, but how expensive?

Today's simulation gives East the same hands he held before. South holds a takeout double hand, about 13+ points with spade shortage and some support for the unbid suits. And North holds a decent spade stopper (KJx or better), 0-3 hearts and no 7 card minor.

This isn't the most wonderful bit of modelling in the world ever, but it doesn't matter much. We're comparing the times when we make 3NT as North with the times when we make it as South. A few deals will slip through where 3NT isn't a realistic contract but it's unlikely that which hand plays it makes much of a difference in these cases.

Over 10,000 deals there were 285 occasions where 3NT made by North but not by South and, interestingly, 193 occasions where 3NT made by South but not by North. On the other 95% of boards, 3NT made from both hands or it went off from both hands.

In terms of IMPs, we lose 0.075 IMPs/board by playing from the South hand.

I must admit that I am a little surprised at these findings and had expected something a fair bit higher, but perhaps I shouldn't have. After all, why should partner's stoppers always be positional? Why shouldn't he be able to duck enough rounds to cut off the preemptor anyway? Here's one of the deals we looked at:

          S: AQ4
          H: KT4
          D: QT6
          C: KJ76
 S: 76             S: KJT9853
 H: QJ6            H: 95
 D: K9753          D: J8
 C: 843            C: 52
          S: 2
          H: A8732
          D: A42
          C: AQT9

Obviously the play is much more comfortable when you have two spade stoppers instead of one, but you'll make 3NT easily enough from either hand. East might have one of the red suit guards, of course, but then you can still make it by guessing which. I'm not suggesting that in any way we're happy to play this contract from the South hand rather than the North hand, just that if we do it's not the end of the world.

So there you have it — wrong-siding 3NT contracts when an opponent has preempted is nothing like as costly as you might have thought.

Gambling in third seat

A friend of mine has been playing a Gambling 3NT opening in third seat, thinking it was the same as first or second seat. I commented that the chances of making 3NT opposite a passed hand were pretty slim and you need to have significantly more to take a shot. That was an understatement. Say you hold:

74 84 72 AKQJT63

Partner is a passed hand, RHO is a passed hand. What odds do you give yourself of making 3NT? Over 10,000 deals, we made the following numbers of tricks:

Tricks   Num
 0        17
 1        78
 2       241
 3       573
 4       759
 5      1071
 6      1452
 7      1925
 8      2753
 9      1098
10        33
11         0
12         0
13         0

You'll make your contract a massive 11% of the time. You'll go 5 off or worse almost 17% of the time. In real life you'll do better than this as oppo have a blind lead and if they get it wrong you can often rattle off 9 tricks, but even if we doubled our odds we're still well short of the kind of percentage we need.

If you happen to be playing a third seat 3NT the same as a first seat one then stop. Right now.

Defence to 3♠, part II

There was a small bug in the program I used in the last post. Some people might have noticed that the cross-IMPs didn't quite add up. It was to do with rounding errors but it's fixed now and I ran the whole test again. I also decided that I'd quite like to measure match point results after all, so those are included. Finally, we now have statistics for all four vulnerabilities and you'll see that it makes a substantial difference. I've also quoted some stats as percentages rather than raw numbers and it makes it much easier to read.

          Non-Vulnerable versus Non-Vulnerable

              Cross-IMPs/board     Makes%        MP %
HCP Freq     3NT    3SX    Pass   3SX  3NT  3NT  3SX Pass

0      1  -14.50   4.50   10.00   100    0    0   50  100
1     24  -13.02   3.48    9.54    83    0    2   56   92
2    183  -11.67   3.16    8.51    77    0    4   58   88
3    634  -10.21   2.38    7.83    74    0    8   56   86
4   1605   -8.74   1.61    7.14    74    2   13   53   84
5   2984   -7.82   1.27    6.55    72    4   17   52   81
6   5142   -6.47   0.92    5.56    67    8   23   52   76
7   8054   -5.39   0.70    4.69    63   11   27   52   71
8  11018   -4.50   0.66    3.84    57   15   31   53   66
9  14228   -3.49   0.51    2.99    53   21   35   54   61
10 16816   -2.69   0.42    2.27    50   25   39   54   57
11 19015   -1.90   0.61    1.29    43   31   43   56   51
12 19769   -1.38   0.78    0.60    39   36   45   58   46
13 19917   -0.63   0.82   -0.19    34   42   49   59   42
14 18692   -0.23   1.12   -0.89    30   47   51   62   37
15 16029    0.38   1.38   -1.76    25   53   54   64   32
16 13401    0.63   1.64   -2.27    22   57   55   66   29
17 10503    1.09   1.86   -2.94    18   62   57   67   25
18  7817    1.30   2.26   -3.56    15   66   58   70   22
19  5464    1.65   2.51   -4.17    12   71   60   72   18
20  3741    1.76   2.93   -4.69     9   75   61   74   16
21  2230    2.21   3.21   -5.42     6   81   62   76   12
22  1371    2.15   3.60   -5.74     5   82   61   79   10
23   778    2.31   4.06   -6.38     3   88   63   80    7
24   398    2.11   4.45   -6.56     3   89   62   82    6
25   186    2.31   4.63   -6.95     1   91   63   83    4

            Non-Vulnerable versus Vulnerable

              Cross-IMPs/board     Makes%        MP %
HCP Freq     3NT    3SX    Pass   3SX  3NT  3NT  3SX Pass

0      1  -13.50   3.00   10.50   100    0    0   50  100
1     24  -11.52   1.31   10.21    83    0    2   56   92
2    183   -9.64   0.74    8.90    77    0   10   53   87
3    634   -8.22   0.03    8.19    74    0   15   51   84
4   1605   -6.81  -0.66    7.47    74    2   21   48   81
5   2984   -6.04  -0.80    6.85    72    4   24   48   78
6   5142   -4.91  -0.88    5.80    67    8   29   48   73
7   8054   -4.18  -0.74    4.92    63   11   32   50   68
8  11018   -3.61  -0.43    4.04    57   15   35   52   63
9  14228   -2.94  -0.24    3.18    53   21   38   54   58
10 16816   -2.41  -0.06    2.47    50   25   40   55   54
11 19015   -2.07   0.58    1.49    43   31   42   59   49
12 19769   -1.89   1.08    0.81    39   36   43   63   45
13 19917   -1.49   1.47    0.03    34   42   44   65   40
14 18692   -1.44   2.09   -0.65    30   47   45   69   37
15 16029   -1.24   2.73   -1.50    25   53   46   72   32
16 13401   -1.26   3.25   -1.99    22   57   46   75   29
17 10503   -1.08   3.73   -2.64    18   62   47   78   25
18  7817   -1.19   4.44   -3.25    15   66   47   81   22
19  5464   -1.09   4.92   -3.83    12   71   48   83   19
20  3741   -1.24   5.54   -4.31     9   75   47   86   17
21  2230   -1.10   6.11   -5.01     6   81   49   89   13
22  1371   -1.30   6.61   -5.30     5   82   49   90   11
23   778   -1.38   7.21   -5.83     3   88   48   93    9
24   398   -1.77   7.77   -5.99     3   89   46   94    9
25   186   -1.63   8.01   -6.38     1   91   49   95    6

            Vulnerable versus Non-Vulnerable

              Cross-IMPs/board     Makes%        MP %
HCP Freq     3NT    3SX    Pass   3SX  3NT  3NT  3SX Pass

0      1  -16.50   5.50   11.00   100    0    0   50  100
1     24  -14.96   4.54   10.42    83    0    0   58   92
2    183  -13.80   4.37    9.43    77    0    1   61   88
3    634  -12.66   3.78    8.88    74    0    3   61   86
4   1605  -11.31   3.08    8.22    74    2    6   59   85
5   2984  -10.32   2.69    7.63    72    4    9   58   82
6   5142   -8.80   2.23    6.57    67    8   15   58   78
7   8054   -7.52   1.89    5.62    63   11   19   58   73
8  11018   -6.33   1.68    4.65    57   15   24   58   68
9  14228   -5.02   1.35    3.67    53   21   29   57   63
10 16816   -3.92   1.08    2.83    50   25   34   57   59
11 19015   -2.66   1.00    1.66    43   31   40   58   53
12 19769   -1.81   0.98    0.83    39   36   44   58   48
13 19917   -0.68   0.81   -0.13    34   42   48   58   43
14 18692    0.08   0.90   -0.98    30   47   52   59   39
15 16029    1.15   0.90   -2.05    25   53   57   59   34
16 13401    1.66   1.02   -2.68    22   57   59   60   30
17 10503    2.44   1.05   -3.49    18   62   63   61   26
18  7817    3.01   1.24   -4.25    15   66   66   62   23
19  5464    3.66   1.33   -4.99    12   71   69   62   19
20  3741    4.01   1.61   -5.62     9   75   70   63   16
21  2230    4.88   1.66   -6.54     6   81   75   63   12
22  1371    4.95   1.96   -6.91     5   82   75   65   10
23   778    5.40   2.28   -7.68     3   88   77   65    7
24   398    5.32   2.60   -7.92     3   89   78   65    7
25   186    5.70   2.69   -8.39     1   91   79   67    4 

              Vulnerable versus Vulnerable

              Cross-IMPs/board     Makes%        MP %
HCP Freq     3NT    3SX    Pass   3SX  3NT  3NT  3SX Pass

0      1  -15.00   3.50   11.50   100    0    0   50  100
1     24  -13.92   2.88   11.04    83    0    0   58   92
2    183  -12.47   2.52    9.96    77    0    2   60   88
3    634  -11.31   1.96    9.35    74    0    5   59   86
4   1605   -9.89   1.20    8.69    74    2   10   56   85
5   2984   -9.00   0.96    8.04    72    4   13   55   82
6   5142   -7.60   0.68    6.92    67    8   19   54   77
7   8054   -6.57   0.63    5.93    63   11   23   55   72
8  11018   -5.62   0.72    4.90    57   15   27   56   67
9  14228   -4.58   0.69    3.89    53   21   31   56   63
10 16816   -3.69   0.66    3.03    50   25   35   56   58
11 19015   -2.82   1.00    1.82    43   31   39   58   52
12 19769   -2.27   1.30    0.97    39   36   42   60   48
13 19917   -1.43   1.44   -0.01    34   42   46   61   43
14 18692   -1.00   1.86   -0.87    30   47   48   64   39
15 16029   -0.30   2.24   -1.94    25   53   51   66   33
16 13401   -0.03   2.61   -2.58    22   57   53   67   30
17 10503    0.50   2.89   -3.39    18   62   55   69   26
18  7817    0.74   3.43   -4.17    15   66   56   72   22
19  5464    1.15   3.75   -4.90    12   71   58   73   19
20  3741    1.25   4.26   -5.51     9   75   59   75   16
21  2230    1.80   4.63   -6.43     6   81   61   77   12
22  1371    1.68   5.10   -6.77     5   82   60   80   10
23   778    1.89   5.59   -7.47     3   88   62   81    7
24   398    1.58   6.11   -7.69     3   89   60   83    7
25   186    1.88   6.27   -8.15     1   91   62   84    4

Note the big difference when we're vulnerable and oppo aren't. It's now only a plus to double them in that narrow 12-14 point range — stronger hands do better to play in 3NT.

Defence to 3♠, part I

Ok, this is perhaps a crazy idea but let's see if we can prove it so using simulations.

Imagine your right-hand opponent opening a preemptive 3. Normal stuff, both sides are vulnerable. You can expect a 7 card suit and, say, 3-9 points with Qxxxxxx as a minimum suit quality. Not insane, but fairly aggressive.

Currently your methods are very likely to be that you double for takeout and overcall 3NT with a balancedish hand with a stop, say 16-22 points or thereabouts. What I want to find out is if there is any value in swapping these meanings about. That is, double with a balanced hand and bid 3NT with a takeout double shape. I told you it was crazy!

Possible advantages of doing it this way:

1. We catch oppo in a penalty more often.
2. We can be less worried about the wide range of our 3NT overcall — there's less need to stretch to invite a slam because if we can make 6NT we have a good chance of 1100 from 3X.
3. If partner bids 3NT anyway then it's often being played from the right side e.g. if he has Qx opposite your Ax.
4. We can act with weaker hands than we might have acted with before (see below).

Disadvantages:

1. Partner can't convert a takeout double to penalties (but sitting under the preemptor, remember).
2. You can't double and bid a new suit with a very strong hand because partner might pass 3NT. You'll have to add some more system to handle those hands.
3. If partner passes your 'takeout' 3NT then the contract will probably be wrong-sided.

You might look at these lists and decide that the disadvantages suck horribly and the advantages, while useful, aren't a major incentive. And, heck, you're probably right. But I think it would be interesting to look into it some more. So let's get simulatin'.

Modelling The Hands

East has 7 spades, 3-9 HCP, 5.5 losers or worse, 2+ HCP in spades, less than 4 hearts. Nothing too controversial there, I hope.

South has a balanced hand with less than 26 HCP, his spade length + spade HCP is 5 or more i.e. Ax, Kx, Qxx, Jxxx or xxxxx (remember, we're balanced).

West has less than four spades and less than seven hearts. He's undefined other than that. The reason he has less than four spades is because with four spades he'd almost always bid 4 over whatever we do so our choice will be irrelevant. We restricted his hearts too to make sure oppo don't miss many biddable heart games and skew the results.

North has a six loser hand or worse. With better, he'd be pushing on towards slam or a suit game contract. He also has less than six hearts and no seven card minor either (with six hearts we'd usually play in 4 rather than try for a penalty or declare 3NT). Finally, our combined HCP is 32 or less. This is so that we don't miss too many slams and thereby unfairly hinder the results of the people playing in 3NT.

Here's a hand that this produces:

          S: KJ5
          H: K752
          D: A752
          C: K8
 S: T              S: Q976432
 H: QJ8            H: A64
 D: KQJ86          D: ---
 C: 6532           C: JT4
          S: A8
          H: T93
          D: T943
          C: AQ97

Yeah, I know South has a 10 count! We'll be doing experiments over the full range of strengths. Hopefully we'll prove that passing is right with a balanced 10 count, but who knows? On this hand 3NT makes 9 tricks. However, 3X goes off 3 for +800. Here's another one:

          S: JT
          H: T653
          D: A74
          C: J943
 S: 82             S: Q976543
 H: Q8             H: A7
 D: QJT6           D: 852
 C: A7652          C: T
          S: AK
          H: KJ942
          D: K93
          C: KQ8

19 points this time. Here, 3NT makes 9 tricks again (double-dummy, you get the hearts right). 3X is only off one trick, though and your +200 is crap compensation for your missed +600. One more hand as a tie-breaker:

          S: T
          H: K73
          D: AQ8765
          C: KJ5
 S: ---            S: A876532
 H: AJT652         H: 9
 D: J94            D: KT
 C: Q974           C: T83
          S: KQJ94
          H: Q84
          D: 32
          C: A62

These are random, I promise! This is obviously a rather unlikely layout, though. 3NT here makes 10 tricks but 3X doesn't fare too well and gets whacked for +1100.

On that last example, we'd probably extract our pound of flesh anyway by passing and seeing partner reopen. Fair enough. I haven't thought about protective auctions in the slightest — for now all I'm looking at is how 3NT fares in comparison to 3X.

Running a Tournament

What we're going to do is run a tournament. We have three pairs with three different strategies for handling balanced hands over an opposing 3 opening.

Pair 3NT always overcall 3NT. Their partner never pulls because he never gets dealt the sort of hands where he would want to pull. Sometimes he'll think about pulling if he's doubled when he holds a six card minor, but he'll always decide to stick it out. West has great judgement. If 3NT is going three off he'll always double it. If it's going exactly two off then he's not quite so sure and he'll double it half the time.

Pair X always doubles to show a balanced hand. West doesn't ever get greedy by redoubling and partner always leaves it in.

Pair P always pass, regardless of their hand. Their partner passes too. West, with his renowned judgement, will always bid 4 if it's makeable and pass otherwise.

Let's look at some more examples:

          S: 3
          H: K85
          D: 953
          C: K97632
 S: KT             S: A987652
 H: AQT            H: 93
 D: AQ842          D: 76
 C: J85            C: Q4
          S: QJ4
          H: J7642
          D: KJT
          C: AT

This isn't so good for Pair 3NT. It goes off 4 and West doubles it for -1100 to your side. In reality, North might pull to 4 but that doesn't appear to do much better. Pair X will concede -930 while passive old Pair P will quietly lose -620. On the cross-IMPs, Pair P have +8.5, Pair X have -1.0 and Pair 3NT have -7.5.

          S: ---
          H: JT64
          D: JT74
          C: A9865
 S: AJ             S: Q765432
 H: K873           H: 95
 D: K8             D: 932
 C: QT742          C: J
          S: KT98
          H: AQ2
          D: AQ65
          C: K3

Mmm, nice preempt! 3NT makes exactly, while 3X is only two off. Pair 3NT win 6 IMPs, pair X win 2 IMPs and pair P lose 8 for their measily +200.

Results

Hopefully that all fits well enough. All that now remains is to sit back for a day and let the computer get on with it. Over the course of 200,000 hands, our tournament yields the following results, broken down into individual point counts for South.

               Cross-IMPs/board      Makes       MP Best
HCP   Freq     3NT    3SX    Pass   3SX   3NT    3SX   3NT

0.       1  -13.50   0.50   13.00     1     0      1     0
1.      32  -12.20   2.11   10.09    25     0     30     2
2.     165  -11.73   2.04    9.63   124     1    150    15
3.     690  -11.26   1.47    9.70   537     6    611    79
4.    1574  -10.10   1.49    8.64  1150    43   1344   230
5.    2993   -8.96   1.24    7.67  2097   128   2421   572
6.    5114   -7.72   1.06    6.74  3396   374   3877  1237
7.    7976   -6.98   1.03    5.94  5006   793   5849  2127
8.   11075   -5.56   0.96    4.66  6360  1734   7589  3486
9.   14042   -4.62   1.12    3.64  7373  2853   9228  4814
10.  17141   -3.70   1.24    2.74  8338  4350  10784  6357
11.  19148   -2.82   1.65    1.56  8195  5964  11654  7494
12.  19732   -2.21   1.82    0.86  7736  7076  11709  8023
13.  19448   -1.47   2.15    0.04  6684  8075  11167  8281
14.  18421   -0.90   2.51   -1.49  5544  8679  10435  7986
15.  16201   -0.49   2.97   -2.62  4081  8537   9148  7053
16.  13327    0.03   3.44   -3.55  2834  7705   7617  5710
17.  10573    0.56   3.65   -4.21  1949  6537   6021  4552
18.   7927    0.99   4.11   -5.09  1152  5331   4554  3373
19.   5662    1.27   4.38   -5.70   662  4044   3281  2381
20.   3694    1.33   4.62   -5.99   371  2736   2208  1486
21.   2398    1.56   5.07   -6.66   168  1901   1484   914
22.   1330    1.41   5.55   -6.88    65  1084    861   469
23.    761    1.87   5.82   -7.64    23   659    496   265
24.    385    2.50   5.69   -8.24     8   355    248   137
25.    190    1.81   6.22   -8.09     2   173    129    61

To explain the figures, let's take those balanced 10-count hands which we said earlier we hoped would do well by passing. Out of the 200,000 tests we ran, 17,141 gave South a 10-count. Pair 3NT lost an average of 3.70 IMPs/board on the cross-IMPs, Pair X gained 1.24 IMPs/board but Pair P did the best with 2.74 IMPs/board. Thank goodness for that, I was worried that I'd end up recommending we all start getting involved with these hands! Of those 17,141 hands, 3X made 8,338 times (about 49% of the time) and 3NT made 4,350 times (25%). So it's not surprising that Pass won out. The last two columns count up the number of times bidding 3NT wins over doubling. Here, doubling has the edge by 10,784 - 6,357. I didn't count matchpoint wins for passing.

The results at the top and bottom of the table shouldn't be taken too seriously as the sample size won't be large enough. Figures in the 5-21 range, though, will generally be fairly accurate.

The most important thing to note is that doubling oppo in 3 does better than bidding 3NT yourself for every single point count. And it's not marginal, either — you win stacks more IMPs by playing for a penalty. The second thing to notice is that passing is only the best option up until the 10 HCP mark. At 11 HCP it's close, at 12 HCP there's only one IMP difference but after that doubling is miles better. This is what I said earlier about being able to act with weaker hands — doubling is better than pass (just) with an 11 count, but you need a 14 count before overcalling 3NT is better than pass.

It should be noted, too, that despite the fact that doubling with a balanced 11 count is net positive on the IMPs, it's super high-variance. Your team-mates might not be best pleased if you come back with -730 or worse a full 43% of the time!

Conclusions

So should we all start changing our system now? Hell no! First of all, we need to look at the downsides. It may well turn out that the cost of bidding 3NT with a takeout double shape is far too expensive. But even if that wasn't too prohibitive, we still haven't really proved anything. You need to look at the system as a whole, not just one decision by one half of the partnership. If we have to guess what to do then doubling is a better guess than 3NT, but it may transpire that passing and expecting partner to do something sensible is better still. We shall see.

It is interesting, though, and I'll keep looking into it. I'd be very interested to hear of other people's thoughts on this.

Punting 3NT

Phil asked:

We all play club pairs type games and we always see daft 3NT contracts on the traveller when we play in 4/ (just because we have an 8 or 9 card fit). Maybe some simulations on the matchpoint benefits/ lack thereof of random 3NT punts would be good. Or just some definitive answer as to how much the computer says they should be losing by...

It's a bit hard to define what a "random 3NT punt" is, so I'm going to reword the question like this:

Partner opens 1NT and we have any balanced hand worth 3NT, regardless of major length. Of the hands where we have an 8-card major fit, how much better is it to play there than to play in 3NT?

In fact, I'm just going to restrict it to hands where we have a heart fit as it makes no difference. The criteria are as follows:

• Partner is 12-14 balanced
• RHO has 0-14 points and 7 losers or worse
• We have 12-18 balanced
• We have 8+ hearts between us

Over 25,000 tests, we see the following:

   Tricks        3NT          4

     0             0           0
     1             0           0
     2             1           0
     3             4           0
     4            12           0
     5            94           1
     6           490          20
     7          1893         160
     8          4785        1129
     9          6660        4898
    10          5555        9249
    11          3780        7075
    12          1528        2195
    13           198         273

NT is best:     10280
Hearts is best: 12619
Both the same:   2101

So, on that evidence, it seems that just punting 3NT has a lot going for it. It's a loser, but not by very much so if you fancy a swing then it might be worth a shot. Incidentally, at IMPs scoring you lose 1.02 IMPs/board by bidding 3NT, so it's really not a good idea.

Some experienced players will be shifting around in their seats now, crying that this is rubbish analysis. Yep, it is. The criteria are too general. We know from playing lots of bridge that if you have thin game values, you'd rather be in the major but if you have plenty of extras then the need to ruff losers isn't so great and 3NT will often make the same number of tricks. Also, we know that with a 4333 hand we will usually just bid 3NT over 1NT regardless of whether we have a major or not as it's likely to play the same. So let's break it down.

Using test runs of 1000:

Your point count

                  12-13         14-15         16-18
NT is best:        345           454           623
Hearts is best:    522           500           371
Both the same:     133            46             6

NT IMPs:         -1.23         -0.96         -0.66

Combined Hearts

                    8             9            10  
NT is best:        421           354           236
Hearts is best:    483           591           689
Both the same:      96            55            75

NT IMPs:         -0.81*         -2.16         -2.76

Your hand shape

                  3433          2533          4432 
NT is best:        467           458           324
Hearts is best:    393           473           561
Both the same:     140            69           115

NT IMPs:         +0.59         -1.07         -1.64

Type of fit

                   4-4           5-3               
NT is best:        339           516 
Hearts is best:    549           401 
Both the same:     112            83  

NT IMPs:         -0.75*         -0.23*

Now, I should probably break it down even further and find out what point ranges are best for 3NT in a 5-3 fit etc. etc. but that's going a bit over the top, I think. Generally speaking: 4333 shapes indicate 3NT; stronger point counts indicate 3NT; 5-3 fits indicate 3NT. Combining these factors will just do what you expect it to do.

Note that punting 3NT is never a really stupid thing to do at pairs. Even if you have a 5-5 heart fit that you're missing, you'll still get a good result about a quarter of the time! Note also that playing in 3NT is almost always a substantial loser at IMPs, the only exception being when you're 4333. So punting 3NT and eschewing your major is purely a pairs manoeuvre.

This is just a brief skimming of this area as the subject of 3NT simulations seems to have been done to death on rec.games.bridge. Try this thread for starters.

So to answer Phil's question, those bastards who punt 3NT and get a good result against you are indeed being lucky, but not as lucky as you might have first thought.

* Edit: see comments for slightly more accurate results.

Kicking Off For Real

And I think with that last post, we'll call our Introduction to Bridge Simulations finished. I hope it made some sense. The example hand I plucked out of thin air on day one didn't turn out to be quite as interesting as I'd hoped but that wasn't the point of it all. The idea was to show the processes involved in doing simulations like this, what sort of things we can find out, what sort of questions we need to ask ourselves, and how we can evaluate the results we get.

I started this blog because there were basically no resources on the subject that I could find. Therefore, thought I, I must be a universal expert perfectly placed to impart my great wisdom. Bollocks! I don't know anything really and I expect you all to point out any flaws or inaccuracies in any of the below.

What next? Posting will still be intermittent (so you'd be a fool to check back daily) but I hope to just get down and run a bunch of simulations — anything that interests me or that crops up when I'm playing. I might even take requests, but don't be offended if I ignore you. Just post a comment.

Do It Yourself

It just occurred to me that I haven't made any mention of just how I run these simulations. I use Deal and GIB, the links to which I just put up on the right. Deal is a very flexible deal generator which uses a programming language called Tcl to produce deals with just about any criteria you like. It's hands down better than anything else I've tried, but is not remotely user friendly unless you have programming experience! I may some day write a tutorial if there's any interest, but it's all there on the Deal website. GIB is a bridge playing program written by Matt Ginsberg. It's a single-dummy program (you can play against it on BBO) but it uses a double-dummy engine at its heart and you can interface this double-dummy engine with Deal. You used to be able to download it from their website, but it doesn't look like you can any more. So you might have to just buy the GIB software, unless anyone can point me to a free (and legal!) version?

Double Dummy Usefulness

I was going to write another long post analysing in detail how useful double-dummy analysis is, but I don't feel it's necessary. For one, it's mostly just about using common sense and experience — you get a feel for what kind of results are useful and what aren't — but also pretty much every simulation we do will involve some degree of assessment so the same topics will come up in future blog posts.

Also, I'm getting bored of this introduction to simulations and want to get on to more interesting things!

I will, though, give you some random bits of crap to use as manure for your thoughts to grow.

• A DD engine declares perfectly, but also defends perfectly. In a lot of hands the two cancel each other out.
• Higher level contracts are usually more accurate than low level contracts. There are less points of decision for either side in a typical 7NT contract than in 1NT and the less decisions that need to be made by a stupid human, the closer to 'perfection' they will get!
• Balanced distributions tend to be more accurate than wild ones. This is because with a wild distribution a lot of tricks will often hinge on one decision which, for a human, is just a guess. In a balanced no-trump contract, the cost of not making a double-dummy decision isn't so severe and you can often get it back. The perfect example is leading against a Gambling 3NT opening. Which Kxxx major suit do you lead from when one will lead to six off and the other will lead to plus three?
• Hands with holdings like AQ10 or KJx will be over-valued as the double dummy engine will always get any guess right. Therefore, you should be mindful when fixing hands with tenaces like this.
• In most cases, when you're comparing two strategies, the strategy that comes out best with double-dummy analysis will also come out best if you use single-dummy. Thus you can decide whether you prefer to play in 3NT or 4 on our example deal based purely on which one comes out top.
• If you're scoring with IMPs or aggregate points, you don't really care if the contract makes one overtrick or two, so any error between DD and SD will be marginalised.
• You're sitting in the pub after a session of bridge and looking at the Deep Finesse analysis. How often do you think to yourself that the number of tricks is completely unrealistic? Occasionally you'll notice it dropping singleton Kings or leading unsupported Aces to give partner a ruff, but for the most part you say: "Hmm, DF says it can make 9 tricks. Yep, 3NT should have made — sorry partner!"
• What is single dummy anyway? The difference between club level play and Bermuda Bowl level play is quite a few tricks! Just treat Deep Finesse as the epitome of expert play.

That is all.

Being Sloppy

Let's say you had a convention where a 1 opening showed either 10 points or 30. You want to run a simulation based upon this opening and so you need to deal out a bunch of hands which fit. So you tell the computer to give you some hands with 10 points and some hands with 30 points and go on your merry way.

Ah, but the fact is that 30 point hands are much rarer than 10 point hands. Much rarer. So if you want to do a proper investigation, you need to deal out the hands with the same proportion as they would occur in real life, otherwise you'll be skewing the data massively. Anyone care to work out how many 10 point hands we should deal for every 30 point hand? No, I can't be bothered either.

The simple way to do this is to just deal out completely random hands with no restrictions (random deals actually, but we'll let the distinction slide) and then pick out all the ones which don't fit. We'll count the points on every one of possibly millions of hands that come our way and only include it in the investigation if it has 10 or 30. This will ensure that the proportion of 10pt hands to 30pt hands in our sample set is more or less as it would be in real life. Computers are super-fast at dealing random bridge hands so the fact that we're dealing a heck of a lot more than we should isn't an issue.

It took my computer about 30 seconds to deal out 10 million completely random deals. Of these, South held 10 points 940,000 times and 30 points a mere 22 times. We've wasted over 9 million deals! We can now perform our analysis on the ones left, knowing that it will broadly mirror reality.

This is the same thing that we did with our example hand. We dealt out millions and millions of random deals and only kept the ones which fit the knowledge we had been given. If we did it right then the deals which we kept will be consistent with the action so far (LHO passed, partner opened 1NT, RHO passed). The full set of rules that we used were as follows:

• North has 12-14 points
• North is balanced
• West has 0-11 points
• West has an 8 loser hand or worse
• East has 0-14 points
• East has a 7 loser hand or worse
• South (you) has the problem hand, 4 A Q 2 A J 7 6 2 J 9 4 2

"But", you say, "I would compete over 1NT with lots of 7-loser hands! Your analysis is flawed and I'm never going to look at your stupid blog again!". And that's a fair point. We originally stipulated that oppo aren't hyper-aggressive but they surely would act with, say:

Q J 10 2 A K 8 7 2 4 J 6 5

That's seven losers so our analysis will include it. But so is this:

4 2 K Q 4 3 K Q 6 2 J 4 2

I'm not completely sure what you're supposed to call with that if not Pass!

The conclusion is, unsurprisingly, that the losing trick count isn't a great way to assess hands for overcalls. Perhaps we should do something more sophisticated like use the Rule of 20/21/22 or count shortage points or implement Binky points or Zar points or a number of other hand evaluation methods. Perhaps we should, and our analysis would undoubtedly be stronger if we did. The question is, though, how much? We don't only want to model the kinds of hands which East can hold, we want to model them with the correct frequency, so how much does it really matter if the odd attractive 7-loser 11-count slips in?

Over 100,000 deals I counted the HCP and the loser count of all the East hands. They were distributed as follows:

HCP

3    :   991
4    :  3123
5    :  7750
6    : 11703
7    : 14802
8    : 15785
9    : 15105
10   : 12677
11   :  8917
12   :  5325
13   :  2827
14   :   995

Losing Trick Count (in half-tricks)

14   : 22143
15   :  4988
16   : 29206
17   :  7738
18   : 21251
19   :  5338
20   :  7104
21   :  1433
22   :   755
23   :    44

You will see that a healthy majority of hands are clear passes. In terms of HCP, you might consider overcalling on some 11-14pt hands but these only account for 18.1% of the sample. If we're looking at losers, we might act on some 7-loser hands (like the example above) and also some 7.5-loser hands which makes up 27.1% in total.

What does it look like if we use the Rule of X (HCP + length of longest suit + length of second longest suit) for overcalling? Here are the stats:

Rule of X

10   :   121
11   :   800
12   :  2591
13   :  5822
14   :  9629
15   : 12991
16   : 15580
17   : 15605
18   : 14158
19   : 10900
20   :  6956
21   :  3536
22   :  1172
23   :   136
24   :     3

We can probably say that we'd be acting on a Rule of 24 hand (say, 14 HCP with a 5-5 shape) but note that, because of the losing trick count restriction, it won't be anything like as good as:

K Q J 10 2 A K 8 7 2 4 J 5

More likely it'll be:

J 6 5 4 2 A J 8 7 2 K K Q

Ok, we'd be bidding but it's not exactly beautiful. We might also get involved with the Rule of 23 hands and some of the Rule of 22 hands. But not all of them. A balanced 14-count fulfills the Rule of 22 and our oppo won't be bidding with that (I just asked them). And even if we add in the Rule of 21 hands (some of which we'd act on; most of which we wouldn't), it only amounts to 4.8% of the sample.

We're not getting anywhere very fast like this, and we won't either unless we sit here and painstakingly map out a detailed hand evaluation metric for overcalling a weak NT when vulnerable. But that's hard to do and I'm too lazy anyway. And I don't believe that we have to. If more than 5% of our sample size is flawed because we're including hands which would have overcalled and therefore do not accurately mirror the problem scenario then I'd be very surprised (at a guess, I'd put it at more like 1-2%).

And what does it hurt us if we include these hands, anyway? Instead, for example, partner will open 1NT, RHO will overcall 2 naturally and we'll still be in a similar position, wondering whether to bid 3NT or try for 4 or perhaps look for a minor game. The decision doesn't change — we're just handicapping ourselves by pretending we didn't see the overcall. The same could be said if RHO overcalls something else. It becomes harder the higher he overcalls, but even if he bids 2 we can still wonder to ourselves whether to bid 3NT (if partner has a stop) or look for a heart game (perhaps by cue-bidding 3 in a way that denies a stop).

What I'm trying to say, in a very long-winded way, is that it would be great if we could model the problem scenario in perfect detail such that every hand is consistent with the knowledge we would have at the table, but that's hard. Much easier is to be sloppy and use crude evaluation systems such as high-card points or the losing trick count or both. If we do this, we'll find that the majority of hands work out just fine and, of the hands which we analyse when we shouldn't, most of them won't make any difference anyway. We don't have to be perfect — getting it right 95-99% of the time is more than enough.

The moral: try not to be sloppy but if you are then don't worry too much!