Caroline Wozniacki has the most to win.
She already is the women's No 1, but that descriptor comes with the oft-repeated clause: "despite never winning a major championship".
Her form seems to have sharpened. She won the Brussels Open on Sunday, her fourth championship of the year but first in four tournaments and first on clay.
She enters a French Open with a less-than-imposing women's draw.
Kim Clijsters is back but hasn't played since Miami, two months ago, and is making her first appearance at Roland Garros in five years. Serena and Venus Williams are not there, the first major without both since 2003.
Wozniacki must recognise her big chance.
The fly in the ointment? She has a baulky thigh; she called for medical treatment in the third set of her Sunday victory. "It is fine," she said. "There are no big problems. It was a small pain. I just didn't want it to get bigger."
Samantha Stosur, finalist a year ago, is in her half of the draw, as is Julia Goerges, who has two victories over Wozniacki this year.
But those are not names to be confused with "Serena", "Venus" or "Justine".
We will not remember "weak field". We will recall "first slam championship".