7 Pairs Discussion in Depth
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Copyright 30 November 1997 Alan Shiu Ho Kwan


I think that most players (especially non-Japanese) believe 
"7 pairs" to be harder than they actually are.  Even though 
you cannot claim discards, the hand is made easier by the 
(easily overlooked) factor that there are fewer tiles that have 
to be related with others (or meet any other restriction).
In a Regular Hand (with 4 sets and a pair), 5 tiles can be anything, 
and the remaining 9 tiles have to be related with these 5 to form 
sets or the pair of eyes.  In a 7 Pairs hand, 7 tiles can be anything,
and only the 7 remaining tiles have to match them.

Consider a hand with 5 pairs to begin with.  To make an 
All Triplets hand, you need to pong 3 times before you start 
calling.  To make a 7 Pairs hand, you need only to draw a tile 
that matches one of the 3 loose tiles in your hand to be calling.
I can't see why the 7 Pairs hand is harder by any significant 
degree, if at all.

In practice, the 7 Pairs hand gives you a lot of freedom and
flexibility because the incomplete part of the hand can
be completed from unconnected tiles, rather than pairs
(or partial sequences for non-all-triplets hands).
For example, if others discarded one of your loose tiles, 
you can easily replace them with the next raw tile you draw.
However, say if you're going for All Triplets, and have a pair 
of middle numbers waiting to be ponged.  If the remaining two 
are for example tied up in exposed sequences in other players' 
hands, then to replace the "dead" pair, you need to replace, 
not one, but two tiles, and these two have to be matched: a 
significant delay for your hand.

Also, in practice you often don't have to commit yourself to
7 pairs until you're quite close; you can easily hold on to
your sequences and partial sequences and decide what to do
after you get the useful draws.

Though some luck is needed to complete a 7 Pairs hand, the
amount of luck needed is not as much as most (non-Japanese)
players would think.  A "lucky" beginning would be like 3 or
4 pairs, about the same as that required for an All Triplets
hand.  You need "lucky draws" to match loose tiles, but
you need lucky draws to match loose tiles for All Triplets
either.  (7 Pairs need 6 pairs to be calling.  All triplets
usually require 5 pairs, plus all that ponging, to get calling.
Once calling, the 7 Pairs hand has the flexibility of a single
call against the advantage of the double-pair-call of having
marginally more available tiles.)

According to a survey on Modern Japanese mahjong games played by
professional players, 7 Pairs is completed 7.0% of the time among
all winning hands, while All Triplets is completed only 1.1% of
the time.  (maajan no kachi kata, ISHIDA Shigeru, Ooizumi Shoten,
p.173)  Although the fact that the Modern Japanese game heavily
encourages concealed hands may have contributed to the large
discrepancy, we should not forget that the 7.0% occurence is in
spite of the rather low value of 7 pairs in Modern Japanese.
Clearly, 7 pairs is not as difficult or rare a pattern as many
players believe, and it would be inappropriate to assign to it
too high a scoring value.