Key facts
- A system bet places every multi of a chosen size from your selections. The count is a combination: 4 selections make 6 doubles, 4 trebles and 1 four-fold.
- Trixie = 4 bets from 3 picks, Patent = 7, Yankee = 11 from 4 picks, Lucky 15 = 15, Canadian = 26, Lucky 31 = 31, Heinz = 57, Lucky 63 = 63, Super Heinz = 120, Goliath = 247.
- Your outlay is the unit stake times the number of bets: a $1 Yankee costs $11, and each way doubles it to $22.
- The TAB's Parlay Formula is the Australian racing version: Formula 2, 3 and 4 over 4 races makes 11 combinations, the same shape as a Yankee.
- In our calculation, with a 5% margin on every leg, a Yankee returns about 88.4% of its outlay on average, against 95.2% for a single.
What a system bet is
A system bet takes your selections and places every multi of a chosen size that they can make, as separate bets on one ticket. Pick three horses for a trixie and you are really placing three doubles and a treble. Each of those lines wins or loses on its own, so one beaten runner knocks out some lines but not all of them.
That is the whole appeal: a straight multi needs every leg to win, while a system can still pay with a loser in it. The price of that safety net is the outlay, because you pay a full unit stake for every line.
System bet types and how many bets each makes
The names come from British bookmaking, and the counts never change. A "full cover" system includes every double and upward; the "Lucky" versions add the singles too.
| System bet | Selections | Singles | Doubles | Trebles | 4-folds and up | Total bets | Cost at $1 a bet |
|---|---|---|---|---|---|---|---|
| Trixie | 3 | 0 | 3 | 1 | 0 | 4 | $4 |
| Patent | 3 | 3 | 3 | 1 | 0 | 7 | $7 |
| Yankee | 4 | 0 | 6 | 4 | 1 | 11 | $11 |
| Lucky 15 | 4 | 4 | 6 | 4 | 1 | 15 | $15 |
| Canadian (Super Yankee) | 5 | 0 | 10 | 10 | 6 | 26 | $26 |
| Lucky 31 | 5 | 5 | 10 | 10 | 6 | 31 | $31 |
| Heinz | 6 | 0 | 15 | 20 | 22 | 57 | $57 |
| Lucky 63 | 6 | 6 | 15 | 20 | 22 | 63 | $63 |
| Super Heinz | 7 | 0 | 21 | 35 | 64 | 120 | $120 |
| Goliath | 8 | 0 | 28 | 56 | 163 | 247 | $247 |
The formula behind the count
The number of k-leg multis you can build from n selections is the combination C(n, k) = n! / (k! x (n - k)!). For four selections that gives C(4,2) = 6 doubles, C(4,3) = 4 trebles and C(4,4) = 1 four-fold, so a Yankee is 6 + 4 + 1 = 11 bets. A full cover bet on n selections always holds 2^n - n - 1 lines, and the Lucky version holds 2^n - 1. We checked every row of the table above in python.
Because the count roughly doubles with each extra pick, the outlay climbs fast. Moving from a $2 Yankee ($22) to a $2 Heinz costs $114, and a $2 Goliath costs $494.
Trixie bet: a worked example
Say you put $5 a line on a trixie with three runners at $1.80, $2.20 and $3.00. The outlay is 4 x $5 = $20.
| Winners | Lines that pay | Return | Profit or loss |
|---|---|---|---|
| None or one | None | $0 | -$20.00 |
| $1.80 and $2.20 | 1 double | $19.80 | -$0.20 |
| $1.80 and $3.00 | 1 double | $27.00 | +$7.00 |
| $2.20 and $3.00 | 1 double | $33.00 | +$13.00 |
| All three | 3 doubles + treble | $139.20 | +$119.20 |
Two winners only get you out of trouble if the prices are long enough. With the two shortest runners winning, the trixie still loses 20 cents. A $2 patent on the same three runners costs $14 and returns $3.60 if only the $1.80 runner wins, $15.92 with the first two, and $69.68 if all three salute.
Yankee bet: what each result returns
A $1 Yankee on four selections at $2.00, $2.50, $3.00 and $4.00 costs $11. These returns come from our calculation:
| Winners | Return | Profit or loss |
|---|---|---|
| Any one, or none | $0 | -$11.00 |
| $2.00 and $2.50 | $5.00 | -$6.00 |
| $3.00 and $4.00 | $12.00 | +$1.00 |
| $2.00, $2.50 and $3.00 | $33.50 | +$22.50 |
| $2.50, $3.00 and $4.00 | $59.50 | +$48.50 |
| All four | $197.50 | +$186.50 |
How likely is each row? If those prices carry a 5% margin and are otherwise accurate, the four runners win 47.6%, 38.1%, 31.7% and 23.8% of the time. In our calculation the Yankee then finds no winner 16.9% of the time, exactly one winner 38.8% of the time (still a total loss), and returns more than its $11 outlay only 14.9% of the time.
Lucky 15: the yankee with singles
A Lucky 15 is a Yankee plus the four singles, so the same $1 a line costs $15. The singles are what change the picture: one winner at $4.00 returns $4, two winners at $2.00 and $2.50 return $9.50 instead of $5.00, and all four return $209. Some bookmakers add bonuses to the Lucky bets; bet365 Australia's racing rules, for example, say its Lucky 15, 31 and 63 bonuses do not apply to tote bets. Any bonus is a bookmaker promotion with its own terms, so check them on the day.
How many winners a yankee needs
At level prices it is easy to see where a Yankee turns into a profit. Each figure is the return on a $1 Yankee ($11 outlay):
| Price of every selection | 2 winners | 3 winners | 4 winners |
|---|---|---|---|
| $1.50 | $2.25 | $10.13 | $32.06 |
| $2.00 | $4.00 | $20.00 | $72.00 |
| $3.00 | $9.00 | $54.00 | $243.00 |
| $4.00 | $16.00 | $112.00 | $608.00 |
With short-priced selections even three winners from four can lose money. A Yankee only suits picks at decent odds, and only when you genuinely expect more than one to win.
System bets at the TAB: the Parlay Formula
The TAB's version for racing is the Parlay Formula. It links 2 to 6 bets across up to 6 races, and the formula number is how many of those races must be successful. Formula 1 places plain singles, and a formula equal to the number of races is an all up. You can take several formula numbers on one ticket.
The TAB's own examples line up with the table above. Formula 2 over 4 races makes 6 combinations ($6 at a $1 base), and Formula 2, 3 and 4 over 4 races makes 11 combinations, costing $11: the same structure as a Yankee. Over 6 races, Formula 3 adds 20 combinations and Formula 4 adds 15, so the pair costs $35 at $1. Pick two runners in a race, or take each way, and the TAB multiplies the combinations for that race. The TAB also says its bonus bets cannot be used on a Parlay Formula.
The margin stacks up on every line
Each line in a system is a multi, and a multi multiplies the margin. If every price carries a 5% margin, in our calculation a single returns 95.2% of stakes on average, a double 90.7%, a treble 86.4% and a four-fold 82.3%. Weighted across its lines, a Yankee returns about 88.4% and a Lucky 15 about 90.2%, because the singles pull the average up. Our page on bookmaker margin shows how to measure that margin in a market before you bet.
Each way system bets
An each way system places the whole system twice: once for the win and once for the place. An each way Yankee is 22 bets and an each way Lucky 15 is 30, so a $1 unit costs $22 or $30. The place half settles at the place price of each runner, and the each way calculator shows how those place terms work on a single.
Pundit tip: before you place any system, work out the return if only your two shortest picks win. If that number is well below your outlay, the system is a long-odds punt dressed up as cover.
Tools for system bets
The system bet calculator totals every line for any combination of winners and losers, and the multi bet calculator handles a single all up. For the other bets on an Australian betting slip, see our guide to bet types explained. If combination bets start to cost more than you planned, our gambling help page lists free, confidential support.
Frequently asked questions
How many bets are in a yankee?
A yankee is 11 bets on 4 selections: 6 doubles, 4 trebles and 1 four-fold. At $1 a bet it costs $11. Add the 4 singles and it becomes a Lucky 15, which costs $15 at $1 a bet.
What is a trixie bet?
A trixie is 4 bets on 3 selections: 3 doubles and 1 treble. You need at least 2 winners for any return. A patent adds the 3 singles, making 7 bets, so one winner still pays something.
Do system bets have better odds than a multi?
No. Each line in a system is its own multi with the same combined odds. A system spreads your money across many smaller multis, so you can collect with a loser in the mix, but you pay for that cover with a bigger outlay and the margin is charged on every leg of every line.
Can you place a yankee or lucky 15 in Australia?
Some licensed Australian bookmakers offer named system bets; bet365 Australia's racing rules mention Lucky 15, 31 and 63 bonuses, for example. The TAB offers the same idea on racing as a Parlay Formula, where you pick the formula numbers yourself.
What happens if a selection in a system bet is scratched?
That depends on the bookmaker's rules for the bet type, so read them before you bet. Once you know how the void leg is settled, a system bet calculator shows what the remaining lines would return.
Related reading
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