Can one play darts on shabbat?
And can one then do archery on shabbat, assuming there are no words or numbers on the target, and the bows remain strung throughout shabbat?
Rabbi Dovid Ribiat in his Sefer Lamed Tet Melachot - The 39 Melachot Vol. 3 Section 3/E)/h (pg. 822 in Melacha 23, Tofair) states:
"One may not stick push pins into a bulletin board whether to hang notes or for any other purpose, because of questions involving Tofair, Boneh and other Shabbos restrictions."
He bases this on a number of sources, one of which is the Biyur Halacha 340:14 DH:"Harei Zeh".
Based on this, it seems clear cut to me that darts or archery (which may also be forbidden because of hotzoah issues) would be forbidden on Shabbat or Yom Tov. As always, consult with your local Halchic authority.