Q: If I know my opponent deserved a point and lost it due to the referee's error, should I rectify the injustice by throwing the next point?
A. In order to answer this question, we have to examine the role of sports in our culture, and of sportsmanship in sports.
In sports, more than in any other area of life, the ostensible objective is completely artificial. If our true objective were to sink the ball into the basket, we would just get a ladder. If we really wanted to circle the course as fast as we could, we would doff our running shoes and hop on a motorcycle. The entire object of sports and games is to establish a conventional and artificial task, which we then "pretend" is real in order to develop our physical well-being, sharpen our skills, improve teamwork, provide an outlet for competitive desires, and so on.
The problem is that we may get so carried away with the charade that we forget the original aim. Spitballs, steroids and the like advance the fake objectives but irreparably harm the real object of the game. The solution is the ethical ideal of sportsmanship. Good sportsmanship is meant to ensure that the original, constructive goal of competition remains foremost. Someone who puts winning before earnest competition is unsportsmanlike, and ruins the game for everyone.
I think this approach solves your question. A sincere but mistaken referee's call is good luck for you, bad luck for your opponent. Luck is an unavoidable part of life, and of sports. Blowing a point in response would promote the ostensible goal of the game, equitable allocation of points, at the expense of the real goal, which is to have all participants give their best at all times.
This seemingly trivial bit of "sports ethics" has a more serious message. The dual nature of sports has a parallel in economic life. The competitive market system is based on competing for money, but this is a fake objective. The true objective is to organize the productive resources of society for the benefit of all. Business ethics is meant to ensure that the original, constructive goal of economic development doesn't get swallowed up by the wholly artificial goal of making money.
This parallel was eloquently expressed by the original theorist of markets, Adam Smith, who wrote in "Theory of Moral Sentiments" that "in the race for wealth and honors and preferments, every man may run as hard as he can, and strain every nerve and muscle, in order to outstrip all his competitors. But if he should jostle or throw down any of them, the indulgence of the spectators is entirely at an end. It is a violation of fair play, which they cannot admit of."
This message is exemplified in a fascinating and very famous story in the Talmud. When the Roman Empire conquered the land of Israel, they brought with them an impressive degree of economic development. The Talmud tells us that three leading sages sat down to discuss Roman-style progress:
"Rebbe Yehuda opened by saying, How worthy are the acts of this nation: they built marketplaces, they built bridges, they built bathhouses. Rebbe Yossi kept silent. Rebbe Shimon replied, saying: All that they built, they built only for themselves. They built marketplaces as a place for prostitutes; bathhouses, in order to pamper themselves; bridges in order to collect tolls." (1)
The kind of selfishness Rebbe Shimon is protesting is not that the marketplaces and bridges were built for utilitarian purposes, and not out of purely philanthropic interest. Judaism doesn't condemn people for advancing their self interest. He doesn't say, the Romans are not worthy of praise because they built marketplaces to trade and bridges to provide convenient transportation for themselves. This would be understandable.
Rebbe Shimon's criticism is that even the underlying utilitarian goal was not foremost. The Romans were not interested in healthy trade, but rather in debauchment; they were not interested in transportation, but only in enriching themselves. They did promote economic development, but what really interested them was a mere side effect. Rebbe Shimon risked the wrath of the Roman authorities to emphasize that this is an illegitimate approach to development.
In business, like in sports, keeping score is a legitimate and valuable way of motivating people and inducing them to give their best. But just as sportsmanship in games reminds us that winning is not what's ultimately important, business ethics reminds us that we don't win the game of life by accumulating the most "monopoly money," but rather by doing the most good with our G-d-given talents.
SOURCES: (1) Babylonian Talmud, Shabbes 33b.