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I found the wording in this problem confusing. I was on the verge of marking the puzzle as “flawed”.

Initially I thought that by “play hard” the setter would mean “play to win”. i.e. the prize money a team would get by winning the match was better than they would get for a draw. But if you go down that route it’s not possible to always choose a 5th match such that both teams are required to “play hard” in the final match. (You can relax what “essential” means, but that still won’t lead you to the required answer).

Instead, by interpreting “play hard” to mean “play to not lose”, we can always choose a 5th match such that both teams in the final match are required to “play hard” (i.e. try not to lose), and this route leads to the required answer.

This Python program runs in 44ms.

Solution:It is essential to have MvN as the fifth match in 10 (out of 81) cases.