Friday, January 9, 2009

The racehorse paradox

One of the readers of this blog suggested that I write about his incredible boardgame losing streak. As I'm tremendously flattered that someone actually found their way here and found the time to read through the posts I'm going to do just that. Now, I don't really know anything about this poor fella's losing streak, but on the subject of losing or winning in games is indeed an interesting one. Why do some people win more often than others?

Let's get the obvious explainations out of the way first. Some people are just better at certain games than others. The more complex a game is and the less random elements it has the more likely that this is the case. I believe Chess is the staple here. The best player will almost always win, and as there is really no limit to how good you can get at this game there is also no limit to how bad you can be in comparison. This is why a grand master can beat an entire chess club simultaniously.

But I don't think this is my reader's problem. In fact, as the losing actually seems to bother him, I suspect he is a rather skilled player, reading through strategy articles on boardgamegeek, analyzing his play. It reminds me of a problem I used to have playing poker a while back. Me and a friend started playing at about the same time but he quickly sped past me in terms of results. He started making lots of money online while I barely broke even. I was frustrated. A lot of the time I felt his plays were rash or even stupid and that he just got lucky. But as time wore on I realized that he had qualities that I lacked. I played safe. By the book. He played hard. With a vengence.

There is something called the racehorse paradox which essentially means that the more competitors in a game and the steeper the prize curve, the more it pays to be agressive and to take risks.

Say two horses compete. One of them is predictable, running at a constant 20 mph (I know jack shit about horses – how fast do they run?). The other is inconsistant, running at 15 mph most of the time, but every once in a while gets excited and pushes to 25 – let's say every fifth race. So if it's just up to those two, we will bet on the predictable horse to win as he will win four out of five races. But what if we add more horses? Let's say we add three more horses who are about as consistant as the predictable horse. The unpredictable horse will still win every fifth race, but the predictable horse's chances have worsened considerably. One of five races will be won by the unpredictable horse and in the remaining four races the other horses are about equal, meaning that they too win one out of five races. And if we add a sixth horse our unpredictable horde is suddenly the favourite.

Psychological factors aside, this explains, in part, why my friend was more successful at poker than I was. We played mostly ten player tournaments, and while I almost always made it to the top four, I very rarely won. My friend on the other hand often got obliterated in early rounds but if he made it to the top he usually managed to win.

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