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Wednesday, October 14, 2009

Efficient go hypothesis

Keep walking by fofurasfelinas from flickr (CC-NC-ND)Efficient market hypothesis states that you cannot really beat the market by much, all the prices are about right, and everybody behaves it more or less rational way. Yes, treating it too seriously leads to ketchup economics thinking, but it's often a good starting point - if you postulate that some prices are seriously wrong, you better come up with a story why they're wrong.

But let's forget about economics for a moment. Something very similar to efficient-market hypothesis applies to the game of go. Unlike most other games like chess and football, go is extremely balanced.

  • Black player, who moves first, pays 6.5 points for the privilege, what makes both players' chances of winning as close to 50:50 as it gets.
  • If one player is stronger, the weaker player gets as many free stones as necessary to get the chance of winning very close to 50:50.
What's interesting is that during the game, it's impossible to make a move that highly increases your advantage, or "beats the market" - if you could get significantly ahead by playing a stone, then the position was already unbalanced before you've done so due to this possibility. Values of positions consist of complex balance of territory, influence, flexibility, good and bad aji, and many other things - if you ask a computer program like gnugo to estimate balance of the board, you will get widely varying numbers with each moves, each totally ridiculous.

Just like on the market we cannot give correct formula for a price, but we know it's right because people trade at it; in go we don't have a formula for value of a position, but we know it's even if good moves by two players led there. If you postulate imbalance, you better come up with a story telling which move was bad and why.

Go players often perform some complex trades of moves called joseki - standard sequences that lead to more or less even results. Again, why even? Because neither you nor your opponent would purposefully play bad moves to fall behind, and if there are no good moves available it means one of you was already losing earlier.
Joseki example - every single move here and the sequence are about even
This requires significant shift in thinking compared to games where you act to get as far ahead of your opponent. You can play go like an index fund - just try to stay even with each move, and let your opponent make some mistakes and fall behind you.

That doesn't mean there's no room for creativity - sometimes there's only one good move to make, most of the time you have multiple good options with subtly different balances. These tiny variations are enough to win - there is no possibility of draw in go (not counting super-ko and such exceptional situations), so even if you get just 1 point ahead through the entire game, 0.01 point advantage per move, that's just enough. It's kind of like high frequency trades, which earn tiny profits, but with sufficient volume it's worth it.

Most professional games end with just a few points advantage for one side or the other. Or one of the players falls behind just a bit, and then risks it all on a great all-board fight to avoid the few point loss.

So as you can see, go is just like market. Except it never leads to crises costing trillions of dollars.

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