System bet calculator: lines, outlay and returns for a Trixie, Yankee or Lucky 15

How to use the system bet calculator

Pick a named bet from the list, or choose Custom to set your own number of selections and the smallest and largest combination. Enter the stake per line and the decimal odds for each selection, then mark each one as Won, Lost or Void. The calculator counts the lines, shows the total outlay and adds up every line that won. The table under the results breaks the return down by doubles, trebles and bigger combinations, so you can see which part of the bet did the work.

Custom mode covers any "n from k" bet. Five selections with doubles to doubles is all 10 doubles. Six selections with trebles to trebles is all 20 trebles. Four selections with singles to 4-folds is the same as a Lucky 15.

System bet types and how many lines each has

Every named system bet is a full cover: it takes every combination from a starting size up to one big multi of all the selections. The line counts below are simple combination counts, checked in our calculation.

The cost climbs fast. Going from a Heinz to a Goliath adds two selections and more than quadruples the outlay, because the number of combinations roughly doubles with each extra selection.

Worked example: a $1 Yankee with three winners

You take a $1 Yankee on four selections at $2.00, $3.00, $1.80 and $4.00. That is 11 lines, so the outlay is $11. The first three win and the $4.00 selection loses.

In our calculation the bet returns $25.80, a profit of $14.80. Those are the default figures in the calculator above, so you can change one result and watch the return move.

The system bet formula

Each line pays the stake times the product of its odds, but only if every selection in that line won:

return = stake x sum of (odds of leg 1 x odds of leg 2 x ...) over every winning line

lines = C(n, smallest) + ... + C(n, largest), where C(n, r) is the number of ways to choose r selections from n.

For a Yankee, C(4,2) + C(4,3) + C(4,4) = 6 + 4 + 1 = 11. For a Goliath, the sum from doubles to the 8-fold is 247. A full cover from singles always comes to 2 to the power of n, minus 1: that is why a Lucky 15, Lucky 31 and Lucky 63 have those names.

Yankee, Lucky 15 or one big multi?

The same four selections can be backed three ways for a similar outlay. Here is what each returns in our calculation, using the prices from the worked example. The multi is an $11 four-leg multi so that it costs the same as the Yankee.

The multi pays far more when everything wins and nothing when anything loses. The system bets give up most of that top prize in return for something back from a partial result. Note that two winners at these prices still lose money on both system bets: cover is not the same as profit. Our multi bet calculator shows the chance that every leg of a multi wins, which is usually lower than it feels.

System bets on Australian racing: the TAB Parlay Formula

Australian tote betting has its own version. The TAB describes a parlay as reinvesting "the winning dividends from one race to a bet on a subsequent race", over up to six races. You choose a Formula number, which is the number of races each combination must win. A Formula 3 over 4 races gives four 3-race combinations. When the Formula number equals the number of races, the TAB calls it All Up, and Formula 1 is a set of separate single bets.

The TAB's ready reckoner shows a full cover over 4 legs is 15 combinations at $1: 4 singles, 6 doubles, 4 triples and 1 quadruple. That is a Lucky 15 by another name. Each way parlays grow much faster, with 80 combinations at $1 each way over 4 legs, because each leg can count as a win or a place. The TAB describes parlays in terms of dividends, and a tote dividend is only declared after each race, so use the calculator with the declared dividends to check a result, or with fixed prices if your bookmaker offers a fixed odds version. The each way calculator handles the win and place halves of a single runner.

Pundit tip: a system bet is a bundle of multis, and every one of those lines carries the bookmaker's margin on each leg. More lines means more margin paid, not more value.

Void legs, dead heats and scratchings

When one leg of a multiple bet is voided, the rules we checked keep the rest of the bet alive. The NSW rules for bookmaker declared betting events void only "the affected leg(s)" when, for example, a venue change hits one leg. The TAB says that when a refunded same game multi is a leg in an all up multi, the all up odds are recalculated with the remaining legs. The calculator treats a Void selection as a winner at odds of 1.00, which gives that result, but check your own bookmaker's rules. If a leg dead heats, the same NSW rules recalculate that leg's return first, so enter the reduced odds for that leg: our dead heat calculator works them out.

If you want the reasoning behind each bet type before you use the numbers, our guide to system bets covers when they are offered and how they are settled. Betting on several outcomes at once is still betting more money in total, so set a budget for the outlay, not the line stake. If it stops feeling like entertainment, free help is available.

Related reading

Betting System bets A system bet turns a handful of picks into every double, treble and bigger multi they can make. Here is how many bets each type holds, what it costs and what it pays. Read more Calculator Each way calculator See exactly what an each way bet pays if your runner wins, runs a place or misses, and when the place half actually covers your outlay. Read more Calculator Exacta calculator An exacta needs the first two home in the right order. Count your combinations, see the cost of a full unit, turn any outlay into a flexi percentage and check your collect. Read more Calculator First four calculator The first four needs the first four runners in exact order. See what a box or standout really costs and your flexi share of the dividend. Read more Calculator Quinella calculator A quinella pays if you pick the first two in any order. See what any quinella box costs, your flexi percentage and what you collect. Read more Calculator Boxed trifecta calculator Work out what a boxed or standout trifecta costs, your flexi percentage for any outlay, and what you collect when the dividend is declared. Read more