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Monty Hall game possibilities
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Door 1Door 2Door 3Host cointossHost revealsWin by stickingWin by switching
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CarGoatGoat02TRUEFALSE
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CarGoatGoat13TRUEFALSE
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GoatCarGoat0 (moot)3FALSETRUE
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GoatCarGoat1 (moot)3FALSETRUE
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GoatGoatCar0 (moot)2FALSETRUE
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GoatGoatCar1 (moot)2FALSETRUE
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33.33%66.67%
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Note: We introduce the concept of a "host cointoss". This allows us to consider both scenarios when both of the boxes the host may open are goats. When one of the remaining boxes is a car, the host has no choice, so the cointoss is not necessary. But we must have two rows for each of these cases anyway.
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NOTE MONTY FALL IS ON A SECOND SHEET
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