So let's say, if you can guess who the champion team is for soccer, such as in World Cup, then you win a car. Otherwise, you win a goat.

There are 4 teams left. Country A, B, C, and D.

And country A will play country B, to go into Final match. Country C will play country D, and go into Final match. Then in the Final match, the champion team will be known.

So you choose Country D. And now you go into a room and cannot watch TV, cannot use a mobile phone or Internet, and cannot communicate with the outside world at all.

Now Monty Hall sits in another room and watch TV for the match between country A and B. Now he finds that country A won the match.

Then he comes to you and the Monty Hall show continues. He said, "now, I can tell you Country B is not the champion team. Will you want to switch your choice?"

Part 1:

Just like Monty Hall opening a door and tells you it is not the car, now he tells you Country B is not the champion team. Will you switch your choice?

Part 2:

What if Monty Hall also watched the match between country C and D and tells you Country C also did not win. Will you switch?

  • 1
    $\begingroup$ It depends on whether you're the kind of person who prefers a goat over a car. $\endgroup$ Sep 15, 2019 at 19:44
  • $\begingroup$ let's assume the goal is to win a car or to win a car, sell it, and buy 20 goats $\endgroup$ Sep 15, 2019 at 19:46
  • $\begingroup$ To clarify: in part 2 MH only tells you country C did not win or he tells you countries B and C did not win? $\endgroup$
    – Dr Xorile
    Sep 16, 2019 at 22:02
  • $\begingroup$ Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) $\endgroup$
    – Rubio
    Sep 29, 2019 at 1:18

1 Answer 1


Original answer (now Part 1) If we assume each team has an equal chance of winning any particular match and that you know A plays B and C plays D in the first round.


Yes. Change to A, which has a 1/2 chance of winning. D must win twice, a 1/4 chance.

Second answer (now Part 2),

no, changing your answer will not increase your chances (with the same assumption of equal chances of winning)

  • $\begingroup$ sorry... I was thinking about the question and answer... now I changed it to 2 parts $\endgroup$ Sep 15, 2019 at 19:46
  • $\begingroup$ For your answer to part 2 (spoiler alert) “no, changing your answer will not increase your chances (with the same assumption of equal chances of winning)” wouldn’t it be the same claim for the original Monty Hall problem? (Each has 1/2 chance of winning) $\endgroup$ Sep 16, 2019 at 0:35
  • $\begingroup$ Perhaps I'm not thinking of it right, but in Part 2 you know A is playing D. I don't see the same situation. $\endgroup$
    – SteveV
    Sep 16, 2019 at 0:43
  • $\begingroup$ @SteveV is right. The difference between the original Monty Hall and this problem is that here, after knowing C did not win, you know for sure that D did win. After these matches teams A and D will have an equal chance to win (both 1/2). In the original problem, you know that Monty Hall opens a losing door, and he knows which door is winning. If either of the two unselected doors was correct (2/3 chance), you will win if you change your bet. $\endgroup$
    – P1storius
    Sep 16, 2019 at 14:36

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