On Apr 26, 9:14 pm, "David Kane" wrote:
"Jürgen R." wrote in ....

If challenger and champion have the same chance of winning
a 24-game match then the champion will retain the title
75% of the time, winning either the match or the rematch.

Because losing the match and winning the rematch *isn't* retaining
the title. It's losing the title and then winning back the title. There
is nothing in mathematics that allows us to equate the cases.

Nothing in the _mathematics_, but one certainly could change the
rules, so that if the challenger wins the match, the match isn't over
till the rematch is played. Then the champion would mathematically
have just the enormous advantage noted.

As long as we don't do that, then, you are right, a rematch is not a
problem for that reason.

But a rematch clause gives a champion an advantage just the same.

Let us suppose that instead of World Championship matches happening
after lengthy debates and a difficult process of finding an agreement
on a venue that will pay the players enough, they happened like
clockwork at fixed intervals. Perhaps every two years.

In the year X, the champion A plays the challenger B. There is also an
up-and-coming strong player C waiting in the wings. The three of them
are very nearly of equal strength.

Year X: A wins 50% of the time, B wins 50% of the time.

Case A winning in year X:

Year X+2-epsilon: B plays C for the privilege of playing for the World
Championship.

Year X+2: A plays B or A plays C. The world champion is A 50% of the
time, B 25% of the time, and C 25% of the time.

Case B winning in year X:

Year X+2: B plays A due to the rematch clause.

So in year X+2, because there's a rematch clause, the World Champion
will be:

A with probatility 50%
B with probability 37.5%
C with probability 12.5%

Without a rematch clause, the World Champion would be

A with probability 37.5%
B with probability 37.5%
C with probability 25%

If the rematch took place in year X+1, and a normal title defence
still took place normally in year X+2, not being delayed by the fact
that a rematch happened, then C wouldn't be shut out of the system
part of the time to A's benefit. A would still have a small advantage,
but at B's expense, I think.

John Savard