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Writing in the Proceedings of the National Academy of Sciences, a University of Manchester physicist has discovered that some games are simply impossible to fully learn, or too complex for the human mind to understand.

In simple games with a small number of moves, such as Noughts and Crosses the optimal strategy is easy to guess, and the game quickly becomes uninteresting.

However, when games became more complex and when there are a lot of moves, such as in chess, the board game Go or complex card games, the academics argue that players’ actions become less rational and that it is hard to find optimal strategies.

This research could also have implications for the financial markets. Many economists base financial predictions of the stock market on equilibrium theory – assuming that traders are infinitely intelligent and rational.

Much of traditional game theory, the basis for strategic decision-making, is based on the equilibrium point – players or workers having a deep and perfect knowledge of what they are doing and of what their opponents are doing.

“In many situations, people do not play equilibrium strategies, instead what they do can look like random or chaotic for a variety of reasons, so it is not always appropriate to base predictions on the equilibrium model.”

“With trading on the stock market, for example, you can have thousands of different stock to choose from, and people do not always behave rationally in these situations or they do not have sufficient information to act rationally. This can have a profound effect on how the markets react.”

The UK Observer ran a contest last year, A bunch of investment managers invested in the best stocks they could find, while a cat named Orlando randomly chose stocks from a list. The cat won.

From the Observer:

While the professionals used their decades of investment knowledge and traditional stock-picking methods, the cat selected stocks by throwing his favourite toy mouse on a grid of numbers allocated to different companies.

The challenge raised the question of whether the professionals, with their decades of knowledge, could outperform novice students of finance — or whether a random selection of stocks chosen by Orlando could perform just as well as experienced investors.

These kind of findings are pretty common (though usually less colorful). The idea is that it’s very, very difficult for anyone — from the smallest individual investor to the biggest mutual fund manager — to beat the market average. In the case of this story, they’re having a cat stand in for the market, to make the professional stock pickers look more ridiculous.

It’s true that some stock pickers do better than average and some do worse. But of course this is what would happen if everybody were picking randomly.

Once you take into account things like management fees and transaction costs, actively managed mutual funds that try to beat the market typically end up doing worse than index funds that passively track the overall stock market.

The ur-text on this idea — definitely worth reading if you want to learn more — is A Random Walk Down Wall Street.