“My career is good,” Rutikanga told me. “I have a lot of clients.”

He is indeed always on the court when I am at Cercle Sportif. But there are not enough members and expats to sustain the dozen or so other players I know. What if Habiyambere never takes the next step? And what about all the other coaches?

Rutikanga said each would give lessons “until he dies.”

Rutikanga added: “He will give lessons, play competitions. He will continue if he doesn’t have a problem — until he isn’t capable of playing.”

Reason to Hope

Across the continent, ever since I saw that newspaper photo of an Ivorian playing tennis during my Peace Corps days, I have asked African players and coaches whether a black player from sub-Saharan Africa will reach the top 100 in the next 10 years.

Rutikanga was skeptical, saying, “We don’t have the players.”

Garanganga said he thought “the level of top African juniors participating internationally has dropped.” And Hagenimana strained to be positive. “Top 200, maybe it can happen,” he said. “Top 100? I can never say no.”

But Ben Makhlouf and Ntwali of the I.T.F. want to believe. Ntwali, who has seen Nahimana, the Burundian teenager, scale the junior rankings, was the most optimistic.

“WTA: Yes, 100 percent,” Ntwali said. “We will see some black girls coming up. For men, within five years we can get someone close to 200.”

There are days I believe, too. Especially when Habiyambere passes me with brutally paced, angled and dipped shots. Or when Rutikanga demonstrates a slight open racket face for a soft volley, the kind of instruction I would pay $75 an hour for in the United States.