Combination Tricast Cost: Permutation Formula and Price Tables
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A straight tricast asks you to name the first three finishers in exact order. Get one position wrong and the bet is dead. A combination tricast – the reverse tricast in betting shop shorthand – covers every possible ordering of your selected horses across the first three places. The coverage is comprehensive. The cost is fierce. Three selections produce 6 permutations. Five selections produce 60. Eight selections hit 336. I have watched punters add horses to their combination tricast slip as casually as adding items to a shopping list, then look genuinely startled when the Tote terminal shows a three-figure ticket price.
This is one bet where doing the maths before you queue is not optional – it is essential.
How Combination Tricast Permutations Multiply
The formula is n x (n-1) x (n-2), where n is the number of horses you select. Three positions, each with one fewer candidate than the last. With three horses you get 3 x 2 x 1 = 6 orderings. That is every possible arrangement of those three runners across first, second and third. Manageable, affordable, sensible.
Add a fourth horse and the count jumps to 4 x 3 x 2 = 24. Four times the permutations from one extra selection. A fifth horse takes you to 5 x 4 x 3 = 60. At this point you are holding sixty separate bets on a single race, each needing a specific three-horse order to land. The average Flat field in 2025 ran at 8.90 runners, so selecting five out of nine is actually a reasonably high-coverage play – but 60 permutations at a pound is 60 pounds committed to one race.
The multiplying effect of adding selections to a combination tricast is significantly steeper than the equivalent effect on a combination forecast. In a forecast you fill two positions, so each added horse increases permutations by 2 x (previous n). In a tricast you fill three positions, and the third multiplier compounds the growth. That is why I always recommend that anyone considering a combination tricast does the multiplication before deciding how many horses to include – never after.
Combination Tricast Cost Table: 3 to 8 Selections
Below are the figures I keep pinned above my desk, covering the practical range. At a 1-pound unit: 3 selections produce 6 permutations for 6 pounds, 4 selections produce 24 for 24 pounds, 5 selections produce 60 for 60 pounds, 6 selections hit 120, 7 selections reach 210, and 8 selections generate 336 permutations for 336 pounds. At a 2-pound unit, double every figure. The Jump average field in 2025 was 7.84 runners, which means a combination tricast covering eight selections on a National Hunt race is essentially covering the entire field.
Look at the jump from 5 to 6 selections: 60 to 120 permutations. Your cost doubles for one additional horse. From 6 to 7 it nearly doubles again. By eight selections you are spending 336 pounds at a one-pound unit on a single race. Unless you are playing at a festival where tricast pool sizes regularly run into six figures, the dividend is unlikely to justify that outlay on any consistent basis.
My personal ceiling is four selections. Twenty-four permutations at a pound keeps the ticket at 24 pounds – a level I am comfortable with on competitive races where the form points to a group of closely matched runners. If I cannot narrow the first three places to four horses, I do not force a combination tricast. I switch to a trifecta wheel with a key horse, which controls cost by fixing one position rather than covering every arrangement.
Combination Tricast vs Trifecta Wheel: When to Choose Which
I get this question at least twice a week from readers: is a combination tricast just a trifecta wheel by another name? No – and the cost difference explains why. A combination tricast takes your selected group and covers every permutation of those horses in the first three places. No horse is anchored. A trifecta wheel keys one horse in a fixed position and wheels the field – or a subset – through the remaining positions.
Take a 10-runner race where you fancy four horses. A combination tricast on those four costs 24 permutations. A trifecta wheel keying one of those four in first and wheeling the other nine runners through second and third costs (9) x (8) = 72 permutations. The wheel is more expensive in this case because it covers the entire remaining field rather than a restricted group. But if you key one horse and wheel just the other three fancied runners through second and third, the cost drops to 3 x 2 = 6 permutations – a quarter of the combination tricast’s 24.
The trade-off is positional conviction. A combination tricast says: I am confident these four horses will fill the first three places, but I cannot order them. A trifecta wheel says: I am confident this one horse wins, and I will cover a range of possibilities for second and third. Neither is inherently better. The right choice depends on whether your strongest opinion is about a group or about an individual.
Where the combination tricast truly earns its place is in races where no single horse stands out as the likely winner but a cluster of three or four are clearly superior to the rest of the field. Novice hurdles with unexposed improvers, small-field Grade 1 chases where the market is tight, five-runner Listed races on the Flat – these are the situations where covering every ordering of a compact group makes more sense than trying to anchor a key horse.
For larger fields, the trifecta wheel almost always wins on cost efficiency. A trifecta wheel cost calculator will confirm that keying one horse and wheeling five or six selections through the remaining positions costs a fraction of a combination tricast on the same number of horses, while still giving you substantial coverage across the most likely finishing combinations.
Reading the Cost Before You Commit
The tables above exist for one reason: to stop you from building a ticket you cannot afford. Combination tricasts are seductive because the logic is simple – pick your horses and cover everything. But “cover everything” has a price that rises faster than most punters expect. Every horse you add does not just create new combinations with the existing field; it creates new combinations with every pair already on the ticket, and those pairs multiply into triplets at an alarming rate.
Before your next meeting, decide your per-race budget. Look up the permutation count for your intended number of selections. If the cost exceeds the budget, drop one horse or switch to a wheel structure. The maths is simple enough to do in your head, and the few seconds it takes can save you from a ticket that eats your entire session bankroll on a single race.
What is the maximum number of selections practical in a combination tricast?
For most bankrolls, four selections producing 24 permutations at a one-pound unit is the practical ceiling. Five selections cost 60 pounds per unit and six cost 120 pounds. Beyond four, the cost escalates so steeply that a trifecta wheel with a key horse usually offers better value for the same spend.
Does a combination tricast pay the same dividend as a straight tricast?
Yes. Both draw from the same Tote tricast pool. The declared dividend is per winning unit – a combination tricast holder with the correct result receives the same per-unit payout as a straight tricast holder. The difference is that you paid for multiple permutations to capture the winning one, so your net profit is lower by the cost of the non-winning permutations.
Created by the ”Horse Racing Wheel bet Calculator” editorial team.
