Probably most people have heard of the Law of Total Tricks. For example, if both sides have an 8-card fit (16 total trumps), the contracts in those two suits will add up to 16 total tricks. This helps a lot in competitive auctions: even if our contract is not making, it is a good “save”; and sometimes, both contracts were making.
After giving some rationale on why it works and what the practical implications are, I put the LOTT to the test using double-dummy analysis. Unsurprisingly, the Law applies quite well (it was verified by others before me 🙂 ). Then, I ask when deviations from the Law are likely in two ways: Does more shape in our hand affect it? Do honours in the opponents’ suit?
I edit my code in “real time” in the middle of the video in case you are interested in how I did it, but of course feel free to ignore that part and skip to the end.
Enjoy and happy LOTTing!!
Comments
7 responses to “Video: gwnn looks at the Law of Total Tricks”
Awkward presentation
Can’t tell if the former comment is a form of criticism or a function of being Anonymous…….Nice summation GWNN
I really enjoyed this, thanks Csaba!
We really enjoyed this one-person jam session! And the results are quite interesting, with some surprises. I never thought, that the 4333 (0.146) shape brings more tricks than 4432 (0.103) or 5332 (0.103). We also can see the importance of the second suit – 5521 (0.411) promises 3 times more than 6331 or 6322, and 2 times more than 5422 (0.194). The absolute numbers show us in both points of view (shape and holdings), that these are just tendencies, to help us to decide, but we can not expect to many differencies in tricks from this. Thank you! 🙂
Thank you for the kind words! 🙂
I suspect that 4333 is still a little worse than 4432, but it is about 4S4H32. But still, 4333 is not much worse than average (0.189), that was quite surprising for me!
The main conclusion is … mostly.. the Law is the law!
A very entertaining and healthy single handed presentation of a subject not commonly discussed.When only one of the two opponent pairs have a SECOND 8 or more cards fit the the law is no longer applicable.The law is ill defined as far as taking into account the number of top honors present/missing in the 8 or more card fitting suit either way.The law has its own limitations which may not be ignored.However,I enjoyed the presentation.Thanks.
Hey Jennifer,
That’s true and I only got around to simulating that “off-camera.” Just as an afterthought (or maybe I’ll make a new video…), here are the numbers as a function of our best minor-suit fit, assuming we’re still playing spades vs hearts:
5: -0.383 (0.4%)
6: -0.186 (10.4%)
7: -0.038 (42.3%)
8: 0.274 (32.5%)
9: 0.767 (12.0%)
10: 1.355 (2.7%)
So there is a second fit about half the time, but the difference between 7 and 8 cards is pretty big! This is (arguably) a pretty big argument in favour of “better minor” openings… That way, we can find double fits easier.