Absolutely, and they usually do (on their own horse, of course!)
A Lay Bet is the practice of betting money on a horse to lose to race.
A horse race in which the owner declares before the race how much the horse will be offered for sale after the race.
If the horse scratches prior to the start of the race, the bettor's wager is refunded.
When you successfully bet a superfecta. This is where you bet on the first four horses to finish the race.
John Brunetti is the current owner of Hialeah Park Race Track.
If you place a bet for a horse to win, place or show it may be as follows: If you bet the 4 horse for WPS your horse has to come in just as stated to Win the race, Place in the race first or second, or Show in the race in the first, second or third.
The owner of the famous race horse, Secretariat, was Penny Tweedy (Chenery.)
If I understand your question correctly, if only three horses race, would you win no matter what? You would only win if you bet on the winning horse to "win." When you bet on a horse race, you also bet on what position that horse finishes. You may bet on a horse to "win, place, or show" or all three (each bet costs more money). If the horse comes in first, second, or third, and you bet all three, you would still get a payout. There are numerous combinations to wagering, Exactas, Trifectas, etc. and even in a three horse race, if you didn't bet correctly, or on the right horse, you could still lose.
A claiming race means that a horse may be "claimed" by another owner/trainer for the stated claiming price for that race. The claim takes place before the race is run. The new owner must take possesion of the horse after the race is over. This prevents an owner/trainer from putting a realy good horse against lower quality horses. Nobody wants to get $5,000 for a horse worth $20,000.