I\'m too lazy to go digging around to see if I can find anything like that.
And why should you when it\'s my assertion :)
As usual Tom you\'re spot on
It is buried at least more than one layer down as the first page does not link to it (I found it using a google search with the site:.... option)
For those following the conversation it is at http://home.netvigator.com/~tarot/Mahjong/mj_7pair.txt
For those who haven\'t read the article ...
Alan says regarding 7 pairs \"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.\"
He mentions earlier that \"You need \"lucky draws\" to match loose tiles, but you need lucky draws to match loose tiles for All Triplets either. \"
But the lucky draws for a 7 pairs hand are required to be self drawn from the wall (final pair excepting) whilst the All Triplets can be taken from any discard or the wall i.e. 100% of the wall potentially (if nobody else is collecting a chow including them)
** WARNING LATE NIGHT CALCULATION **
Start off with a set of 144 tiles remove the 4 seasons and the extra four tiles (either all red fives, flowers, or four regular fives if playing with red fives) leaves you with a starting set of 136 tiles.
From those 136 tiles you need to remove 14 tiles for the kong box and 4*13 tiles for the other players hands leaving 70 tiles.
For the pung hand this leaves you 70 tiles to potentially pung from the wall (either through self draw or from unwanted discards) plus potentially a further 8 from the players hand if they are held in the original deal .... this leaves you wanting 4 tiles of 16 tiles with 70 to 78 draws/discards
Consider 7 pairs ... you would not consider going for it without at least 4 pairs (You often see advice saying 5 pairs or some very early matches). you are looking to match off those pairs in the 70/4 draws left (yes I know the last one may be ronned) this leaves you with a 7 unmatched pairs. Drawing a tile to match 7 (of a total of 16 types of tiles) .... sorry didn\'t mean to scare anyone ... but to simplify the maths a little lets say that about half the time you are not going to match the tile for the first tile reducing to a tile to match 3 tiles then a single wait with only a quarter of the available
It\'s far too late to derive the maths involved but they do seem very in favour of the pungs having a lot more draws to draw similar tiles.
Alan\'s statement of
marginally more available tiles
for the pung and describing the 7 pairs\' final single wait (3 max available tiles) as an advantage over the two wait options of the all pungs\':
(i) two remaining pairs (4 available tiles) ... most players would obviously choose to be in the situation of having two pairs remaining than a pung and single tile
(ii) single tile awaiting (3 max available tiles) same as the 7 pairs last wait
Obviously this is a very simplistic view... it does not take into account other players collecting pairs, chows, keeping dangerous tiles and so on.
But it does seem to support the view of a harder 7 pairs hand as rewarded by MCR and other rules.
One consideration that Alan is silent upon is that most experienced players would not rule out either hand at the beginning of the game preferring to wait and see if the pung or more pairs appear first. If your existing pairs are certain premium tiles (e.g. winds, dragons and fives if playing red fives in Riichi) then your opponents are less likely to ditch these tiles in your favour preferring to wait a few draws to see if they can use them. In this situation you are more likely to end up matching a 5th pair than a 1st pung which would distort the amount of times 7 pairs comes up in tournament play. According to Alan (and I have no data to argue) 7 pairs comes up around 7% of the time in Japanese tourneys .. there are other considerations here as well as in Japanese rules 7 pairs may also pick up Menzen Tsumo, Tanyoo chuu amoungst other doubles bringing the right 7 pairs to a good total. Also 7 pairs, as you are limited to a single wait, most will declare riichi on a concealed hand as they have to keep their hand concealed until the winning tile anyway. You will avoid declaring riichi if some of the tiles have gone and you wish to keep open whilst you reorganise you last tile to one with the most remaining tiles left (but then you are likely to riich then instead).