## Friday 5 October 2012

### The journey of Tenhou

Considering that I recognize appropiate tactics since like a month ago (with 200 plays already accumulated), the recent result sounds really good here. Different from the Canton style or Taiwan style, the result from Japanese mahjong is accounted every 2 'rounds', the points calculation and yaku patterns promotes the defensive tactics to a very large extent. Like many sports, somehow you need some luck to allow you to score in the offending side, but defending is more about determination, alertness, calculation and skill, and most people treat the Japanese styled mahjong with the highest technical level about different styles of mahjong.

Raising the rank is quite time-consuming but sometimes through playing against the public you can really know your ability throughly.

Well... it's hard to talk about them in English...

I don't think I'm good enough to deal with tactics systemetically yet, but there's one point I would like to stress with:

As an echo with the passage I written about, different games has their own index of dependence on luck and randomness, but as long as they're not completely random (an example for completely random game would be the jackpot 777 machines in casino... that's why you should never play in casino but you'll always lose as your skill isn't helping you.), through a large enough number of plays the confidence interval of ability to play can stil be distingusihable among different players. Some of the games doesn't allow a large number of plays (at least at the competition level) but mahjong isn't one of them. Through a large number of play we can have a series of statistics to deal with. One of the most significant statistic is the percentage of ranking. In a 3 -players mahjong assuming complete randomness the expected result should be like :
1: 0.333, 2: 0.333, 3: 0.333

However, as you can see above the percentage of ranking really differs quite a lot. In private multiplayer room my percentage of 1st rank is almost 50% with a large enough plays (300). If you have studied some basic statistics you will know that a hypothesis testing --- chi square test here. You can actually work out yourself, but the about statistics is showing evidence that tactics is significant to your ranking.

Despite the statistical arguement, we can also use 'existance' to support our arguement inversely. As most players know, the overall ranking depends on the pts, and sometimes the pts you lose for 3rd is more than you earn per 1st. That is, to raise your rank you have to get 1st more than 3rd in a certain ratio --- under a completely random system this is possible but the iteration expectation  length is much much longer than the entire situation. Mathematically if a point start at 0 at t = 0 and when t goes by 1 unit, the point goes left or right randomly. Then at t = k the expected maximum distance from origin is 1/sqrt(k). Similarly here: If you are going to get a net +10 ratio you expect to have 100 plays; but when the ratio of 1st:3rd is 4:3 (for most cases), the net difference required increases as number of games increases, and as a result the games required increases dramatically.

You can try this from the following Python code:

from random import random
def randomwalk(netdiff=10,trial=20,plus=1,minus=-1):
for i in range(trial):
x = 0
count = 0
while x < limit:
a = random()
if a < 0.5:
x += plus
else:
x += minus
count += 1
print count
randomwalk()

Now, try randomwalk(10,20,1,-4.0/3)? What will happen?

It shows that it's nearly impossible to raise the rank under completely random system, and that's why we need tactics, we need to defense to avoid getting the third, and this is how 'gambling' stuffs can be 'scientific'.

There are far more stuffs in mahjong involves statistical analysis or even probability calculation, and I think more of them will come soon.

1. >>>and most people treat the Japanese styled mahjong with the highest technical level about different styles of mahjong.

Actually no. Lemme introduce the rules which the International Mahjong competition(http://en.wikipedia.org/wiki/World_Series_Of_Mahjong) is using

http://home.netvigator.com/~tarot/Mahjong/ZungJung/index.html

1. My statement is based on the spread of variance against players with different ability to play.

If possible I'll show related statistics in a few coming passages.

I would define technical level by decision made to reduce loss and maximize gain. In other mahjong system, making a big one and loses for a few more is beneficial in most case, but it's false for the Japanese styled one. Such system forced people to defense more, hence showing one's ability to play to a larger extent.

'Attacking requires luck but you don't need so for defending' is a quite famous quote that is true in different field like sports, board and tile games. With maximized efficiency you still may not be able to win from the game, but optimizing defensive decision would definitely reduce your loss in long term.