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DOI: 10.1145/2492007.2492030
Peter Winkler
Puzzled
Wins in a Row

Each of these puzzles involves game-playing strategy. If you are sufficiently clever—and sufficiently unmotivated to work hard at being clever—you can solve them all without resorting to algebra. Here is the premise: You have applied to join a chess club and been told that to qualify you must play three games against Ioana (the last new member), winning two games in a row. “Who gets the white pieces?” you ask and are told you and Ioana alternate and you get to decide whether to start with white or with black.

1.Knowing that the probability of beating Ioana is better with the white pieces (first-move advantage), should you choose white or black for the first game?

2.Suppose now that prior to the match, you
discover Ioana is a former
City Champion of Bucharest.
Complaining, you persuade
the club to give you the
following concession:
You must still beat Ioana
two games in a row, but now
you get to play her as many
as 17 times, alternating
sides as before. Should you
choose white or black for
the first game?

3.You managed to win two games in a row
from Ioana and are now
a member of the club.
However, to become an officer
of the club, you must beat
Ioana 10 times in a row,
with 49 games to do it. Yipes!
This may be more than you
can handle, but to maximize
your chances, should you start
with white or with black?

Readers are encouraged to submit prospective puzzles for future columns to [e-mail]. Peter Winkler ( [e-mail]) is William morrill Professor of mathematics and computer Science at Dartmouth college, hanover, nh.