When a race results in a dead heat, the dead heat shall not be run off. When two horses run a dead heat for first place, both win and place pools shall be distributed as place pools; when two horses run a dead heat for second, one-half the place pool shall be distributed among the holders of place tickets on the winning horse, and one-quarter of the place pool shall be distributed among the holders of place tickets on each of the two horses finishing second. In each such case, the show pool shall be distributed among the holders of tickets for show on the first three horses which finish. In the event of a dead heat for show, one-third of the show pool will be distributed among holders of tickets on the horses which dead heat for third.