illegal bookie; unlicensed bookmaker
Refers to an individual or operation that takes bets on horse races without official authorization, outside the legal pari-mutuel system.
The police raided an illegal bookie in the downtown area.
ノミ屋 is a more general term for an illegal bookmaker, often used for various sports or races, while 私設馬券屋 specifically refers to horse racing.
Compound of 私設 (privately established) + 馬券 (horse racing ticket) + 屋 (shop/person), literally 'private horse-racing-ticket shop'.