Let us put all our cards on the table right at the beginning of this long chat. Two means a quinella and three represents a trifecta. You need two horses for a quinella and you need three horses for a trifecta. If you want to box a quinella you are still only required to outlay one unit, whereas in the case of a trifecta, your outlay increases sixfold.

This is because it doesn't matter with a quinella which way the horses finish, whereas with a trifecta, if you are going to cover all possibilities, you must combine them in six different ways.

Where the whole thing gets quite out of hand with a trifecta (for the average punter, anyway) is the addition of more runners. For example, a box of four runners will increase costs by 300 per cent from \$6 to \$24. If you want to add a fifth runner, then that runner is going to cost an additional \$36 (i.e.150 per cent more). A box of six runners will add another \$60 (100 per cent) for a total outlay of \$120. Seven runners will set you back \$210 and eight runners will bring it up to \$336.

Just to complete this horror story, if you want to tie up an average l2 horse field in a box trifecta, for one miserable dollar, your friendly TAB Lady will invite you to part with \$1320.

I assume that you have just partaken of a very large Scotch and that you are ready to face the rest of the bad news. Guess what? It's time to get happy, because the good news follows. And the good news is that it would only cost \$66 to couple or box the entire field for a one dollar quinella bet. And, I already hear you saying, the dividend would be much smaller.

That is dead right. But, consider this for a moment, and then you might well decide that a multiple quinella bet can have the edge on many trifectas. I want you to dream up a situation where a trifecta pays \$1000 and a quinella pays \$83.

I have chosen these figures because the quinella is then paying one-twelfth of the trifecta dividend. This is quite speculative on my part, but a four-figure trifecta is most likely to attract a decent quinella, unless the third placegetter is a huge longshot and the first two are relatively shortpriced commodities.

In my experience, if the favourite wins the race, two significantly long-priced horses are needed to run second and third to achieve a four-figure trifecta. Most punters appear to throw the favourite into their boxes somewhere. Surprisingly, this seems to be untrue of the "first four" pools. The number of big first four dividends containing the favourite, especially when it runs fourth, seems to suggest that punters are more adventurous with this form of betting.

That was just an aside, but I thought it was worth including, as you might like to play around with it. Back to the drawing board: you can (many readers have probably worked it out already) have 20 units on the quinella box for one unit on the trifecta in our 12-horse field. Had you placed 20 units on the imaginary quinella that I proposed above, you would have received \$1660 for a profit of \$340. On the other hand, one unit bet on the field for the trifecta would have seen you out-of-pocket to the tune of \$320.

Now of course I set that situation up. How else do I explain that quite often the quinella is a much more logical bet than the trifecta? I cannot tell you categorically that you will make more money, or lose less money, by betting quinella as against trifecta.

But I can assure you that there are times when it makes a lot of sense, and that even if a trifecta pays a huge amount of money (\$1000) you can drop money on it if you are betting multiples. Needless to say, a \$6 three-horse box on a successful trifecta in that particular example was a much happier investment than \$6 outlaid on the winning quinella (\$500, give or take). Twice as happy, in fact. But you still had to get it.

Let's go back to what I said a while ago. I said that, in theory, you could have 20 units on the quinella for every unit on the trifecta if you are boxing a field of 12. That is how I got that figure of \$1660 for 20 units, while the trifecta for one unit paid a mighty thousand bucks.

Had the trifecta paid \$1660, guess what?

Before I do this, will you agree with me that 1660 bucks is a pretty good trifecta?

Okay, we agree on that. Some readers have probably already twigged that the \$1660 dividend was necessary to make the same profit, give or take a dollar, that we got from the quinella.

The quinella paid us \$340 profit for an outlay of \$1320 and the trifecta returned \$340 for that same outlay. I had to get that trifecta up to nearly \$1700, give or take, before I could square things with the 20 units on the quinella.

Next question: is this unusual? To answer this you would have to take a large sample and make the appropriate comparisons.

The table below shows NSW TAB quinella and trifecta dividends for the weekend just gone (as I write). Long-time readers know that I don't bluff, and if it turns out the wrong way, so be it, we will travel a slightly different way.

There was not one major trifecta all day. No mind-blowing biggie. The biggest was \$2518.20 at Sandown. The asterisk in Sydney 4 means that the first and second placegetters dead-heated, so there were two trifectas. I just added them together for the total dividend if you were betting the field, because you would receive both dividends.

The burning question is, how many starters were there in each race? For example, if we take the eighth race in Melbourne and we find there are only eight starters, a trifecta box would cost us \$336 and the equivalent quinella bet would be for 12 units. This is because the quinella box for an eight-horse field would cost \$28, which is one-twelfth of \$336. Twelve lots of the quinella would return to us around \$435, a great deal less than the trifecta box would return.

Sorry to spoil the party, but actually there were 15 runners in the eighth at Sandown. Your box trifecta would have set you back \$2730.

You just lost \$212.

A box quinella would have cost \$105, so you could have had 26 units on the combination for the equivalent outlay, and unfortunately lost heavily. The third placegetter really put the money into the trifecta and on this occasion my idea backfired. The ninth race was far more friendly as you can work out for yourself, but the trifecta still had the wood on the quinella. For the same reason, as we will see below.

Such are the vagaries of multiple betting that I can only place these anomalies in front of you and invite you to make your own decisions. Would you like to
consider some more? I will give you the runner numbers for each race so you cart make your own comparisons.

In Sydney they were 12, 8, 11, 14, 13, 12, 14 and 16. The Melbourne runner totals were 11, 11, 5, 13, 12, 13,13,15 and 11. Adelaide provided 12, 10, 7, 8, 9, 9, 12 and 12. Up in Brisbane they managed 12,9,10,12, 12, 17, 12 and 13.

The easiest way to calculate a field quinella is to subtract 1 from the field and start adding, deducting one each time. For example, for a 12-horse field, you start with 11 then 10 then 9 then 8 then 7 then 6 then 5 then 4 then 3 then 2 then 1. Add them together and you get 66.

If it helps, all you have to imagine is that you have A coupled with B,C,D,E,F,G,H,I,J,K and L (eleven combinations). Then you have B into C,D,E,FG,H,IJ,K and L (ten combinations). Then you will have nine combinations, eight combinations, down to the final one, which will be KL.

As you can see, you are adding. With the trifecta you must multiply. As shown above, the trifecta numbers expand very quickly. The method for calculating any box trifecta is to subtract two from the number of candidates for first place, and subtract one from the number for second place. We leave the third place totals alone. Some people do this the other way around; it doesn't make any difference where a box is concerned. And so a 12-horse field box trifecta is calculated thus: 12 x 11 x 10 = 1320. Or 10 x 11 x 12 = 1320. Doesn't matter which way.

The easy way to understand this is that something has to win, and when it wins it cannot then run second or third. So there is one less possibility for second place. Similarly, something has to run second. When it has run second, we now have two horses which cannot run third. Other way around? Okay, imagine something has to run third, so it can't run second or first. Something has to run second, so there are now two horses that cannot run first (they have run second and third). So at one end or the other of the calculation, you will take two off, then you will take one off the horse total in the middle, and you will ignore the other one.

Just remember the one basic rule: add them for the quinella and multiply them for the trifecta.

Now that you know the numbers involved in each race on that one day, you will be able to make some interesting comparisons. True, there are only 33 races involved in this brief sample, but there are nearly 400 horses involved. Also, 26 of the 33 races had what I would call a decent field size by Saturday standards. It may be that you decide to throw Adelaide out as unrepresentative in our sample. I have found that generally it doesn't pay to twiddle around with statistics, but perhaps in this case, where one is out of line with the others, we could be best advised to ignore the one with the small numbers. Your choice.

Having a look at the third placings might also provide us with some more information. Remember the obvious, which is that quinellas do not have third placings, and so this is where a fundamental difference will reside (note the final two races at Sandown). F means favourite and EF is for equal-favourite.

Going down the Sydney list, the third placegetters were at win odds of 16, 10, 2.5 (EF), 8, 3.6 (F), 5, 12 and 1.5 (F). Melbourne win odds about the third placegetters were 6, 16, 1.8 (F), 9, 9, 16, 9, 30 and 16.

In Brisbane they were 8, 3.6, 25, 8, 2 (F), 5, 3.8 (EF) and 14. Adelaide odds were 5.5, 9, 5, 2, 6, 5, 6 and 7. So although the Adelaide numbers were down, there is something to look at there, because no third placegetter in Adelaide ran as favourite. That could be interesting, given the small fields. Let's have a quick look at what Adelaide produced with regard to quinellas and trifectas.

Interestingly, it looks to be right in line with our idea that the third placegetter needs to pump some cash into the trifecta. Nobody is claiming that we have established anything foolproof here. My idea has been to alert you to the possibilities that a field quinella may have. Another way of looking at this is to realise that in a 12-horse race, you can cover the field in the quinella for a little bit more than it would cost you to cover five horses in the trifecta. In a 10-horse race you can cover the field in the quinella for 45 units, whereas the equivalent trifecta bet would cost you 16 times as much (720 units).

There is a lot here to take on board. Just play around with it, think about what might have been, and don't expect miracles. One last thought (don't take this too seriously, just be aware of it). The Melbourne Cup usually has 24 runners (23 this year). The box trifecta would cost you \$12,144. That way lies madness. But to box the quinella would cost you \$276. If you take a horse to stand out win in the trifecta, with the field to run second and third, you are effectively quinellaing the second and third placegetters. But that would cost you 506 units and you still have to get the winner. It's just a thought.

By The Optimist

PRACTICAL PUNTING - JANUARY 2003