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.