Heavenly and Earthly Hands
Martin Rep
I have never spoken to anyone who ever made the Heavenly or the
Earthly Hand. Nor did they know anyone who ever made one of these
hands.
Coming to think of it, this is rather surprising, since *any*
combination will do for this special hand. So any four of pungs and/or
chows, and one closing pair.
How come this hand is yet so extremely rare?
Explanation: A Heavenly Hand is when East goes out on the initial deal
Earthly Hand: Depending on what rules you play, South, West or North
make an Earthly Hand either on Easts first discard, or on their first
self-drawn tile, or on any discarded tile in the first round.
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Cofa Tsui
news:bnumavkdmivckf54b...@4ax.com...
> Hi all
>
>
> I have never spoken to anyone who ever made the Heavenly or the
> Earthly Hand. Nor did they know anyone who ever made one of these
> hands.
Martin, you probably have forgotten me ;-) I won at least 3 Heaven hands
ever since I started playing mahjong. I couldn't recall any winning on the
Earth, though.
> Coming to think of it, this is rather surprising, since *any*
> combination will do for this special hand. So any four of pungs and/or
> chows, and one closing pair.
> How come this hand is yet so extremely rare?
I don't know how to compile a logical comparison, but I think this is
reasonable. A hand is delivered at random at start, but a winning hand has
to meet certain set combinations of the pieces. We achieve those set
combinations through several exchanges of pieces during the game play.
(Should the Heaven ever be so frequent, mahjong games could be quite boring
to play with, I guess.)
> Explanation: A Heavenly Hand is when East goes out on the initial deal
> Earthly Hand: Depending on what rules you play, South, West or North
> make an Earthly Hand either on Easts first discard, or on their first
> self-drawn tile, or on any discarded tile in the first round.
Nice appendix (I mean, to those who are familiar with different sets of
terminology)!
Cofa Tsui
www.iMahjong.com
Julian Bradfield
> "Martin Rep" <mr...@mahjongnews.com> wrote in message
> > I have never spoken to anyone who ever made the Heavenly or the
> > Earthly Hand. Nor did they know anyone who ever made one of these
> > hands.
>
> Martin, you probably have forgotten me ;-) I won at least 3 Heaven hands
> ever since I started playing mahjong. I couldn't recall any winning on the
> Earth, though.
The combinatorics of this is a bit nasty, and I don't feel inclined to
work it out (maybe Alan would do it!).
However, I can say that in the few thousand random games
played while testing my xmj program, Heavenly Hand has occurred once.
If you don't mind waiting a week or two, I could play a hundred thousand
hands and see what happens!
Dee
> How come this hand is yet so extremely rare?
I have not seen any Heavenly hand in my playing. I have only seen an
Earthly hand once.
> Explanation: A Heavenly Hand is when East goes out on the initial deal
> Earthly Hand: Depending on what rules you play, South, West or North
> make an Earthly Hand either on Easts first discard, or on their first
> self-drawn tile, or on any discarded tile in the first round.
Our table rules allow the following: flower replacements and kong
replacements do not matter (i.e., if East wins after replacing
flowers, it is still a Heavenly Hand). And our rule for Earthly Hand
is winning before that player makes a discard -- with pungs/kongs and
so on, it is difficult to determine what is a "round".
Tuomo Salo
Heavenly hand should not occur more often than once every 18000 deals.
Accuracy of that estimate is bad. In reality it is rarer.
Julian Bradfield <j...@inf.ed.ac.uk> writes:
> The combinatorics of this is a bit nasty, and I don't feel inclined to
> work it out (maybe Alan would do it!).
> However, I can say that in the few thousand random games
> played while testing my xmj program, Heavenly Hand has occurred once.
>
> If you don't mind waiting a week or two, I could play a hundred thousand
> hands and see what happens!
to avoid waiting, here's a way to calculate a very crude upper bound
for the probability of the heavenly hand:
since the combinatorics is nasty, it is useful to simplify:
1: after drawing a tile, it will be put back to the wall to keep the
calculations simple. resulting inaccuracy is negligible in comparison
to the next simplification:
2: whenever the probability "tree" would branch, avoid that by choosing
the branch with optimum probability to represent all the branches
with these assumption, we can get:
first five tiles drawn can be anything. probability 34/34.
best branch: the tiles are unique 3's and 7's.
HAND: 3b, 7b, 3c, 7c, 3d.
6th tile must be at most 2 tiles away from the existing tiles:
1b - 9b, 1c - 9c and 1d - 5d will do. probability 23/34.
best branch: it happens to be next to a existing tile.
HAND: 2b, 3b, 7b, 3c, 7c, 3d.
7th tile: acceptable: 1b,4b-9b, *c, 1-5d. probability 21/34.
best branch: 2c.
HAND: 2b, 3b, 7b, 2c, 3c, 7c, 3d.
8th tile: acceptable: same as above, minus 2c and 3c. probability 19/34
best branch: 1b.
HAND: 7b, 2c, 3c, 7c, 3d. (completed chows are not interesting)
9th tile: same as above, minus 1b and 4b. probability 17/34.
best branch: 1c.
HAND: 7b, 7c, 3d.
10th tile: acceptable: 5b-9b, 5c-9c, 1-5d. probability 15/34.
best branch: 2d.
HAND: 7b, 7c, 2d, 3d.
11th tile: acceptable: 5b-9b, 5c-9c, 1d, 4d. probability 12/34.
best branch: 1d.
HAND: 7b, 7c.
12th tile: acceptable: 5b-9b, 5c-9c. probability 10/34.
best branch: 7b
HAND: 7b, 7b, 7c.
13th tile: acceptable: 7b, 5c-9c. probability 6/34.
best branch: 6c.
HAND: 6c, 7c.
14th tile: acceptable 5c, 8c. probability 2/34.
total: 2*6*10*12*15*17*19*21*23 / 34^9 =~ .0000555
which is about once in 18000 deals.
since the estimations here are very crude, i expect this probability to drop
by a decade or two when the calculations are carried out to the detail.
please feel free to correct any errors i have made, the "correct answer"
would also be interesting to see. (the Other Approach should be easier when
calculating this probability without estimates, that is, "all possible
14 tile combinations out of 136 tiles" versus "all winning combinations"
> "Cofa Tsui" <cofa...@hotmail.com> writes:
>
> > Martin, you probably have forgotten me ;-) I won at least 3 Heaven hands
> > ever since I started playing mahjong.
Wow :-)
-bass
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John Hwang
>I have never spoken to anyone who ever made the Heavenly or the
>Earthly Hand.
Personally? No. But I've had the computer make it against me.
I don't like it scoring maximum at all, as it's too much of a lucky swing.
--
--- John Hwang "JohnHw...@cs.com.no.com"
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