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Kris's Wall of Memories |
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''A man always has two reasons for doing anything - a good reason and the real reason.'' - J. P. Morgan |
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Monday, October 24th 2011, 22:36 Linear scoring for Hong Kong Old Style (OLS) mahjong Hong Kong Old Style (HKOS) mahjong uses an exponential scoring system that lowers skill and greatly increases random luck. Exponential scoring made sense in the late 19th century when there were very few ways to double your score, unlike modern systems with many opportunities to increase a hand's potency. Directly using the faan value of the hand as the score, without translating faan into points, is both a simpler way to keep points and actually quite superior in statistical terms. Most HKOS rules are aware of the lack of balance in an exponential system, so they either slow it down using modifiers such as half-exponential and faan-laak, or just use an additive scoring system. Both approaches are ineffective for different reasons. For house-rules like the faan-laak, these systems have a tendency to become more complicated over time, analogous to introducing more and more epicycles to fix the broken Earth-centric theory of astronomy. With the additive system, a probabilistically correct point system always creates dozens of unrelated scores for the player to memorise. Faced with complicated rules, players will just simplify it themselves, exactly the reason that gave us the ridiculous exponential system in the first place. A more appropriate objective would be to fix in place the simplest system possible that roughly approximately mathematically sensible values. In pure combinatoric terms, hands with higher faan values do become exponentially more rare, but this is a wrong comparison. Conditional probability is a much better measure of true difficulty because it removes irrelevant alternatives and concentrates on player decisions. For example, it's correct that a pure-suit hand (6 faan) is eight times harder than a mixed-suit (3 faan) if I go for pure-suit every game no matter what horrible tiles I start with, which is nonsense. A more sensible strategy would instead be mixed-suit if I already start with some tiles or a pure-suit if I start with even more, two situations with relative odds that is obviously much less than eight times. Naive use of combinatorics just ends up rewarding lucky players that start with good hands more often; all stochastic games have luck but we should strive to minimise the luck factor. The World Series of Mahjong 2011, the biggest annual tournament for the game, uses a set of rules almost identical to the statistically-consistent Zung Jung scoring system. To show that simply adding faan is a reasonable approximation to true relative odds, I am going to score common HKOS hand patterns using both faan and Zung Jung points with the table:
The only major difference is in rare limit hands but these differences are mostly philosophical and easily adjusted.
Saturday, May 7th 2011, 18:45 Fine traditions of British democracy A group of 9 British friends are deciding what to have for dinner. Without a concensus, they decide to pick the idea with the most votes. 2 chose pepperoni pizza, 2 chose Hawaiian pizza, 3 chose steamed vegetables and 2 chose seafood pizza. So they settle with steamed vegetables with green tea. In other countries, they would probably end up with pizza for dinner. The British have their own values, I suppose; cultural differences can sometimes be very difficult to understand, and all we can do is accept it and move on.
Sunday, April 10th 2011, 14:58 Logarithms, India and China Came across a chart with purchasing price parity (PPP) by country, in averages and medians. It got me wondering why the US is worried about China but somehow forgetting India. Growth for both countries in 2010 was around 9%. India PPP $2750, China PPP $5380; so it's around double, which sounds scary. But assuming around 9% growth for the next few years, a better question is how many years is India behind China? Basic numbers say (ln(5380) - ln(2750)) / ln(1.09) = 7.787, or around 8 years. So India is around 8 years behind China in economic development, which sounds a lot less dramatic. In fact it is even less because growth is faster in the beginning then later on. Respectable news outlets like Economist, New York Times or Murdoch-Corp (Wall St. Journal) always play the China-threat card and forget India. They are very similar: over 1 billion people, little natural resources, great cultural diversity, linguistic barriers, high income inequality, suffers mass poverty and is overshadowed by rampant government corruption. In India they had the License Raj, in China the communist economy. Both of them mixed their economy with free-market-reforms towards the end of the 20th century, but China did it about 10 years before India. That, I think, accounts for almost all their differences. Political, geographical or cultural "reasons" don't seem to matter. If one is worried about Asian-threats to Western-dominance, at least be consistent. Either they are both a threat or they are not.
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