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In riichi mahjong, a concealed pinfu hand is worth 20-fu if it goes out on a tsumo. However, a hand with no points that has been opened gets a 2-fu bonus for no reason other than being an open pinfu. Even if the hand has another yaku to go out on (since yaku is only given for pinfu if it remains concealed), the final score is calculated with a minimum of 30-fu (due to rounding) when going out on a tsumo.

One effect of this is that it is impossible to make a 20-fu 1-han hand, since any hand that goes out with 20-fu would be guaranteed two yaku: one from menzen tsumo (1-han) and one from pinfu (1-han).

Other than that, I can't see any reason why open pinfu should be getting those two extra fu. Is there any actual reason for it, or is it "just one of those things" that's lost to the history of this game?

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" even if it goes out on a tsumo" Wikipedia claims that a pinfu hand can only go out on a self drawn tile. What do you mean by even if – user1873 Apr 16 '12 at 4:39
@user1873 pinfu just means it's a no-point hand. the pinfu yaku needs to be a closed hand on a tsumo, but a hand can still go out as kui-pinfu (open pinfu) with a different yaku. – goldPseudo Apr 16 '12 at 4:46

I wonder is it related in any way by the fact that it is the lowest possible score?

THE SMALLEST POSSIBLE SCORE Many charts won’t have a value for 20 Fu, 1 Han. That’s because you just can’t make a hand that cheap.

What happens if you make an open Tanyao using Shuntsu only, a Ryanmen wait, and win by Ron? Should be worth 20 Fu, 1 Han right?

Actually, such a hand is called “kui-pinfu” or open pinfu, and will be scored as 30 Fu, 1 Han. Since a kui-pinfu is the only way to get 20 Fu, 1 Han, we can thus say the lowest possible score for a hand is 1000 points.

Unrelated to kui-pinfu is the 30 Fu, 1 Han hand won by Tsumo. Such a hand is called “gomi”, because of the payments (500, 300 = 5, 3 = go, mi), and because “gomi” means “trash”.

Wikipedia has this to say, since a no-points hand must be self drawn, add 1-han yaku of self pick to the hand.

The reason why there are no scores in the 1 han/20 fu cell is that such a hand is impossible. The only 20-fu hands are the no-points hand (pinfu, 平和) where the winning tile is self-drawn.However, since a no-points hand must be closed, making the win via a self-drawn tile automatically adds 1-han yaku of self pick to the hand. Therefore, a 20-fu, 1-han hand cannot possibly exist.

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There is no very good answer to this question. To directly answer your question: it's just one of those things that's lost in the history of Mahjong. A similar question would be, why is a tsumo-pinfu hand only worth 20 fu? Tsumo is worth 2fu by itself, but for whatever reason, Mahjong evolved so that tsumo-pinfu is only worth 20 (in fact, this combination is the ONLY way to get a 20 fu hand).

One possible reason could be that as Mahjong developed, people liked the idea that the smallest possible hand is worth 1,000 points (30fu, 1han). One can also speculate that it is similar to tsumo, in that open tsumo is worth 2 fu as sort of a consolation for not getting a yaku (though, menzen-tsumo gives both the yaku and the fu, except in the case of tsumo-pinfu). But other than speculation, there is no given reason for why tsumo-pinfu should be worth 20, but pinfu with some other yaku by ron is worth 30.

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To clarify this matter, we first have to understand kui-pinfu. Kui-pinfu happens if one wins by claiming a discard with an open hand with melds and waits to which no fu is awarded, the hand is not 20 fu but counted as a total of 30 fu.

Hence, it is similar to the rule that chitoitsu is 25 fu and not rounded up.

In conclusion, a pinfu is worth 1 han 20 fu + 10 fu (menzen-kafu) if ron and 2 han 20 fu if self drawn(with menzen-tsumo) while a kui-pinfu is always 30 fu.

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