By Tony Kelzenberg

Since I was a kid, math has always been “my go,” and I have studied the probability of the horse races since my early twenties. In this article, I will propose Quaddie ticket making that I call a “single/shotgun approach.”

Basic Game Probability
How familiar are Aussies with the game show “Let’s Make a Deal (LMAD)?” The basic premise is a contestant (usually dressed up in a festive costume), is selected by the show’s producers to play in a game sequence in front of the cameras. In the first phase of a LMAD game, the contestant works with the show’s host on an easy game where the contestant would be hard pressed not to win at least $500. After reaching this level of competence, the host will ask if the player would like to get an even LARGER prize while forfeiting the $500 – the catch being the prize is hidden behind curtain #1, #2 or #3 (in other words, the contestant has three choices). One of the other curtains hides an acceptable parting gift, and one of the three curtains contains a prize worth less than $40 – this is called a “Zonk.”

In the above case, the contestant has a 1 in 3 chance in winning, and a 2 of 3 chance of losing value (the parting gift is designed to be a small loss). What does this have to do with the Quaddie? The Quaddie is 4 rounds of potential “Zonks,” where a horse can win that we either could not afford to use on our Quaddie tickets, or was a horse we just didn’t like. Our goal as players is to minimize our potential outlays in Quaddie betting capital while maximizing our profit potential when we do win.

Quaddie Probability and Risk
In any probability game of “fair pieces,” whether it be horses, fair dice, or un-manipulated card games, what happened in the past does not affect future games. In other words, the first race in the Quaddie will not affect the second, third or fourth race of the Quaddie. That helps us as players, because it makes much easier to estimate the risk of a Quaddie play.

Suppose that we choose three horses in each race of the bet, and we estimate we have a fifty percent chance (1/2) on winning each of the four races. As the field sizes increase it would be hard to come up with a ticket based on three horses that can secure a 50% chance for EVERY race, but I just want to set a baseline.

The win probability on getting all four races correct would be the multiplication of the win probabilities for all four races (this is where the independent race assumption comes into play):

½ x ½ x ½ x ½ = 1/16 = 6.25%

Another way to look at it, the typical punter will go 16 Quaddies before hitting one. Of course, some very sharp punters will do quite a bit better, and some will do not nearly as well (as in all aspects of life, some people are better at punting, and some are better as estimating punter probability).

Cost of a Quaddie and Expectation Value
In the States, we call the Quaddie the much less romantic “Pick 4,” but the bets are the same. The base unit for a Pick 4 bet Stateside is $0.50 (50 cents) per combination, and I will use that base unit in my calculations here, as it makes the math easy. If this blog posts generates more interest in “Quaddie Economics,” I will follow up with a blog post centered on the Australian system.

So from the example above, we anticipate hitting one Quaddie for every 16 plays. How much money do I need to make on our successful Quaddie play to be profitable?

Here is a table that relates cost per Quaddie bet to Profitability:

Average Cost per Quaddie Play                                    Expected Break Even Point on Winning the Quaddie
$30                                                                                                                    $480
$40                                                                                                                    $640
$50                                                                                                                    $800
$100                                                                                                                 $1,600
$200                                                                                                                 $3,200

As with every other bet, the more one bets, the more one needs to win on the back end. I think the table makes a pretty compelling case that keeping Quaddie plays under $50 or less is probably the way to go if one is playing the Quaddie by oneself. Getting partners is always appreciated too. There is a saying over here that “10% of something is much better than 100% of nothing.”

Quaddie Ticket Structure
If a punter wants to keep costs low, by far the easiest way to do it is to SINGLE the best bet one likes in the four-race Quaddie sequence. This will also allow the punter to spread quite a bit in the other three legs. How to spread? I think one has to use “form” horses and anti-form horses. Form horses are logical, maybe even slightly unders, but have a big chance. Anti-form horses are horses that have some hidden form, are bigger prices and can really juice your Quaddie payoff. A typical ticket I would play would be:

Proposed $40 Quaddie ticket structure (50 cent base)
(4x1x5x4x$0.50)

Race 1
Four horses (two form, two anti-form)

Race 2
My SINGLE (Best Bet)

Race 3
Five horses (three form, two anti-form)

Race 4
Four horses (two form, two anti-form)

This ticket structure above allows for a lot of coverage. My SINGLE has a high probability of being unders. That is not my concern – the single is a pari-mutuel bridge to get to the three other races that the crowd may not have identified the right winners. In other words, I am gambling I can interpret the form more effectively that the other punters over the four race sequence. By spreading fairly wide I have probably a better than 1/16 chance if my single is the right single. Of course, my single may not be another punter’s single. Everybody looks at races differently.

Now, I am going to suggest another strategy to punters that have more disposable income, or partners. This would be what I call a “buy the race” strategy. Let’s imagine that there is a race where the top two favorites in a big field (say, 14 horses) look heavily unders, I can’t find a horse I like in said race, and I can identify a horse I really like in one of the other three races for my SINGLE. A more expensive ticket can be played but it might have much profit potential.

Proposed $112 Quaddie ticket structure – BUY A RACE (50 cent base)
(4x1x14x4x$0.50)

Race 1
Four horses (two form, two anti-form)

Race 2
My SINGLE (Best Bet)

Race 3
Fourteen horses (“ALL”)

Race 4
Four horses (two form, two anti-form)

Other Factors I Consider
I never play a Quaddie when the track is Heavy (we call that “Yielding” in the States). It is hard enough to hit a Quaddie as it is – 94% or more of all Quaddies lose – make the probabilities in one’s favor BEFORE one bets.

Summary
The Quaddie, while a lot of fun and potentially very financially rewarding, is very much a low percentage play. Costs should be minimized by playing smaller tickets and/or working with financial partners. Finding a key SINGLE is a way to make the bet more economical AND easier to win. If one race is hard to handicap in particular, that might be a time to buy the race by hitting the “ALL” button and try to back into a big score. I also recommend not playing a Quaddie if the track is “Heavy.”