But then there are a few yaku that, for one reason or another, are usually not considered, or passed on in favor of other yaku instead.
Little Three Dragons
This is far from the rarest yaku in the game and does happen occasionally. But unless two copies of the third dragon tile has been discarded already, people seem to have a habit of holding onto them in hopes of that elusive limit hand. After all, with a limit hand scored as 13 faan, that third dragon pung is essentially worth 9 faan on its own. It takes a lot of restraint to accept the smaller guaranteed win rather than aim for the less-likely limit hand.
Rob the Gong
Of course, this is the Holy Grail of worthless yaku. In my entire mahjong history, I have once managed to Rob the Gong, and that was in Japanese Riichi style, where there's only a 1 faan minimum. In Hong Kong Old Style, with our 3 faan minimum, this yaku is more of a theoretical concept that a practical thing. With the exception of 13 Orphans, you can only Rob the Gong to complete a chow, so your hand obviously can't be an All Pungs hand. That means that your initial hand likely had to be going towards a Half Flush or a Self-Pick + Concealed + All Chows. Even if you are aiming for one of these hands, or you get a couple of your own flowers, you still need an incredible amount of luck to be in the position to Rob a Gong.
- Another player has to draw two copies of your winning tile.
- A third player has to discard another copy of that tile.
- The second player must choose to pung on it.
- The second player must later draw the final copy of that tile.
- The second player must choose to promote their pung to a gong.
- You must be set up to win at that time with at least 2 other faan.
Four Concealed Pungs
This yaku is primarily based on lucky draws, but it has another trait that makes it so rare and elusive: The little voice in the back of your head that promises safety. If you want to earn this limit hand, you have to silence the voice of rationality in your mind and embrace insanity. Even if you're lucky enough that you open with two concealed pungs and two pairs, what happens when someone discards a copy of your first pair? Of your second? Can you stay the course and bet on the one-in-a-million chance of drawing both of your remaining tiles, or should you go for the much more likely All Pungs hand? If the last copy of your fourth pung is discarded, do you accept the cheaper All Pungs, or do you try to make another new pung?
Eight Bonus Tiles
Yes, this is an entirely luck based yaku with such low odds that you will never see it in your entire life. (Assuming no one gets any bonus tiles in their opening hands and all tiles are drawn in the end, the odds of one player drawing all 8 bonus tiles are 1/(4^8) = 1/65536 = 0.001%). Even beyond that, when the player draws the seventh bonus tile, they have to give up on the guaranteed 3 faan win that this (also incredibly rare) yaku can give them. You might by now recognize the pattern, that the most uncommon yaku require you to throw away common sense and rationality and chase after that one-in-a-million dream.
EDIT: And yet somehow we've now seen someone score this yaku once...
Eight Dealer Keeps
Even if you end up on a lucky streak, to keep the dealer position for eight hands is an incredible feat. In an incredibly defensive game, you might have a 50% chance of a hand ending in a draw. If all four players have an equal chance of winning, that gives you a 12.5% chance of winning, meaning a total of 62.5% chance that the winds will not shift. To keep the winds from shifting for eight games is a 0.625 ^ 8 = 2.3% chance! And that's assuming the best case scenario with defensive games, not to mention that other players might intentionally deal into cheap hands to change the wins and yank away your chance of earning this limit hand.
Four Gongs
To hell with this hand.
