(FORTUNE Magazine) – Dear Annie: I am a 31-year-old executive at a company headed by a friendly but fiercely competitive CEO. We get along fine, but here's the thing: We both play racquetball, and he's mentioned repeatedly that we should play sometime. I keep putting off setting a date for a game because I'm an excellent player and I'm pretty sure I would crush him, which I'm afraid would be career suicide. Should I agree to play? If so, should I play to win? -- Killer Backhand

Dear KB: If he brings it up again, then, yes, do play. And play to win. He's not going to respect you, and may well take it as an insult, if he senses you're not really trying. Moreover, it's unlikely that the crushing victory you anticipate will do your career any real harm. Reams of psychological research show that as a rule, people like people who are similar to themselves. So the odds are, if this CEO is a real competitive-tiger type, your determination to wipe the floor with him will mark you as a kindred spirit. On the other hand, if he reacts badly to being trounced, then he's all hat and no cattle, as they say in Texas, which is valuable information to have. I've heard many managers say that they learned more about their colleagues and bosses on a golf course than they'd have figured out in a million business meetings. A showdown on a racquetball court, whoever ends up winning, could be quite illuminating.

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