Tuesday, April 25, 2017

Covered Xiangqi # 2 : Mathematics Statistic - >Probability

Covered Xiangqi # 2 : Mathematics Statistic - >Probability 

Let do some maths before move to next steps.

Below is the definition of Probability derived from wiki.

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is unbiased, the two outcomes ("head" and "tail") are both equally probable; the probability of "head" equals the probability of "tail". Since no other outcomes are possible, the probability is 1/2 (or 50%), of either "head" or "tail". In other words, the probability of "head" is 1 out of 2 outcomes and the probability of "tail" is also 1 out of 2 outcomes, expressed as 0.5 when converted to decimal, with the above-mentioned quantification system.

Another example: Throwing a dice.
When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6. Therefore the probability of any one of them is 1/6.

In general, Probability of an event happening = Number of way it can be happened / Total number of outcomes

However,  Probability is Just a Guide
Probability does not tell us exactly what will happen, it is just a guide.

Now back to Covered Xiangqi.

This is very important for a player to understand probability. The player needs to calculate the probability for a covered piece to be discovered during the entire game. Not only that, the player also needs to calculate the probability for his opponent's covered pieces as well. 

The probability for next covered piece to be discovered will be changed after a piece was discovered. In other words, the player needs to calculate the probability for each move.

However, bear in mind that probability does not tell you exactly which piece will be discovered. It is just a guide! It only can help you to make a decision whether to discovered any piece or not. The actual outcome still depend on your LUCK, but good calculation in probability will increase your LUCK's level. You have higher chance to discover the piece that you wish if you do your math well!

During the initial setup, each player owns 16 Xiangqi pieces, 15 of them are covered. Only the king is discovered.

Therefore for the first move, the probability to discovered a covered pieces that you wish are as below diagram.

So, based on statistic, mostly you will discover a pawn at the first move!

Let do a simple quiz.

Diagram below shown a Covered Xiangqi's  middle game. Black had discover all his pieces, whereas Red still has 2 covered pieces. One covered piece "Pawn Like" stays on File 9, and another discovered piece "Cannon Like" stays on File 2.

Based on the Red's discovered pieces, Red still has a cannon and a horse have not discovered yet.

Now questions:

1) What is the probability for covered piece on File 9 is a Cannon?
2) What is the probability for covered piece on File 2 is a Horse?
3) Based on current situation, Red to move. What is the best move for Red and why?

Post your answers on the comment box.

Have fun!

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