Q: Are we allowed to raffle off prizes at a party or youth group on Shabbos or Yom Tov?
A: Chazal prohibited holding raffles on Shabbos and Yom Tov, because it is like buying and selling (Rambam, Hil. Shabbos 23:17; O.C. 322:6).
Mishnah Berurah (322:25) cites from Magen Avraham (322:9) that even for purposes of mitzvah, raffles are not allowed on Shabbos (but may be permitted on Yom Tov when they cannot be done beforehand).
Nonetheless, Magen Avraham allows holding a lottery to choose who should get an aliyah or be chazzan, because nothing tangible is granted, like the lottery in the Beis Hamikdash which Kohen would do the daily avodah. Nonetheless, some authorities do not allow even this lottery by choosing paper notes but rather by counting fingers or opening a sefer and choosing by page number or the first letter on the page (M.B. 322:24; Shemiras Shabbos K’Hilchasah 16:48).
Therefore, one should not raffle off prizes on Shabbos, even for the purpose of a mitzvah, such as father-son learning (Orchos Shabbos 22:112-113).
However, Ketzos Hashulchan (146:32[70]) understands that Shevus Yaakov might allow raffles done verbally without paper notes so that in cases of need, one who raffles off prizes verbally for the purpose of a mitzvah has what to rely on (Piskei Teshuvos 322:10[106-109]).