Here is the formula for working out the probability (and therefore the correct odds) for a quinella combination:

P1*P2/(1-P1) + P2*P1/(1-P2)

Where P1 = probability of horse 1 winning (expressed as decimal) and P2= probability of horse 2 winning.

The first part is the probability of an exacta for horse1-horse2 and the second is the exacta probability for Horse2-Horse1 - add them together and you get the quinella probability for 1-2.

A couple of examples might help here.

Suppose you have two selections for a race, the first one you assess as a 2-1 chance (ie. 33.3% chance of winning) and the second is a 5-1 shot (ie. $6.00 or 16.67% chance of winning). First we convert the odds to decimal winning chance so P1 (probability of horse 1 winning) is 0.33333 and P2 is 0.16667 If we put these figures in our equation we get:

0.3333*0.1667/(1-0.3333) + 0.1667*0.3333/(1-0.1667)
= 0.15
So the chance of this quinella coming up is 15% which gives a TAB price of 1/0.15=$6.67

So you would bet if the quinella approximate was at least $7.00 (or probably $8 or $9 to allow for price changes and a profit margin)

Now if you don't do your own assessments of winning chances you can use the TAB approximates as a guide (there are generally fairly good if you removed the margin). To do this convert the win approximate to a percentage and then remove the margin. For example if we look at MR6 today the final Tabcorp approximates for the winner (Mistegic) was 3.00 and the second runner (Shaye Spice) was 10.60. Converting these to decimal gives us 0.3333 (1/3) and 0.09434 (1/10.6) but these still have the TAB margin included - we need to multiple each value by 0.85 to remove the margin which gives us 0.2833 and 0.0802 (so in theory Mistegic was given a 28% chance of winning and Shaye Spice an 8% chance). Putting these figures into our formula gives:
0.2833*0.0802/(1-0.2833) + 0.0802*0.2833/(1-0.0802)
=0.0564 or a TAB forecast price of $17.72
So that Quinella option should have paid $17.70 on TAB (If the TAB win estimates were an accurate indication of winning chances). The actual Quinella was $17.60 (Tabcorp), $17.10 (NSW) and $18.50 (Unitab). So the Tabcorp div was almost spot on, NSW was slight unders and Unitab was slight overs.

As always I am happy to try to answer any questions or clarify anything if I have confused you!

_________________
"So certain are you. Always with you it cannot be done. Hear you nothing that I say?" - Yoda

[ This Message was edited by: becareful on 2002-08-17 19:05 ]