Homework SourseThere are two teams of ghters Team A and team B Team A has t
There are two teams of ghters: Team A and team B. Team A has the following players; Rhonda, Cat, and Julianna. Team B has Holly, Miesha, and Amanda. We know the following information. Holly will always beat Cat, Miesha will always beat Julianna, Cat will always beat Amanda,and Rhonda wil lalways beat Miesha. Inevery other possible match,each player has a 50% chance of winning. In the next event there will be two, equally important, ghts (ght i and ght ii), so each team must select two different ghters - one for ght i and one for ght ii. Determine the best strategy to select ghters for each team, and state if team A or team B has an advantage. Hint 1: Each team has six possible pairs of ghters. Hint 2: Suppose that the value of winning a ght is 1 and the value of losing is -1. The ghts where each ghter has an equal chance have an expected value of 0.
Solution
Team A :
expectation of win for Rhonda = +1 ..
expectation of win for Cat = -1 + 1 = 0..
expectation of win for Julianna = -1...
so, they should select Rhonda and Cat!
Team B :
expectation of win for Holly = +1 ..
expectation of win for Miesha = -1 + 1 = 0..
expectation of win for Amanda = -1...
they should select Holly and Miesha!
for the 1 st fight...Best strategy is to pick the strongest player!
A should choose Rhonda and B should choose Holly !
for the 2nd fight, Cat and Miesha!
as you see the expectations are exactly the same for both the teams!
so, one team doesn\'t have any advantage over the other!
like this, you can formulate in excel!
| Rhonda | Cat | Juliana | Total | |
| Holly | anybody | holly | anybody | = +1 ( note that : this is holly\'s total expectation) |
| Miesha | rhonda | anybody | miesha | = -1 + 1 ( miesha\'s total exp) |
| Amanda | anybody | cat | anybody | = +1 ( amanda \'s total exp) |
| Total | =+1 ( rhonda\'s total) | =-1 + 1 =0 ( cat\'s total) | = -1 ( juliana\'as total) |
