I think that I didn't quite get the figures right.

With no rematches, if we have three chessplayers of equal ability who
are the contenders for the World Championshp over three cycles, with A
the champion and B the challenger, and C the outsider, in the first
year, we have:

Year X: A faces B.
A is the new champion, 50%
B is the new champion, 50%

if A wins:
Year X+2:
B is the challenger, 50%
C is the challenger, 50%

so
A remains champion: 50%
B becomes champion: 25%
C becomes champion: 25%

and if B wins, the symmetric equivalent is true, so indeed we get:

A is champion: 37.5%
B is champion: 37.5%
C is champion: 25%

In the year X+4, the three possible cases are the same as those above,
and so we just convolute them again:

A = .375 * .5 + .625 * .25
B = .375 * .5 + .625 * .25
C = .25 * .5 + .75 * .25

for

A: 34.375%
B: 34.375%
C: 31.25%

With rematches, if B wins in year X, the case in year X+2 becomes B
plays A with 100% probability, so the combination of the two cases is
then:

A is champion: 50%
B is champion: 37.5%
C is champion: 12.5%

The histories a

AA: 25% - and no rematches
BA: 25% - B gets a rematch
BB: 25% - and no rematches
AB: 12.5% - A gets a rematch
AC: 12.5% - A gets a rematch

So in year X+4, we have the possibilities

AAA: 12.5
AAB: 6.25
AAC: 6.25
BAA: 12.5
BAB: 12.5
BBB: 12.5
BBA: 6.25
BBC: 6.25
ABA: 6.25
ABB: 6.25
ACA: 6.25
ACC: 6.25

which add up to

A: 43.25%
B: 37.5 %
C: 18.75%

which is a considerable advantage to A, and an even more considerable
disadvantage to B, in year X+4 compared to

A: 34.375%
B: 34.375%
C: 31.25%

without rematches.

But if we think that rematches are a valid thing, since the changing
of the guard should be truly decisive, if we separated the rematch
from the regular title defense by having it take place between normal
title defenses, and in addition to them, then the advantage given the
champion is considerably mitigated.

Here, we have:

First, in year X, A meets B, each one wins with probability 50%.

If A wins, then in year X+2, A meets either B or C with probability
50% as in the cases above.

If B wins, then B plays A in year X+1, each one winning with
probability 50%.

So the cases in Year X+2 a

AA: 25%
AB: 12.5%
AC: 12.5%
BaA: 12.5%
BaB: 6.25%
BaC: 6.25%
BbB: 12.5%
BbA: 6.25%
BbC: 6.25%

leading to the chances of each player being the World Champion in that
year as:

A: 43.75%
B: 31.25%
C: 25%

compared to

A: 50%
B: 37.5%
C: 12.5%

with rematches, and

A: 37.5%
B: 37.5%
C: 25%

without rematches.

So the inequality is much more limited, and it affects only B, and not
C, if rematches are made ancilliary.

John Savard