Sun Bin - The crippled strategist


This is the first post in my blogging trail, or trial, in which I would like to introduce Sun Bin (孙膑). Sun Bin was one of the greatest strategist in history. He was crippled as he lost his knee-caps, but he was anything but lame. He also wrote his own Art of War.

He was said to be a descendant of the renowned Sun Tze. His brilliance outshined his classmate Pang Juan (庞涓). Pang became jealous and tricked him, which resulted in his loss of knee caps in the State of Wei (魏).

Sun managed to escape to the State of Qi (齐), and re-started his career there, advising Tian Ji (田忌). He demonstrated his brilliance by helping Tian to win a horse racing against The King of Qi.

The problem was fairly simple. But it was remarkable he solved it 2500 years before operation research was invented.
Tian had 3 horses, let's call them A, B, C.
Horse A was from the top breed and the fastest, B the middle breed, and C the slowest.
Tian and the King gambled by holding 3 races. It usually started like this: Tian's A breed vs King's A breed, and so on. Every single time Tian lost by split seconds in all 3 races.
When Sun heard about this. He told Tian Ji if he listened to him, he would definitely win the next race.

So what was Sun's trick? You are welcome to post your solution as a comment or email me to ask for the answer.

(Today this problem is still widely applicable in a number of a places, e.g., the Thomas/Uber Cup in Badminton World Team Champions. It is also a classical problem in game theory)

Among his well known ploys are:
Tian Ji Sai Ma (Horse Racing for Tianji 田忌赛马)
Wei Wei Jiu Zhao (Besiege Wei to Rescue Zhao 围魏救赵)
Jian Zao Huo Di (Reducing Stove To Fool Enemy 减灶惑敌)
Jin Chan Tuo Ke (Shedding Shell Like a Cicada 金蝉脱壳)


Anon said...

The horse racing story is different from game theory. In (standard) game theory, both parties are assumed to be intelligent and rational, and they both use their best strategies (best responses to the other party's strategy). The horse racing story is one-sided. In game theory you would have to allow the king and Tianji to respond to each other's strategy. The result of Tianji's story is not an equilibrium.

Anon said...

Sun Tze's Art of War has the same problem---it's one sided. One can imagine what will happen if both parties of a war have read Sun Tze. Sun Tze is a great thinker, but not a game theorist in the modern sense.

Sun Bin said...

HH, yes, you are right.

sun bin's horse racing is the first to formulate the game theory problem, with the king sticking to a known strategy. considering that it was 2500 years ago, it was very innovative.

sun tze's art of war discuss about generic (high level) strategy and principles to follow. imho it is quite different from game theory approach (which are tactical moves, instead of strategic moves)

Sun Bin said...

bingo! :)

the king was first puzzled and then impressed after the race, and wanted to appoint Sun as his general. But Sun declined, explaining that "as a handicap he will not be respected by his soldiers". Instead, he asked the King to appoint Tian and promised he will be Tian's advisor.

Anonymous said...

To: Iron_Jackal_TW

You really sound more appaling than intelligent.

(P.S. I am not Chinese or Asian)

Anonymous said...

Sun Bin,

You have an unique blog.

One great distinction between Sunzi's and Sun Bin's view of strategy is that Sun Bin focused on understanding the mindset of the targeted opposition before deciding on any act of influencing it.

Look at those well-know ploys. Ask yourself this question- What was the common connection between all of the ploys? He understood the psychological tendencies of his opposing counterpart.

I am glad you liked my JadeDragon.com article on Sun Bin.

I should improve it one day.

Anonymous said...

Two more points. Unlike his ancestor, Sun Bin was content to win effectively by prevailing in two out of the three races. He pragmatically knew winning a war in a complete mode is impossible.

While everyone reads Sunzi, how many of them really understand the black art of strategic assessment.

Thanks for your time.