Showing posts with label game theory. Show all posts
Showing posts with label game theory. Show all posts

2007-01-07

The phenomenological explanation to the Roland Soong strategy in horse racing

Flipping through the older issues of the Next Weekly I found the story of Roland's trick in gambling over the other side of the estuary (ESWN Dec - scroll to #99). He bet on the foreign jockeys and won.

My hypothesis is that Roland's strategy applies not only to Macau, but also to HK, and more or less everywhere else. If there is a betting combination that allow me to bet on all the foreign jockeys in HK, or even Australia or in UK, I would have done the same as Roland did. Roland was lucky to found that in that particular race the combination (betting on 5) allowed him to pick out those foreigners.

Why? there are a few explanations, let's call them phenomenological, or "Darwinian"/"anthropic" (i.e. what we see is the results of natural selection)

  1. It was said that these foreign jackeys mostly have had some trouble/offence in their own home countries, which are the main reason for them to move to Macau. Therefore, one can assume that they are in general better than their peer (for the same price). i.e. if you go into the shop, a good with defect will usually sell for a discount. If this defect is unrelated to the specific task (e.g. a scratch at the surface for a mobile phone), for the same price, wouldn't you buy one with more advanced functions?
  2. The cost of foreign jockeys are usually higher than local ones. e.g. they need to be provided with housing, travel and other benefits. Otherwise, wouldn't the owner hire some local people instead? If one assume that value correlates to skill, and that capitalists do not overpay on average, these foreign jockeys should have better average results

Do not believe me? look at the soccer fields in Japan and China, and tell me the average goals scored per season of the foreign and local players. Then let's see if the same applies for England and Brazil. My hypothesis is that the same phenomenon applies.

There are some caveats here.

  • e.g. if one looks at racing courses in a city where people would go even if they make less money. e.g. one with good food, entertainment, environment, etc. such as Sydney or Paris. Rule #2 does not really apply. i.e. one does not need to pay a premium to attract foreigner to come. Hong Kong may qualify as such an example for some people,for its entertainment and low tax, etc. i.e. those who do not care about air quality or its dismal living area. But I suspect many people do care. I wonder if someone would provide Roland with such stats

Disclaimer: this is a purely academic discussion. I have never in my life set my feet on the race course in HK. Now I would explain why I wouldn't create a hedge fund to bet on this.

Now, having understand this, does this help us win in the race course?

  1. We know foreing jockeys have an edge, but we do not know what is the % of their edge over the local guys. Such difference might have already been compensated in the odds calculation of the jockey club (i.e. the pay-out rate for the favored jockeys are 1:1.2, while for the less fovored could be 1: 8)
  2. However, let's still assume that most people are less informed, so the odds do not reflect this biase in probability. Then we have another factor to consider (which is why I never gamble in casino or with the HK Jockey Club). For every $100 the gamblers put in, perhaps only $60 or less will be pay-out. As government tax and jockey club expenses and profit have consumed the rest. As a result, one needs an odd of over 100/60=1.67 to average out. So unless I can be sure that these foreign jockeys are more than 67% better than the local guys, I would still say Roland was just lucky

Does this mean you always lose to the house? Not really. I usually would bet when there is jackpot, e.g. Mark 6 or 3T. Because those losers in the previous game are subsidizing the game. Where there are 2+ jackpots in the Mark Six (Lotto in US), the odds (for first prize) is usually higher than 100%. With only one jackpot it might still be under 100% payout. The pay-out rate is usually published, one needs to compare the size of the jackpot with the total gambling amount (not the amount of first prize) in that game, and the pay-out rate.

2005-06-03

Sun Bin - The crippled strategist


Hello,

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)