So it's a 2 x 2 zero sum game.

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If S is a terminal state, then the value is just the utility of the state given by the definition of the game.

Bentham's idea is the following the right thing to do the just thing to do it's to maximize utility.

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Tell me what Min's strategy is by putting in probabilities in these boxes, and then tell me the value of the game, the expected utility to Max.

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Bentham's utilitarianism is sometimes summed up with the slogan the greatest good for the greatest number.

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That's going to be true or false.

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It has a periscope telescope

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If you don't have a zero sum game, either because there're more than one player or just because there are different outcomes, then you can't really quite say that min is the opposite of max.

Here's a game tree for a stochastic 2 player game.

It turns out that that also is q 7 12.

That's illegal in many games, right? gt gt Yeah. gt gt That's the hard part.

Minimal casualties, maximum effectiveness that's us.

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I used a Unertl scope, fixed power of ten.

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Here it's 1.

We talked about mostly turn taking games where 1 player moves and then another moves, and the trick is how to work against an adversary who's trying to maximize his own utility and thus minimize your utility.

We can also maximize the logarithm of this expression, which is 3 times log pi 5 times log (1 pi)

I needed tools that were robust, modular, highly efficient and optimized,

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