From conclusion No. 2, we understand that the average difference between trumps and tricks will be three quarter of a trick. Since on average there will be an (almost) equality, it follows that deals with extra tricks are balanced by deals with fewer tricks.
From conclusion No. 3, we see how often trumps and tricks really are (almost) equal. And the result, only 40%, is considerably less than one may expect, given the incredible support the Law has got from players at all levels from all over the world.
From conclusion No. 4, we understand that deals where there is a difference of one (up or down) are more common than deals where there is an equality.
From conclusion No. 5, we learn that deals where there is a difference of at least two (up or down) will happen a little more often than on every eighth deal. On a 32-board match, expect 4 such deals.
In deciding which trump suit was best and how many tricks the sides could
take with each of the the four suits as trumps, Ginsberg said that the
contract was always played from the right side (for the declaring side).
Any bridge player knows the importance of this factor, but for
some reason, Vernes never mentioned it, when he introduced the Law to the general
public.
It is easy to construct deals where North-South's best trump suit is,
say, spades, and if North is declarer they take one, two or even three tricks
more than if South is declarer. In that event, in counting the total
tricks, how many should we count for North-South on such a deal ?
The correct answer is "It depends on who is the declarer," but Vernes and all
his followers simply skipped the issue.
As the Law is formulated, it is incomplete, and on many deals it can't give us an answer.
It was wise of Ginsberg
not to repeat Vernes' omission, but when he also stated that "of two (or three)
suits of equal length, the trump suit was picked randomly,"
he was no longer talking about total tricks. Why ?
Because it is not unusual that
when one side has two or more trump suits of equal length,
one of them will
produce more tricks than the other. If we correct for that — as we did ourselves
in our statistics — the result will be that some of the deals which Ginsberg
called –2 will instead be –1 or 0 (or even +1), some of his –1 deals will be 0
or more, some of his 0 deals will be +1 or more, etc.
The effect of this
correction is that Ginsberg's claim that there is a slight tendency towards
fewer tricks than trumps is (a little bit) wrong. If we study total tricks
(which assumes "best trump suit" for each side), there is instead a slight
tendency towards more tricks than trumps.
But only if the contract is always played from the right side.
In a way, we like Ginsberg's approach, however.
In real life, it is not easy to realize when our 8 diamonds are better than
our 8 spades, for instance, and since bridge is a game of errors, even at
the very top, his "practical approach" appeals to us. But if he randomizes "the best suit", then why not
randomize the declarer too. And if we do that, the result will be that
everything move further to the left, i.e. that the tendency towards fewer tricks
will be even stronger than in the study.
So, for practical
purposes, to say that "The Law of Total Tricks" is right on 40% of the deals
is a little too high. Instead, 35-37% will be closer to the mark. Or, put differently,
slightly more often than every third deal.