Some of you may have already got your copies of the book published last year by David Bird and Taf Anthias. I only recently got mine but thought I'd share with you an example problem from it as a demonstration of what it contains (it contains lots of examples) and how surprising some of its suggestions are.
Just before I start I need to set the scene. Imagine you are
West, South opened the bidding with 1NT (15-17) and North raised directly to 3NT (without using Stayman, so probably without a four-card major). Finally assume you're playing a teams match and you have to select your lead from the following beauties:
West (You)
10 3
K 8 5 2
9 8
Q 10 7 6 2
How would you rank the leads, to give your side the best chance of defeating the contract?
I'll just ask you to guess the correct order (best first) between the 10, the 2 and the 6:
If you want to know where the answers are derived from, what the book does is to simulate a large number of hands and select just those where North and South have hands consistent with the 1NT-3NT auction. For each of these, perfect defence and play are assumed and it's worked out which leads succeed and which fail. After lots of simulations you can get a good idea of how good the different leads are.
For bonus points, have a go at the 'easier' problem of finding the best lead from:
A Q 8 2 A Q 9 6 9 7 3 J 10
(on the same 1NT-3NT auction)
None of my opening leads seem to work, but here goes...
ReplyDeletePartner has nothing much and the major suit holdings look horrible to lead away from so I think I'm stuck with leading a minor and hoping he's not making 9 tricks. CJ looks safer.
In answer the the bonus question, yes you can play it safe. But it appears that with such a good hand, the odds favour an aggressive lead trying to take the contract off before declarer sets up nine tricks (mainly in the minors). The best two leads are far and away the major suit aces!
DeleteBoth major suit ace leads are worth a set about 32% of the time. The next best leads of a low spade, low diamond, low heart or club jack are all around 21-22%. Sure there's a little bias from leading an ace that the simulations assume you find the right switch -- but not enough to make up this big a gap.
So here's the rather amazing answer... no-one got the right order!
ReplyDelete(naturally there's a little bit of leeway here, and the first two best leads are close)
Spade Ten = 17.7%
Club Six = 17.5%
Heart Two = 15.7%
Diamond Nine = 14.1%
Partner has average spade length of 4.7 cards, and only about 2.0 average clubs. The spade comes out on top!
Even at Matchpoints the ranking order is the same (if you order by average number of defensive tricks you get), although the club gets even worse.
Spade Ten = 3.10 tricks
Heart Two = 3.08 tricks
Club Six = 3.04 tricks
Diamond Nine = 3.01 tricks
Well I'm still leading a club :)
DeleteSurprised that a diamond is significantly worse than a spade. Is this because of the lack of Stayman, or is Tx actually a better holding to lead from than 98? I mean, what if you switch the diamond and spade holdings?
It's *all* about the lack of Stayman. You could change the spot cards all you like in the pointy suits and the spade will always thrash the diamond. The book makes a rather large point about this. The assumption is that North doesn't have a four-card major (allowing 3433 and 4333 shapes doesn't make a lot of difference but a little).
Delete>So here's the rather amazing answer... no-one got the right order!
DeleteWell... I guess your poll shows one vote for the spade>club>heart ordering. I imagine that the blog machinery allows you to check who cast it :)
Nope I think they're anonymous... and that vote was made after I'd written the post with percentages. :) I'll talk some more on this when I'm back from a mini-conference. :)
DeleteDavid
How accurately have these figures been measured, anyway? The numbers seem close in some cases, does the book say what sample sizes it was using? Of course if you look at enough hands then the variance becomes less significant than the inherent biases in the double-dummy method, but it would still be interesting to know whether we've actually done enough simulations to know with confidence that, say, one particular lead really is 0.02 tricks better than another.
ReplyDeleteSo the book doesn't go into a lot of detail (at least in as far as I've got so far) other than say it's a across 5000 deals so that the averages are trustworthy [my words].
DeleteI've just tried knocking up the same simulation: 1NT-3NT sequence with the West hand as above. I gave South a 15-17 semibalanced hand (no singletons, void, 7m, or 6M) and also ruled out 5M4M22 hands. I gave North: fewer than four in each major; no more than 14pts; no less than 8pts; if 13-14hcp it needs to be semibalanced; and 8-9hcp rejected if semibalanced.
I've got the following (over 10000 hands):
S10: 10.6%
H2: 10.1%
D9: 7.5%
C6: 9.7%
C10: 8.1% (for fun comparison)
On the error front it would be fairer to run separate tests for each lead (to remove correlations) but ordinarily we're just saying that every lead of a spade ten has a fixed chance of breaking the contract. At around p=10% over 10000 hands we're talking an expected standard deviation between two percentages of 0.42% [I've done a quick Binomial approximation calculation] *if* they really are equally good leads. Thus a gap of 1% in performance would indicate a 5% of better rare event if the leads were equally good. As I said above, though, these leads are correlated since they were calculated on the same hands.
I also wonder slightly why the book has such better chances of beating the contracts. I guess in my hurry I haven't been as generous to the defence in dealing parameters described above?
On my final point, the big advantage to declarer to be able to take rather good lines of play double-dummy I guess might be the reason that I'm seeing such low % contract defeats. Or maybe I'm just not letting bid 3NT as a punt on enough hands. At the borderline I currently do block:
DeleteJx xxx AQJTxx xx
But I permit:
x Jxx AQJTxx xxx
So I'm not sure I've disallowing enormous numbers of North hands that would punt 3NT.
Here are the results of two other sims with 20000 runs (so 0.3% is standard deviation (for purposes of the variance of the difference between two percentages).
DeleteFirstly for South 15-17 semi-balanced but not 5M4M:
S10= 10.68%
H2= 9.925%
D9= 7.54%
C6= 9.695%
CT= 8.205% (for amusement)
Secondly for South 15-17 balanced:
S10= 10.76%
H2= 9.185%
D9= 7.68%
C6= 8.725%
HK= 6.285% (for even more amusement)