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hegemonicon comments on Positioning oneself to make a difference - Less Wrong
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The prime tenet of successful strategy in any domain - chess, life, whatever - is "always act to increase your freedom of action". In essence, the way to deal with an uncertain future is to give yourself as many ways of compensating for it as possible. (Edit: removed confused relationship to utility maximization).
It's much more difficult to apply this to a life-sized board, but it's still a very strong heuristic.
No, this gives a utility of 1 to every action. You have to find some way to explicitly encode for the diversity of options available to your future self.
If you're programming a chess AI, that would translate into a heuristic for the "expected utility" of a position as a function of the number of moves you can make in that position (in addition to also being a function of the number of pieces other player have).
Hrm, I'm not sure if I just miscommunicated or I'm misunderstanding something about utility calculations. Can you clarify your correction?
Utility calculations are generally used to find the best course of action, i.e. the action with the highest expected utility. If every possible outcome has a utility set to 1, a utility maximizer will choose at random because all actions have equal expected utility. I think you're proposing maximizing the total utility of all possible future actions, but I'm pretty sure that's incompatible with reasoning probabilistically about utility (at least in the Bayesian sense). 0 and 1 are forbidden probabilities and your distribution has to sum to 1, so you don't ever actually eliminate outcomes from consideration. It's just a question of concentrating probabilities in the areas with highest utility.
Does that make any sense at all?
(Ciphergoth's answer to your question is approximately a more concise version of this comment.)
You're right both in my intended meaning and why it doesn't make sense - thanks.
The expected utility is the sum of utilities weighted by probability. The probabilities sum to 1, and since the utilities are all 1, the weighted sum is also 1. Therefore every action scores 1. See Expected utility hypothesis.
Thanks. (Edit: My intended meaning doesn't make sense, since # of possible outcomes doesn't change, only their probabilities do. Still a useful heuristic, but tying it to utility is incorrect).
The way chess is different from life is that it's inherently adversarial; reducing your opponent's freedom of action is as much of a win as increasing yours (especially when you can reduce your opponent's options to "resign" or "face checkmate").
And I don't think that heuristic applies without serious exceptions in life either.