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Comment by tbrownaw | Hacker News Reader

If you know more than nothing, the best choice is often still random -- just with different weights applied to the various options, which I hear can be calculated with something called game theory.

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Under what circumstances is that the case?

Let's suppose, for instance, that two roads diverge in a yellow wood and you have reliable information that road A is the correct path with 90% probability and road B is the correct path with 10% probability. The normal person takes road A and will be right 90% of the time.

On the other hand, if you try to be probabilistic about it and follow road B with 10% probability to reflect its 10% probability of being the right road, then your chances of picking the right road are 0.90.9 + 0.10.1 = 82%.

Maybe there's a more complex situation where the weighted random decision making is a better idea, but I'm not seeing it right now.

Since my background is poker, I'll use an (overly simplified) example from there.

There are situations where you want to manipulate your range (set of hands) in a given spot so that your actions make up a certain distribution.

For example, if you want your range to be made up of 30% bluffs, you can figure out how often you get to that spot with a bluff and how often you get to that spot with a strong hand. Since you're always continuing with the strong hand, you can then know what percentage of the time you need to continue to bluff in order to accomplish this. Since it doesn't matter which of those hands you choose to bluff with, it generally makes sense to use randomness to decide in the moment.

I don't play poker, but from what I understand, the reason for including randomness in your decision is to throw your opponents off. I.e. You're playing against people who try to predict your behavior, so you throw in a random component to make it harder for them.

In decisions not involving active adversaries, deciding at random doesn't give you anything over a deterministic solution.

Nearly, but just to nitpick, you're not including randomness, you're actively making a choice to make the resulting pattern difficult to distinguish from randomness. So, sometimes you raise by a large amount because you have a strong hand. You don't want other players to be identify that you have a strong hand by the fact that you just offered a large raise, so you have to also bluff sometimes, raising when you really don't have the cards. Your actions are not random, but they are perceived as random by the other players.

It happens when you're competing. Suppose you're trying to find some buried treasure that you know at the end of one of the roads. But another tribe is trying to kill you, and will be waiting at the end of one of the roads. In that case your best strategy (and theirs) is to make the choice of which road to take probabilistically.

Well, this is a much complicated problem. You need to answer at least following questions:

- what is your utility of finding a treasure and not getting killed?

- what is your utility of not finding a treasure and not getting killed?

- does the other tribe know your utility distributions?

I'm pretty sure there's a solution to this that involves probability and fixed points but does not involve flipping a coin to chose a road.

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