It is beyond comprehension how anyone can question the lack of place pool wagering in a three horse race; rather than quoting random rules, let's consider the State Regulations from Kentucky.
https://casetext.com/regulation/kent...ution-of-pools
Section 3. Pools Dependent Upon Entries for Live Horse Races.
(1) Except as provided in subsection (3) of this section, when pools are opened for wagering all associations may:
(a) Offer win wagering on all races with four (4) or more betting interests;
(b) Offer place wagering on all races with five (5) or more betting interests;
(c) Offer show wagering on all races with six (6) or more betting interests.
(d) Offer Quinella wagering on all races with four (4) or more betting interests;
(e) Offer Exacta wagering on all races with four (4) or more betting interests;
(f) Offer Trifecta wagering on all races with five (5) or more betting interests;
(g) Offer Superfecta wagering on all races with six (6) or more betting interests;
(h) Offer Big Q wagering on all races with three (3) or more betting interests; and
(i) Offer Super High 5 wagering on all races with seven (7) or more betting interests.