Three Doors Game Objective: [Select a car] First stage: Event: [Select] Result: [Select a car] or [Select a sheep] Second stage: Event: [Change] or [No change] Result: [Select a car] , [Selected sheep] Final result: Probability: The result of the second stage needs to be weighted with the result of the first stage. The trigger of the second stage event is based on the result of the first stage. We see that the first stage result has only two possibilities: a sheep or a car. Based on the above results, no matter what event is triggered in the second stage, the result is determined, and there are only two possibilities for the second stage, "change" or "not change", so there are a total of 4 possibilities.
Then we make the following assumptions: In the first stage 1, the result of the player's [choice] behavior is the probability of [selecting a car] 1/3. The second stage 1.1. Trigger the behavior of [Do not change], and the result is that the probability of [Selecting a car] is 1. 1.1.1. Probability: In Assumption 1, the final probability in the case of [Do not change] is 1/3*1=1/ 3 1.2. Trigger the behavior of [Change], and the result must be [Selected Sheep]. Therefore, the probability of [Selected Car] is 0. 1.2.1. Probability: In Assumption 1, the final probability in the case of [Change] is 1/3* 0=0 Hypothesis 2: In the first stage 2, the result of the player's [choice] behavior is [selected sheep], then the probability is 2/3. In the second stage 2.1, the behavior of [do not change] is triggered, then the probability of [selected car] is 0, 2.1.1, that is to say, the total probability is 2/3*0=0 in the case of [no change] in Assumption 2. 2.2, triggering the [change] behavior, then the probability of selecting a car is 1 2.2.1, Under assumption 2, the probability of [selected car] in the case of [change] is 2/3*1=2/3. To sum up: 1.1.1 and 2.1.1 are the probability of [selected car] in the case of [do not change] The only two possibilities, the probability of which is 1/3*1+2/3*0=1/3 1.2.1 and 2.2.1 are the only two possibilities of [selected car] in the case of [change], and the probability is 1/3*0+2/3*1=2/3 In the final result, if you want to select a car, the selection probability of "Change" is 2/3 higher than 1/3 of "No Change".
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