Three way football tournament probability?

I'm getting the following, but I'm not totally sure.

A and B should have equal chance, whatever that chance is.

Focusing on how C can win, C can't win on "trials" 1 or 2, but can win on the 3rd "trial" if

one of the following occurs - ACC or BCC - the total prob. here is 1/4.

Then C can win on trial 6 if the following occurs - ACBACC, BCABCC - total prob of 1/32.

It looks like it continues in a similar manner - C could win on trial 9, 12, ..

And you get an infinite series 1/4 + (1/32) + (1/256) + ...= 1/4 + [(1/32) + (1/32)(1/8) + ...]=

1/4 + [1/32/ [1 - 1/8]] = 1/4 + 1/28 = 2/7.

So there is 5/7 left for A and B, which gives prob of 5/14 for A and B.

I agree with Leonard.

aa = 1/4

bcaa = 1/16

acbaa = 1/32

bcabcaa = 1/128

acbacbaa = 1/256

1/(2^2) + 1/(2^4) + 1/(2^5) + 1/(2^7) + 1/(2^8) + ...

= sum from 1/4 to 1/(2^n)

minus the sum from 1/8 to 1/(8^n)

= 1/2 - 1/7 = 5/14 = Pr(A wins)

So Pr(B) is also 5/14 and Pr(C) is 2/7.

This can also be done with a transition matrix.

You need to look at the total sample space:

0.25 for A winning a tournament in two games PLUS

0.25 for B winning after two games PLUS

0.25 for C winning after three games PLUS

THEN there is a .25 chance of a fourth game which will be between A and B with .0625 chance of A winning the tournament and .0625 chance of B winning the tournament.

so the P(A winning) = 1/4 + 1/16 + 1/64 + ... = 1/3

It appears that even though A and B play first all three of them have an equal chance of winning the tournament

Do you mean two games in a row? or two tournaments in a row?

If it's just winning two games in a row:

If they are evenly matched, there is a 50% chance of winning against team B.

Then there is a 50% chance of winning against team C.

So that's a 25% chance (1/2 * 1/2 = 1/4) of winning two games in a row, which is winning one tournament.

But if you mean two tournaments in a row, Team A gets a bye for winning the first one, so wins against the victor of Team B and C. With another 50% chance of winning that, to win three games in a row, and two tournaments:

1/4 * 1/2 = 1/8

The probability is 12.5%.

Yes! Amen to 3, 8, 10, 13 and 19!