N.Y. Comp. Codes R. & Regs. tit. 9, § 4217.14 – Triple.

(a) The triple (or other approved name) is a form of pari-mutuel wagering. Each bettor selects in order the first, second and third placed horses in the designated triple race. The triple pool shall be held entirely separate from all other pools and is not part of a daily double, exacta or other wagering pool.
(b) [Reserved]
(c) Races in which triple pools shall be conducted shall be approved by the commission and shall be clearly designated in the program.
(d) The design of triple tickets shall be clearly and immediately distinguishable from other pari-mutuel tickets.
1. (1) Failure to select, in order, the first three horses shall result in a payoff on triple tickets selecting the first two horses in order; failure to select the first two horses shall result in a payoff on triple tickets selecting the winner; failure to select the winner to win shall cause a refund of all triple tickets.
2. (2) If less than three horses finish, payoff shall be made on tickets selecting the actual finishing horses, in order, ignoring the balance of the selection.
  (g) Dead heats.
  In the event of a dead heat or dead heats, all triple tickets selecting the correct order of finish, counting a horse in a dead heat as finishing in either position dead-heated, shall be winning tickets and distribution shall be made in accordance with established pari-mutuel practice relative to dead heats.
(e) Scratch.
If a horse is scratched or declared a nonstarter, no further triple tickets may be issued designating such horse, and all triple tickets previously issued designating such horse shall be refunded and the money deducted from the gross pool.
(f) Failure to select a winning combination; short finishes.
(h) Coupled entries and fields are permitted in trifecta races. In such races no wagers may be accepted or issued (including “wheel” or “box” type bets) which couple the same coupled entry or the same field in the same combination.
(i) No triple wagering shall be conducted on any race having fewer than six betting entries. If fewer than six betting interests start, the triple shall be declared off and the gross pool refunded. If time permits, with the approval of the judges, a track may schedule exacta wagering in place of triple wagering.
(j) This section shall be prominently displayed throughout the betting area of each track conducting the triple, and printed copies of this section shall be distributed by the track to patrons upon request.