Women are allowed to try and qualify for snooker tour, but nobody has managed it yet. Reanne Evans was even given a place on the main tour without having to qualify.
She won 61 consecutive matches in the women's game, but failed to win a single match on the 'main' tour. That's how big the gap is at the moment.
The problem is that, generally, women at the moment are of a lower standard than the men, in both darts and snooker.
This has nothing to do with any sort of ridiculous notion that women cannot play such sports, but, in my opinion, because they simply aren't offered the chances and encouragement when they are younger that men are.
More men are encouraged to give darts, snooker etc. a go when they are children; if they express an interest they are more likely to be encouraged rather than put down: therefore they get more practice time, more confidence etc.
Hopefully the increased coverage of the women's games will inspire more to take them up. I suspect it will take a few years, but in five or perhaps ten years time I'd expect to see women competing with men at a good level in both darts and snooker.
en.wikipedia.org/wiki/Reanne_Evans
"After winning 61 consecutive women's matches and defeating reigning world champion John Higgins 4–3 at the 2009 Six-red World Championship,[8] Evans was awarded a wild card on the professional main tour for the 2010–11 season, enabling her to enter all ranking events at the qualifying stage. This made her the first woman to play on the main snooker tour since Allison Fisher in 1994–95.[9][10][11] Evans failed to win a match throughout her season on the tour, suffering 18 consecutive defeats.[12] She entered Q-School, but was unable to qualify for the main tour in the 2011–12 season.
"In the 2012–13 season, Evans won enough Q-School matches to earn a "top-up" place in the qualifying rounds for the 2013 Wuxi Classic, competing as an amateur.[13][14] In her qualifying match, she defeated Thailand's Thepchaiya Un-Nooh 5–4 to become the first woman to reach the final stages of a professional ranking snooker tournament.[15] Originally scheduled to play world number 2 Neil Robertson in the last 64, she then became one of four players selected to play an extra wildcard round against local Chinese opponents, a system she publicly criticized.[16] She traveled to Wuxi and played Chinese teenager Zhu Yinghui in the wildcard round, but lost 2–5.[7]
"In March 2015, Evans has been awarded a place in the qualifying rounds of 2015 World Snooker Championship.[17] She lost her opening match 8–10 to 1997 world champion Ken Doherty.[18]"