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Vladimir Ulanowsky is playing Keith Smithson in atwo-game chess match. Winning a game scores 1 match 19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1029 point, and drawing a game scores 12match point. After thetwo games are played, the player with more match points isdeclared the champion. If the two players are tied after twogames, they continue playing until someone wins a game(the winner of that game will be the champion). Duringeach game, Ulanowsky can play one of two ways: boldly orconservatively. If he plays boldly, he has a 45% chance ofwinning the game and a 55% chance of losing the game. Ifhe plays conservatively, he has a 90% chance of drawing thegame and a 10% chance of losing the game. Ulanowsky’sgoal is to maximize his probability of winning the match.Use dynamic programming to help him accomplish thisgoal. If this problem is solved correctly, even thoughUlanowsky is the inferior player, his chance of winning the match is over 12. Explain this anomalous result.

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 100P

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Vladimir Ulanowsky is playing Keith Smithson in a
two-game chess match. Winning a game scores 1 match

19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1029

point, and drawing a game scores 1
2
match point. After the
two games are played, the player with more match points is
declared the champion. If the two players are tied after two
games, they continue playing until someone wins a game
(the winner of that game will be the champion). During
each game, Ulanowsky can play one of two ways: boldly or
conservatively. If he plays boldly, he has a 45% chance of
winning the game and a 55% chance of losing the game. If
he plays conservatively, he has a 90% chance of drawing the
game and a 10% chance of losing the game. Ulanowsky’s
goal is to maximize his probability of winning the match.
Use dynamic programming to help him accomplish this
goal. If this problem is solved correctly, even though
Ulanowsky is the inferior player, his chance of winning the

match is over 1
2
. Explain this anomalous result.

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