A quaddie strategy decides how many runners to take in each leg from your estimate of each runner's chance, so the ticket's cost, chance of landing and share of the dividend fit your budget. It cannot pick winners, and the arithmetic is harsh. Four legs you each cover at a 50% chance land together only 0.5 x 0.5 x 0.5 x 0.5 = 6.25% of the time, about one ticket in 16.
The method has four steps: put a chance on every leg, decide where to bank and where to spread, look for runners the market underrates, and size each ticket so a long run of misses fits your budget. Quaddie betting covers how the bet works, and horse racing betting the wider race day.
Why four legs make a long shot
The legs are separate races, so their chances multiply:
chance of landing = leg 1 x leg 2 x leg 3 x leg 4
A leg's chance is the combined chance of the runners you take in it. To turn prices into chances, the simplest method takes 1 / price for every runner and scales the results to add to 100%. That proportional method shrinks every runner's chance by the same factor; other methods take more off the longshots, so the choice matters most for a roughie. With illustrative coverage, the same in every leg:
| Chance you cover in each leg | Chance the ticket lands | About one ticket in |
|---|---|---|
| 50% | 0.5 x 0.5 x 0.5 x 0.5 = 6.25% | 16 |
| 60% | 0.6 x 0.6 x 0.6 x 0.6 = 12.96% | 7.7 |
| 70% | 0.7 x 0.7 x 0.7 x 0.7 = 24.01% | 4.2 |
| 80% | 0.8 x 0.8 x 0.8 x 0.8 = 40.96% | 2.4 |
Covering 80% of every leg sounds safe, yet the ticket still misses more often than it lands. The leg you cover least does the most damage, because it multiplies against the others. So winning a quaddie comes down to covering the winner in every leg, which means spending most of your combinations where the race is hardest to call.
How many runners to take in each leg
There is no set number. Each runner you add multiplies the whole ticket's cost by the leg's new number of runners over its old number, and the jump is steepest at the bottom:
| Runners in the leg | Cost of the whole ticket | Rise |
|---|---|---|
| 1 to 2 | 2 / 1 = x 2 | +100% |
| 2 to 3 | 3 / 2 = x 1.5 | +50% |
| 3 to 4 | 4 / 3 = x 1.33 | +33.3% |
| 4 to 5 | 5 / 4 = x 1.25 | +25% |
| 5 to 6 | 6 / 5 = x 1.2 | +20% |
That curve is why a ticket need not be the same width in every leg. A banker, one runner alone in a leg, multiplies the ticket by 1, so it adds nothing to the cost, and it suits a race where one runner stands well clear. A spread leg takes several runners and suits an open race. The price of a banker is that the ticket ends whenever it loses.
A scratched banker is not refunded. Under rules 9.2(a) and 9.3 of the Tabcorp tote rules Racing and Wagering Western Australia adopted, gazetted in 2010, its money moves to the leg's most-backed runner in the win pool when that race's betting closes. The leg then runs on the tote favourite, not your pick. Exotic scratching rules works a ticket through it.
Some shapes, with the flexi a $36 outlay buys (flexi % = outlay / combinations x 100):
| Runners per leg | Combinations | Cost at $1 a combination | Flexi at $36 |
|---|---|---|---|
| 2, 5, 1, 4 | 40 | $40 | 90% |
| 3, 3, 3, 3 | 81 | $81 | 44.44% |
| 5, 5, 5, 5 | 625 | $625 | 5.76% |
| 8, 8, 8, 8 | 4,096 | $4,096 | 0.88% |
The last row is below the floor in those 2010 rules, which set the smallest flexi bet at 1c a combination, or the operator's own minimum if higher (rule 3.5(a)): 4,096 x $0.01 = $40.96. Flexi betting covers how flexi is applied, and the quaddie calculator works out any shape.
Spreading changes the swings, value changes the average
A quaddie pays from a pool, so what a combination pays depends on the money on it. Suppose that money sat on every combination in line with its true chance. Each would then return the same on average:
average return per $1 = chance x dividend = chance x dividend pool / money on it
With money on it = chance x money bet, that comes to dividend pool / money bet: the pool's payout share, the same for a 1-in-20 combination as a 1-in-2,000 one. In that pool, ticket shape only changes how the returns arrive: a tight ticket lands less often with a big share of each dividend, a wide one more often with a sliver. Neither beats the payout share, which is below $1 because the operator takes commission, unless a carried-in jackpot outweighs it.
Real pools are not that tidy, and the gap is the only place a strategy can add anything. Rate a runner above the share of the money backing it, and combinations through it should pay more than their chance deserves; rate it below, and they pay less. The useful question in each leg is which runners the market has wrong, and your answer can be wrong too. Trifecta strategy applies the same idea inside one race.
Risk: Betting involves risk. Your ratings can be wrong, a ticket built on them still needs four winners, and the commission comes off whatever shape you choose. See responsible gambling for limits and support.
Value roughies and the size of the dividend
A roughie, a long-priced runner, changes the dividend because few tickets hold it. A combination's fair dividend before commission is 1 divided by its chance. With illustrative fair chances of 40%, 15% and 52% for the winners of the first three legs:
| Leg 4 winner | Chance of the combination | Fair dividend per $1 |
|---|---|---|
| A 21% chance | 0.40 x 0.15 x 0.52 x 0.21 = 0.006552 | 1 / 0.006552 = $152.63 |
| A 6% roughie | 0.40 x 0.15 x 0.52 x 0.06 = 0.001872 | 1 / 0.001872 = $534.19 |
The roughie's combination is 0.21 / 0.06 = 3.5 times rarer and pays 3.5 times as much, so on the market's own numbers it is no better value. It becomes value only if its true chance is above the 6% the market gives it.
If its real chance is 10% and the pool backs it as a 6% chance, combinations through it return about 10 / 6 = 1.67 times the payout share on average; if it is 3%, they return half. Your rating is only an estimate of which is true, and a roughie earns its place through that estimate, never through the size of the dividend it would bring.
Risk: Betting involves risk. A 10% runner loses 90% of the time, even when it is value, and a ticket built around one can miss many quaddies in a row. See responsible gambling for limits and support.
A hypothetical quaddie, worked end to end
An illustrative meeting, not a real one, with fair chances worked from each race's prices with the margin taken out:
| Leg | Leading runners and fair chances | Rest of the field |
|---|---|---|
| Race 5 | Runner 4 40%, Runner 1 22%, Runner 7 13% | 25% |
| Race 6 | Runner 6 17%, Runner 2 15%, Runner 11 14%, Runner 3 12%, Runner 8 10% | 32% |
| Race 7 | Runner 1 52%, Runner 5 18%, Runner 3 11% | 19% |
| Race 8 | Runner 2 26%, Runner 10 21%, Runner 5 15%, Runner 12 6% | 32% |
You rate Runner 12 in Race 8 at 10% rather than the market's 6%, taking the extra 4 points from runners you would not back. Two tickets for the same $36:
| Ticket A: three a leg | Ticket B: shaped | |
|---|---|---|
| Race 5 | 4, 1, 7: 75% | 4, 1: 62% |
| Race 6 | 6, 2, 11: 46% | 6, 2, 11, 3, 8: 68% |
| Race 7 | 1, 5, 3: 81% | 1 as a banker: 52% |
| Race 8 | 2, 10, 5: 62% | 2, 10, 5, 12: 72% on your rating |
| Combinations | 3 x 3 x 3 x 3 = 81 | 2 x 5 x 1 x 4 = 40 |
| Flexi at $36 | 36 / 81 x 100 = 44.44% | 36 / 40 x 100 = 90% |
| Chance of landing | 0.75 x 0.46 x 0.81 x 0.62 = 17.3% | 0.62 x 0.68 x 0.52 x 0.72 = 15.8% |
On the market's 6% for Runner 12, Ticket B's chance is 0.62 x 0.68 x 0.52 x 0.68 = 14.9%. With illustrative dividends, three results show what each shape buys:
| Winners of races 5 to 8 | Dividend per $1 | Ticket A | Ticket B |
|---|---|---|---|
| Runners 4, 2, 1 and 10 | $142.60 | $142.60 x 36 / 81 = $63.38 | $142.60 x 0.90 = $128.34 |
| Runners 4, 2, 5 and 10 | $412.80 | $412.80 x 36 / 81 = $183.47 | $0: the banker lost |
| Runners 4, 2, 1 and 12 | $496.20 | $0: no Runner 12 | $496.20 x 0.90 = $446.58 |
On your rating, Ticket B lands almost as often as Ticket A, 15.8% against 17.3% (14.9% on the market's numbers), and holds twice its share of each dividend. It spends its combinations on the open Race 6 and on Runner 12, and banks the Race 7 favourite, which is its weakness: Ticket B is out whenever Runner 1 loses, 48% of the time, as in the second row.
Twice the share is not twice the return. Every combination on Ticket B runs through that 52% favourite, so the dividends it lands are smaller on average, and if the market's chances are right the two $36 tickets return the same on average. Ticket B's only extra is Runner 12, which 2 x 5 x 1 x 1 = 10 of its 40 combinations run through. If your 10% is right, Ticket B averages (30 + 10 x 10 / 6) / 40 = 1.17 times Ticket A's return.
Risk: Betting involves risk. Ticket B's extra return rests on your 10% for Runner 12 being right, and either ticket misses more than four times in five. See responsible gambling for limits and support.
Splitting a budget across quaddies
Quaddie tickets miss most of the time, so how you divide a budget matters too. Two ways to spend the same $40 you have already set aside, on tickets with an illustrative 15% chance each and dividends of a similar size:
| Plan | Chance one or more lands | Share per landed ticket | Average dividends |
|---|---|---|---|
| One $40 ticket at 100% on one quaddie | 15% | 100% | 0.15 x 1.00 = 0.15 |
| Four $10 tickets at 25%, one on each of four quaddies | 1 - 0.85 x 0.85 x 0.85 x 0.85 = 47.8% | 25% | 4 x 0.15 x 0.25 = 0.15 |
The average is the same; the second plan swaps one large share for smaller, more frequent ones, so results swing less. It is a way to divide a budget set before the day, not a reason to play more quaddies. The early quaddie and the main quaddie on one card are separate pools, so the same arithmetic applies. Two $20 tickets at 50%, one in each, land at least once 1 - 0.85 x 0.85 = 27.75% of the time, for the same 2 x 0.15 x 0.50 = 0.15 average.
Runs of misses are long even for well-built tickets. At a 6.25% chance a ticket, 20 misses in a row happen 0.9375 to the power of 20 = 27.5% of the time, and 40 in a row 7.6%.
Choose an outlay small enough that 40 misses in a row would not use up your budget, and leave it unchanged after misses: raising it after a dry spell buys the same chance of landing at a higher cost. Bankroll management covers setting the budget, and a deposit limit on your betting account puts a ceiling on it.
Risk: Betting involves risk. Splitting a budget smooths the swings without changing the average, and unless your ratings beat the pool's or a carried-in jackpot outweighs the commission, that average is below what you stake. There is no guarantee of profit. See responsible gambling for limits and support.
Shaping mistakes, and when to skip a quaddie
- Spreading every leg the same. Three runners a leg treats a 52% favourite and an open handicap alike, and pays for it in combinations.
- Adding runners for comfort. A fourth runner in a three-runner leg costs a third more on the whole ticket.
- Banking a runner you rate no higher than the market. It cuts the cost, but it rests the whole ticket on one race without adding value.
Skip the quaddie when your ratings match the market in every leg: with no runner rated above the money backing it, the shape of the ticket changes only the swings, and the pool's payout share sets the average.
Leg prices on the Terminal
On the Terminal, prices from 40+ bookmakers across racing and sports sit beside Betfair back and lay, and for racing, value is judged against Betfair's own market, one way to turn each leg into fair chances. Like any tote dividend, a quaddie dividend cannot be compared before it is declared. The Terminal's prices come from reads on a repeating cycle and can trail a bookmaker's own, so check each price in your account before betting.
Betfair prices start with Terminal View, and a free account opens a limited view of the Terminal with live odds; plans and pricing sets out what each plan shows. Betfair is a trade mark of its owner, and B337 is not affiliated with it. For free and confidential support call 1800 858 858 or visit gamblinghelponline.org.au.
Risk: Betting involves risk. A fair chance built from the exchange is an estimate, and a ticket built from good estimates still needs four winners in a row. See responsible gambling for limits and support.