Feeling particularly auspicious on a Chinese New Year day, and trying to escape the subliminal effects of the endlessly-repetitive new year songs being played at the malls, Miss Loi joins a game of mahjong with the Trusty Webmaster, her friend Miss Thong, and … umm … a complete newbie who’s there simply because of 三缺一.

In one particularly tense game, with only **16** tiles left to be drawn, three of them happened to be “waiting” for the same tile: a green 發财 – Miss Loi to complete her 十三么 (The Thirteen Wonders), Miss Thong to complete her 大三元（The Three Scholars), Trusty to complete his pair for his 大四喜 (Four Great Blessings). As for the Newbie, well … let’s just say that everyone would be happy if she doesn’t 詐胡 in the first place.

Given that:

- The final 發财 lies amongst the last 16 tiles.
- It’s now Miss Thong’s turn, followed by Trusty Webmaster, Newbie, and Miss Loi, in that order.
- Being THE Newbie with absolutely zero sense of strategy, she has a probability of 0.5 of throwing out
*any*tile that she draws.

Calculate the probability that Miss Loi will win this game and sweep the table with her 十三么 *by the time it comes to her turn*!

Please note that Miss Loi does NOT advocate nor encourage any form of gambling but nevertheless she hopes that this will make all you be more aware of the odds you might be facing in the next few days of the festive season 😀

**恭喜發财!**

**WARNING:** As not everyone is familiar with the rules of the game, there is absolutely ZERO chance that an exact question like this will appear in your test or exam, though it may assume other forms, like drawing some coloured balls from a sack *yawwn*

## 12 Comments

曜

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Alas... the only Mahjong I play is the "match the same tiles" type, on the arcade machines 🙂

曜

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Wah FoxTwo you're not Chinese??? 🙂

曜

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Arrgh! Screw probabilities! I flunked that royally years ago. I say, you WILL have a great year ahead Miss Loi, abound with calm, health and peace and determination in the temple!

曜

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imp, and you'll have a faerie year abound with great travels, great food, and love all around you 🙂

P.S. Errr ... probabilities are probably one of the most practical and down-to-earth topics in maths. Take this case ... you see ... if you're a true-blue

mahjong tai-taithere are really onlytwoways in which Miss Loi can win when it reaches her turn 😉曜

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Err... no SMC, I'm Chinese. I just never bothered to learn how to play Mahjong the proper way 🙂

Besides, the only thrill of playing Mahjong is to win money, and since I'm a non-gambler, no incentives to learn it.

曜

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In my City everyone like playing Mahjong I am from chinese

曜

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Yah~Wishing you ratmarkable probability on the mahjong table.

曜

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FoxTwo:Relax ... just pulling your leg 😀game:恭喜恭喜！您现在在大陆哪里过年啊？ByPasser:Oh thanks! Wishing you many many Thirteen Wonders!曜

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You changed the question!!!!

From a 中 tile you changed it to a 發 tile!

CHEAT!!! :p

曜

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Shhh ... not so loud!

Miss Loi's already feeling utterly ashamed that her wily 老千 maneuver was caught by a

mahjongnewbie!But then again, the question essentially remains unchanged, and don't you agree that a 發财 sounds more prosperous than a 紅中? 😛

曜

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P(a person is good in both mahjong and maths)=1/100

Is the answer 15/16 X 14/15 X 13/14 X 1/13 = 1/16 (assuming all other players didnt discard their tiles)

or 15/16 X 15/16 X 15/16 X 1/16 = 3375 /65536 ? (assuming all discard if not the 發财 tile)

P.S.If this question ever comes out in exam i will probably write P(win)=1/2 (win or lose XD).

曜

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LOL first of time Miss Loi would like to state that such a question will

confirm chop stampNEVER EVER appear in your exam ... Heee ...So we have:

To obtain the probability of Miss Loi winning, you'll need to add up all the possible cases that she will win i.e.

自摸 Case!i.e. P(Miss Thong doesn't draw the 發) x P(Trusty doesn't draw the 發) x P(Newbie doesn't draw the 發) x P(Miss Loi draws the 發)Thank You Newbie Case!i.e. P(Miss Thong doesn't draw the 發) x P(Trusty doesn't draw the 發) x P(Newbie draws the 發 AND foolishly throws it out for Miss Loi to win!)∴ P(Miss Loi wins!) =

(15/16)(14/15)(13/14)(1/13) + (15/16)(14/15)(1/14 x 1/2)

= 1/16 + 1/32 = 3/32

So

Anoneemerswould you like to join us at the mahjong table? 😉