Since the thunder-level shock of Serena Williams hobbling away from her showdown against Maria Sharapova with a pectoral injury, there still might be a Russia-United States climax to this French Open.

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Williams on Tuesday expressed satisfaction with early medical opinions on her injury and might yet make it to Wimbledon. Meanwhile, there is plenty of drama left in this tournament.

Certainly, the Americans will be there at the finish, as Sloane Stephens secured a semi-final spot against her compatriot and friend Madison Keys with a so-easy 6-3, 6-1 win on Court Philippe-Chatrier over the Russian shot-maker Daria Kasatkina. Keys, who lost to Stephens in the 2017 US Open final, booked her spot with a more difficult 7-6- (5), 6-4 win over the player who put Johanna Konta out of these championships in the first round, Yulia Putintseva.

They have a clear day to rest ahead of their rematch on Thursday, while on Wednesday the world No1, Simona Halep, looks in good shape to beat the resurgent Angelique Kerber in the first quarter-final, and Sharapova will be buzzing after her walkover gift from Williams, to take on the reigning Wimbledon champion, Garbiñe Muguruza.

A Halep-Sharapova semi-final looks likeliest from those options – and Stephens might just have enough on Keys to reach the final ahead of them.

After taking just 70 minutes to dismiss the artful Kasatkina, she said, “I’m super-excited again to have my best result here. Being in another semis of a slam is amazing.”

Asked how she and Keys might avoid each around the locker room before playing such a high-profile match again, she said, “When we get on the court, it’s time to compete. But, before that, we are not going to be weird and awkward. Now I just have to go find her, because I need to tell her some juicy stuff.

“ I think everything will be normal. And then when we get on the court. Until then, we’re the same girls as always.”

As for her demolition of Kasatkina, the 14th seed, she realised what she had to do from the first ball, and that was to nullify her opponent’s brilliance.

“I knew I had to come out and keep swinging,” she said. “Sometimes I start well and sometimes a little sluggish. I knew I needed to keep swinging no matter what, even if it was very close. When I got my opportunity at 4-3 to break, I was like, It’s go time.”

Keys had to work harder for her win and said later, “I was down a break in the first so, to be able to get that back and play a lot better after that, was really great.”

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She said she drew on previous battles here to maintain her composure under pressure. “Being down a set point against [Naomi] Osaka the other day and being able to win that point in the tie-breaker, those are the moments where you feel, like, you get through it, and that just helps you later in the tournament.”

She confirmed rumours, also, that her coaching arrangement with Lindsay Davenport had changed.

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“She’s no longer going to be ‘the’ head coach, but I will always have a relationship with Lindsay. And whenever she’s at a tournament, she will be around and be helping out. And there’s still going to be weeks where she’s going to be there.”

And as for her ongoing rivalry with Stephens, she is comfortable with the prospect of being thrown into matches with her on a serial basis.

“We don’t really have boundaries. I don’t think that’s going to change. That’s never really stopped us before, so I don’t think we’re going to have that issue. That would just be weird and awkward. Before every match, no matter who the opponent is, I’m trying to get used to how they play. I lost to Sloane at the US Open, but I feel on clay it’s a little bit of a different match-up.”