One of the options in horse race betting is to bet a trifecta. You are betting that the horses your pick will finish first, second and third in that order. You can, however make things a little easier if you choose a trifecta box where you are betting a certain number of horses to finish in the top three, in any order. Let’s look at trifecta horse betting.
Offered at most racetracks in denominations as low as $1, a $1 trifecta box of horses 4-5-6 would include six $1 combinations at a cost of $6 and would pay out if the order of finish were 4-5-6, 4-6-5, 5-4-6, 5-6-4, 6-5-4 or 6-4-5.
The cost of a four horse $1 trifecta box would be calculated as follows:
(4 x 3 x2) x $1 = $24 (24 $1 combinations.)
The cost of a five horse $1 trifecta box would be calculated as follows:
(5 x 4 x3) x $1 = $60 (60 $1 combinations.)
Below follow the calculated costs of $1 trifecta boxes:
$1 trifecta box of 3 horses = 6 possible combinations = $6.
$1 trifecta box of 4 horses = 24 possible combinations = $24.
$1 trifecta box of 5 horses = 60 possible combinations = $60.
$1 trifecta box of 6 horses = 120 possible combinations = $120.
Trifecta Wheel Using One Horse as a Key
A trifecta wheel allows you to play a horse in one position in combination with all the other horses in the field to finish in the remaining two positions.
8-horse field, a $1 trifecta wheel of 3-All-All (horse three to finish first with the other 7 horses to finish second or third), would result in 42 possible $1 combinations at a cost of $42 and would pay off if horse 3 won the race and any of horses 1,2,4,5,6,7,8 finished second or third. You could also play additional trifecta wheels with the 3 horse wheeled in second or third (All-3-All or All-All-3) for the same cost of $42 each.
To calculate the cost of wheeling one horse in one position (first, second or third) with the remainder of the field to finish in the other two positions, multiply the number of horses in the field minus 1 by the number of horses in the field minus two, and multiply that number by the denomination of your bet.
To calculate what it would cost to wheel a horse in one position with ALL in the other two positions in a 6-horse field, you would multiply (5 x 4) x $1 = $20 (20 possible combinations.)
In a 7-horse field, you would multiply (6 x 5) x $1 = $30 (30 possible combinations.)
Below follows the cost of wheeling one horse in one position with ALL remaining horses in the other two positions, based on field size:
4 horse field $1 trifecta wheel = (3 x 2) x $1 = $6 (6 possible combinations.)
5 horse field $1 trifecta wheel = (4 x 3) x $1 = $12 (12 possible combinations.)
6 horse field $1 trifecta wheel = (5 x 4) x $1 = $20 (20 possible combinations.)
7 horse field $1 trifecta wheel = (6 x 5) * $1 = $30 (30 possible combinations.)
8 horse field $1 trifecta wheel = (7 x 6) x $1 = $42 (42 possible combinations.)