[The four following questions are a follow-up to our answers to questions 8, all from the same person. We have once more split it in parts: 10a, 10b, etc.]
You didn't answer perhaps my most important question. Why do you use statistical analysis to dubunk the Law and then use annecdotal evidence only to trumpet WP+SST? Where is the data that proves that your way of predicting how many tricks your side can take is accurate? I need to know what % of the time it is dead-on, what % of the time it is off by one trick, two tricks etc and in which direciton. And in the same way you did it to debunk the Law, i.e, [say] 250 deals when you are predicting 8 tricks, 250 more when you are predicting 9 tricks, etc. Why isn't such data presented? How can it not be there? Without presenting it, (A) we just don't know if your approach is accurate and (B) you give an analyst like me the impression that your real goal is just to debunk The Law and not to uncover Truth. In my heart I don't believe that's your purpose but...
To see how often the Law is right is (relatively) easy, since all we have to do is check whether total trumps equal total tricks. As shown, it happens roughly 40% of the time, given that both sides play in their best trump suit, and from the right side (if not, the hit rate falls a few percentages).
With all 52 cards on view, our WP+SST formula will be right on target almost always. There are a few exceptions, which we will tell you about on this site, but they are few, so if we say that our formula will be correct more than 90% of the time we are on the conservative side.
It's no secret that we either take tricks by power (honors) or with aid of our distribution (ruffs or long cards in side-suits). Therefore, it can't be surprising that a formula based on those concepts will predict more accurately than a formula which stresses a factor (the number of trumps) which sometimes is useful, sometimes not.
You say: If 18 trump and 18 tricks, 9 and 9, it doesn't follow that bidding on automatically give you a good result. You say if my side can make 8 tricks in H and they 10 in S what did your competing to 3 do? The answer to that is: If they can make 10 tricks in S, presumably they will bid 4 on their own whether or not you bid 3. Your bid of 3 is irrelevent. You have defended your position by presenting an irrelevent case! So, when I said that following the Law would seem to get you good results 73% of the time, I meant that by doing so, we would achieve par or better on the board. In this case you cite, we would achieve par, because they were on their way to 4 anyway.
Time to Tell the Truth:
If you don't like our example of a Lawful 3 pushing them up in 4 (which probably isn't as rare as you think it is), say that you have spades and they hearts. If you pass over their 3, they may be satisfied with that, but if you compete to 3 they may take the push hoping that either side makes its contract.
When we say the Law is wrong on a given deal, we mean that total trumps and total tricks are not equal. But when you write "the Law is wrong", we assume you mean "following the Law is wrong". But if you contract for as many tricks as your side has trumps, you are not assured of "beating or achieving Par" even if total trumps equal total tricks. Part of the time your result will be good, part of the time it will be indifferent, and part of the time it will be bad.
A priori, our goal on any bridge hand is the one you state: to equal or beat Par. We agree with you there. But when the bidding becomes competitive, objectives change, and sometimes Par is the worst result you can achieve, for instance when you can double the opponents for +500 or pass and collect +200. If you follow the Law with your nine trumps and score +140, why do you consider that to be a 'good' result?
Regarding going for 1100 on ruffs after bidding 4 over 4 in a Lawful manner, when they're on for 1430 but slam isn't bid: Are you saying that bidding 4 was wrong because we ran into unexpected ruffs? What happened to the luck factor you speak of in your book? It certainly isn't a great Law result; but it isn't a bad one as you've implied; it's just an unlucky one. You go on to cite a more 'mundane' example of going -100 vs their +110. You say Law people call this a good result. Mel calls it a Par result (imps), therefore a good one. [you conveniently ignore, of course, the real world possibility that when we bid over their 110 contract, they may go one higher and go minus].
Nobody can deny that luck has a role to play. And we would never dream of saying stupid things like 'just follow our recommendations and nothing bad will happen to you'. Bad things do happen; and even if your decision was excellent, it may turn out badly due to unforseen good or bad luck.
When the opponents bid on and go minus instead of plus, you obviously have a good result. But you mustn't forget that such things happen both when you follow the Law and when you break it. If we have eight hearts and bid 3 over their 3, which pushes them to 4 down one, when 3 also would have been one down, our 3-over-3 with eight trumps has beaten Par. Following the Law by passing over 3 wouldn't have.
There is another real world possibility which you didn't mention, namely that if you bid over their +110 contract, they may double you for +200 or more.
Your final case is where you say bidding on is OK – you'll make your contract but it would have been better off to defend – either because there are fewer tricks than trumps or that you will make an overtrick. If there are fewer tricks than trump ('27% of the time' you quote me), it is conceded by me that following the Law is the losing option. Using your example, letting them play 3 for down 2 would be better for us.
But you have missed the obvious! If we can in fact make 10 tricks and we follow your advice, we should be using SST and WP and figuring we can go plus in 3, you say we should bid 3! You say there is an opportunity cost in using the Law in this case, but the same opportunity cost exists following your methods! Remember what you said in response to my last e-mail:
Our rule of thumb for part-score battles is: 'If your estimation says your contract will make, go ahead and bid it...'
Yes, we would also bid 3 and miss the opportunity ... unless we did a similar analysis for the opponents and it showed that they were almost sure to go down. Then, we might rethink.
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