So here, there's a 1 3 chance of each of these.

For the chance nodes, all the possibilities are equally probably.

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And here is my answer. You can really read off the formula that I just gave you.

Well, it's going to be the probability that you initially picked wrong.

If min plays 2, so strategy 1 is the dominant strategy, and that should have probability 1.

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She then proceeds to the next most probable number.

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Another way to think about it is, when you first make your initial pick, there's a one third chance that it's there, and there's a two thirds chance that it's in one of the other two doors.

OK.

So this equals 15 64.

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And they all tell you, Yes, we have won the lottery.

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What is the probability of randomly guessing the correct answer on both problems?

And I want you to tell me what the strategy is, whether it's pure or mixed.

And we solve that, and that works out to P 1 4.

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But we have trouble accessing our outcomes.

So I wanted to make sure that I really got a loaded coin.

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That's his choice, and a noble one.

So what I mean by that is, a node can be pruned away if evaluating the nodes is not necessary to figure out what the best moves are for max and min.

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What choice?

Choice.

So you actually have a two thirds chance of winning.

Then the value of the state for the action go up would be obtained as follows.

So five in fifteen that's the same thing as 1 3 that I pick a fair coin.

Probability

Phil, the odds against