Of Dice and Mooncakes

Sunday saw my family's celebration of the Chinese Mid-Autumn Festival, more commonly known as the Mooncake Festival, and probably much more commonly known as "that weird time of the year when the local Chinese buy a lot of egg-based pastries of different sizes".

The Mid-Autumn Festival is actually an acknowledgement of the Autumn Equinox, that time in the latter part of the year when the moon's at its biggest and brightest. The Chinese hold quite a lot of myths about the moon -- I daresay that we were probably responsible for that whole "man in the moon" perception in the first place. Mooncakes came into the scene around the 14th century, when they assisted in the overthrow of Mongol rule in China: Rebel conspirators used mooncakes to smuggle critical messages between agents of the Chinese resistance, and were therefore able to plan an exact date and time of revolution. (The entrie caper most likely remains one of the few historical events made possible by a bunch of pastries.)

The origins of the dice game, however, remain shrouded in mystery. I'll go out on a limb right now, though, and wager that it really has absolutely nothing to do with Mongols, revolutions, or orbiting lunar bodies.

From an international context, few people seem to know about the dice game. Its influence is most strongly felt in parts of Southern China as well as a number of Asian nations with a strong Chinese contingent; The Philippines happens to be well aware of the game in this regard, although not all Filipinos have actually experienced it. For some reason, my family has a long-standing habit of bringing one or two such guests to our Mooncake celebrations and having them join in the festivities.

The game is rather simple in execution: All you need is a wide-mouthed ceramic bowl and a set of six six-sided dice. Each of the dice must be marked with the standard pip-based formations of the numbers one to six, with the "one" and the "four" in red and all others in black.

Something like this:


All players then sit in a circle around the dinner table. The first player simply takes the six dice and throws them into the bowl, taking note of the numbers that appear face-up. Certain configurations win a prize for that player, after which the bowl is passed on to the next person and the cycle repeats until all the prizes have been won. If any of the dice jump or fall out of the bowl, then you lose your turn for that round; If all the prizes for a given configuration have run out, then future appearances of that configuration win no further prizes.

The prizes for the game are built on a system of six tiers, with each tier having a limited number of prizes available. There are 32 "sixth-place" prizes, 16 "fifth-place" prizes, and so forth... all the way up to a single "first-place" prize reserved for the luckiest of dice throws. The game is actually primarily based on occurrences of the "four" value -- the more fours you roll, the better the prize.

Sixth-place prizes are awarded to people who roll one four:


Fifth-place prizes are awarded to people who roll two fours:


Fourth-place prizes are awarded to people who roll three fours:


Third-place prizes are awarded to people who roll four of any number except four:


Second-place prizes are awarded to people who roll either a full sequence of all six numbers, or three of one number and three of another:



And finally, the first-place prize (zhungyuan) is given to the lucky soul who manages to roll four fours, five of any single number, or better:




As the game involves nothing beyond throwing six dice into a ceramic bowl, it is entirely luck-based (despite what the gamblers in the family would have us believe). This makes it impossible to touch on any sense of strategy for the game, but at the same time allows it to act as a virtual heaven for statistical analysts. From what I understand, the game's probabilities are actually slightly flawed, and it therefore presents a good endeavor for the mathematically-minded among us.

As with most dice games, this one also maintains the concept of an "ultimate throw" -- in other words, the best configuration possible. This is composed of either six fours, or six ones:



If you somehow manage to throw this configuration on your Mooncake festival dice, you get all the prizes in the game.

Let me repeat that just so that its magnitude can sink in: You win all the prizes in the game for that year, regardless of who has won them already. Some modern celebrations actually leave this rule out completely so that everyone can get their fair share of prizes, but the chances of such a throw are actually so rare that people will be all too willing to commemorate such an event. That, and they'll keep the set of dice for posterity's sake.

The Mooncake festival dice game doesn't seem to be practiced very often outside the confines of Asia, but it makes for an interesting exercise in thought and preparation. The prizes, for that matter, are almost always mooncakes in some form or another: Smaller versions make up the minor prizes, while the zhungyuan is invariably a massive three-pound monster that can't simply be consumed by one person. (The winner is encouraged to share his good fortune, after all.)

The loose settings for the game tend to allow any kind of adjustment; Some families make up their own "house rules" as they go along. The prizes can just as easily be more useful objects rather than perishable pastries: Some families play for groceries or gift certificates, while the more financially successful clans may even play for money. (These practices, I think, are usually offset by the condition that the prizes each year must be provided by the first-place winner of the previous festival.)

All in all, the dice game that takes place during the Mid-Autumn Festival is, I believe, an integral part of the celebrations that does not seem to hold any discernible connection to tradition. To dwell on the point further, it's an event that probably creates its own tradition as it goes along. It's literally one of the highlights of the year for the local Chinese community, and it's a welcome repast for the few game theorists and mathematicians among our circle.

In short, it's also one of those nice festivals where you can throw six dice into a ceramic bowl without any consideration for strategy whatsoever, and not get accused of gambling your way into a bunch of prizes. That's probably why I look forward to it every year, I suppose. :)