You've played in three games of zarball!

You've played in five games of zarball!

But are you game for the Royal Zarball Tournament?

This is how the tournament works:

**First Round**

A vs B = I

C vs D = J

E vs F = K

G vs H = L

**Second Round**

I vs J = M

K vs L = N

**Final Round**

M vs N = WINNER!!!!!

********

Here are the competitors and your chances of beating each of them:

You, the Prisoner

Prince - 1/1 chance as usual. You can always beat the Prince, every time

Queen- 1/2 chance as usual. You can beat the Queen half of the time

King- 1/4 chance as usual. You have a quarter chance of beating the King

Duke- 1/3

Earl- 2/3

Jester- 0. The Jester will beat you every time- I mean, all he does in his spare time is juggle! But don't worry- the Jester's only weakness is the Peasant, who beats him every time

Peasant- 1/2, except when playing the Jester. The Peasant beats the Jester every time

Except for the special cases of the Jester, Peasant and Princess, the chances stay the same for beating you when they play each other (however they must be made relative to each other).

For example, if you have a 1/3 chance of beating the Duke and a 2/3 chance of beating the Earl, it follows that the Duke is twice as good as the Earl, so if they played against one another, the Earl would have a 2/3 chance of winning, and the Duke would have a 1/3 chance of winning. However this isn't true.

Okay, so down to the actual question:

You failed to escape your imprisonment the first two chances... this is your last chance, says the King. He is allowing you to arrange the starting bracket of the Royal Zarball Tournament. Remember the key in this post- the 8 starting positions are the letters A through H.

How should you arrange the eight competitors on the bracket to give you the maximum chance of winning the Royal Zarball Tournament and go free? What is that chance? Is there more than one solution?