Each team has three players ranked 1 through 3, where the player ranked 1 is the strongest player of the three, and rank 3 is the weakest. In the tournament, each player from one team is paired against one player from the opponent in a head-to-head match. If a player’s ranking is A and his opponent’s ranking is B, then the first player’s probability of winning the match is B ÷ (A + B).
The Nets win the coin toss, which gives them the privilege of determining the pairings.
What is the Nets best pairing strategy, and using that strategy, what is their probability of winning the tournament by winning a majority of the matches?
pairings=perms(1:3);
for i=1:length(pairings)
teamB=pairings(i,:);
expected=0;
for member=1:3
expected=expected+ ...
teamB(member)/(member+teamB(member));
end
fprintf('%2d %2d %2d %10.8f\n',teamB,expected)
end
finds, if each of the respective rankings of the opponents' team vs 1, 2, 3 rankings of their own team, the expected value of number of wins is:
opponents expected
vs your number of
1 2 3 wins
3 2 1 1.50000000
3 1 2 1.48333333
2 3 1 1.51666667
2 1 3 1.50000000
1 3 2 1.50000000
1 2 3 1.50000000
The optimum strategy is to pit you own no. 1 against the opponents' no. 2; your own no. 2 vs their no. 3 and your no. 3 against their no. 1.
|
|
Posted by Charlie
on 2024-12-15 14:49:14 |
computer-aided solution
