CAR-vs-PIGS LOTTERY

   In the Car-vs-Pigs Lottery there are three identical, closed boxes, one contains a brand-new car, the other two contain pigs. The contestant is challenged to guess which box contains the car. After he has made his choice, the conductor of the lottery opens one of the other two boxes, which is revealed to contain a pig. The contestant is then allowed to change his choice of box if he wishes to do so. What is the optimal strategy for the contestant ?

Strategy 1 - Always stick to initial guess. In this case the second opportunity to guess is irrelevant, only the initial guess matters. The probability of the initial guess to be correct is 1/3, so the probabilty of the contestant winning the car with this strategy is 1/3.

Strategy 2 - Make second guess at random. In this case the first opportunity to guess is irrelevant, only the second guess matters. The second guess is between two boxes, one of which contains the car. The probability of a correct choice and the contestant winning the car with this strategy is thus 1/2.

Strategy 3 - Always change second guess. In this case the contestant will win the car if his initial guess was wrong (since he always changes his guess at the second opportunity). The probability that his first guess was wrong is 2/3, and the probability of the contestant winning the car with this strategy is thus 2/3.

     These results can easily be verified by a computer simulation.

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