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 😀
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*
