That figure of 11% making 3NT goes down to 5.4%!
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
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.
4 comments:
Good work M. I've got one more scenario for you that might be plausible in 3rd seat, and that's a 6 (or 7+) card solid minor with 3+ controls outside. I'd be interested to know what frequency we can attach to those hands. I ran a few quick simulations (on the assumption that hand was held) but with nothing quite so sophisticated as what you have.
First of all I think that the minor only needs to be headed AKQJ. With a 6 card suit you're only not cashing if the clubs are split 511 or 502 or worse. Partner might even have a stiff T (useful if you have two aces). I ran four quick (1000 deal) simulations based on the outside holdings (for interest and to get a quick guestimate). The following hands make game:
1) South is A74 84 A2 AKQJ63 ~65%
2) South is A74 84 K2 AKQJ63 ~49%
3) South is AK4 84 72 AKQJ63 ~45%
4) South is K74 K4 K2 AKQJ63 ~64%
[Note that for the above I have given South the worst possible residues by making the short suits weak so that oppo are more likely to be able to cash 5]
Overall that is ~56%. By itself 56% may or may not be good enough. Going back to one of my original questions though; how much will you tolerate for the benefit (in terms of preemption) of opening 3NT rather than 1C?
In reality the worth of 3NT vs 1minor in 3rd seat would have to be factored at minimum along the lines of:
1) + The % of time you make when you're allowed to play there when you wouldn't have otherwise got there
2) + The % of time oppo now defend incorrectly due to their inability to communicate in the auction / info that your bidding would give away
3) + The % of time oppo go wrong in the auction when they otherwise wouldn't have
4) - The % of time that oppo take you for a large number (important at teams)
5) - The % of time you're in 3NT when you would have otherwise got to a superior 4/5/6minor
6) +/- if partner is allowed to pull and gets to a better / worse contract than if you had opened 1minor
and probably a lot of other things besides, including of course your observation of frequency. I'm sure that 3NT showing AKQ AKQ AKQ AKQ and one small card, with relay responses including some sort of jack ask / length ask, will aid finding the 7NT contract (or not) that everyone else is only guessing at. It's 100% perfect and foolproof, but not so frequent...
As a potential for #6 above you might like to let partner pull to 4 minor with 4 card support and say 0-6 points (or base it on say 0/1 controls), and allow them to leave it in with 7+ points (or 2+ controls). If they are right 90% of the time then you reduce the number of making games a fraction, but drastically increase the number of making contracts (even though some will still go down). So many simulations... you could run until Christmas with this one :o)
Well, over another million deals we had a solid 6+ card minor with 3+ controls on the side 1426 times. Which is more frequent than 6-5 in the minors (though a lot less frequent than 5-5 in the minors, which was 3904).
So on this basis it might have some merit. I'm not so sure though. The traditional gambling 3NT can win in the following ways:
1. A preemptive action. Oppo now struggle to bid the right game or bid game at all.
2. You get to play in a poor 3NT and make it when a more revealing auction would prompt the right defence.
3. You get to play in a cold 3NT which you wouldn't have bid otherwise.
Now it seems to me that your suggestion has little merit as a preempt — you hold 17+ points! Also, because 3NT is more likely to be cold, it has less value as a means to fool oppo into letting it through. And finally, because you're so strong, you're unlikely to miss game through normal bidding. All it takes is a 1/1 response and you'll force to game (go on, do a sim to judge how often 3NT will make opposite a non-response).
So, in sum, I don't see much value in opening these hands 3NT instead of 1 of a minor. On the 1400 hands you'll hold per million, I doubt if you'll gain on very many at all. In fact, there are times when you're more likely to make 3NT by bidding it slowly! Everyone knows to lead an Ace against a gambling 3NT to look at dummy, but against a 'normal' 1C-1S-3NT auction, you'll probably lead 4th highest of your strongest red suit.
Your question about probability is a difficult one. We're not measuring the probability of success of a contract, we're measuring the frequency of success of a contract. I suspect that on some deals the two concepts are similar but on others they're not, but I haven't really got my head around the subject yet.
There are indeed a lot of sims to do on this subject, but I'm not sure it's worth it. I think I've shown that opening a normal Gambling 3NT in third seat is pointless. And if you want to up your strength to make it more likely that you'll make your contract, you're upping it so high that you're not losing anything by opening it lower. And the frequency of holding this hand is so low that there are better things to use it for.
I'm not so sure that I agree with the 17+ 3NT not being preemptive. You've got huge distribution (with a 6-7 card minor) that wipes out around 6 of your 10 points within that suit in terms of defensive value. So if partner really has very little then oppo are quite likely to have game on. If partner does have a little something for us, say one ace, then oppo most likely have a very cheap save at the 4 level. It's not inconceivable that a double game swing could be on by opening 3NT.
M said: "Everyone knows to lead an Ace against a gambling 3NT to look at dummy, but against a 'normal' 1C-1S-3NT auction, you'll probably lead 4th highest of your strongest red suit." I'd have to disagree with this (to some extent) too. Look at the outside 3-control hand Kxx Kx Kx AKQJxx, and give partner one ace (a 4 count too much to ask?) If LHO holds or neither of the missing aces 3NT is cold. If both then we make as soon as he leads one. If the aces are split LHO has to NOT lead the ace in order to take the contract off. Defending a traditional 1st or 2nd seat gambling 3NT opening I agree it (usually) doesn't hurt to cash an ace as you know it isn't sat over declarer's king. You see dummy and then know whether to continue or switch. Against a 3NT with outside controls opening bid you half expect declarer to hold the king ... so you don't want to lead the ace. Of course not leading the ace may allow declarer 9 tricks when you could have been cashing 5 in that suit. So I actually think, if anything, it is harder to defend the 3NT opening than 1C-1S-3NT.
I do overall agree (you've convinced me!) that 3NT as a 3rd seat opening has less merit 'to play' than something strictly pre-emptive in style.
I Michael! Long time reader, er, occational poster. Anyway, I don't usually post unless I've been drinking, and that usually means that I've missed something like:
(i) she's a minger; or
(ii) she's married; or
(iii) I led a heart!
Anway - what are the odds then of actually making 3NT (gambling) when partner is UNPASSED. I mean, if you need close on a 20 count to make opposite a passed hand, how often does a solid 7 card minor with nothing outside make game opposite an unpassed hand? And when it does make, how often will partner have such a whale as to make the whole pre-empt exersice pointless anyway?
In short, should we be dumping the gaming 3NT altogether for something more usful (beer enqu. maybe)?
Post a Comment