Place Betting Question.

[Chrome Prince]

If a horse is $1.50 a place, it has a 66.67% chance of running a place.
Anyone like to guess what chance it has of running third?

Reason I ask, is I noticed that Betfair pay three place dividends on late scratchings in fields of 8 runners.
Meaning the bookies pay 2 place dividends and the Tote pays three.

It was $1.50 on Betfair and around $2.00 with the bookies.

So if I arb the horse, if it loses I win nothing, but lose nothing either.
If it runs first or second I win the arb.
If it runs third, I lose my stake.
For a $10 stake I win $5 or lose $10 (if it runs third), or breakeven.

If it runs third 33.33% of the time, I breakeven.
Any more I lose, any less I win.

My guess is that it runs third 22.22% of the time, meaning I have to win.
But my probabilities could be wrong.
Surely it can't be that simple, or maybe it is because the scenario doesn't happen often enough.

[UselessBettor]

Chrome Prince,

Your Maths are very, very, very wrong.

A horse that is 1.50 does not have a 22% chance of coming first, 22% chance of coming second and 22% chance of coming third. Your thinking too simply.

Here is a better example of understanding.

Lets take a horse that is priced $4.00 for the win and $1.50 for the place.
The horse has a win chance of 25% (1/4) assuming a 100% priced market. So its placing 2nd and 3rd is actually 66% - 25% = 41%. Divide this by 2 and you have 20.5% which is already worse then your 22%.

Another horse that is priced $2.50 for the win and $1.50 for the place.
The horse has a win chance of 40% (1/2.5) assuming a 100% priced market. So its placing 2nd and 3rd is actually 66% - 40% =26%. Divide this by 2 and you have 13% which is really worse then your 22%.

My examples above are very simple and really a bad way to rate a placing chance. In fact I would say they are very very wrong too. What you want to understand is who won the race leaving a percentage for 2nd and 3rd.

Lets use my $4 priced horse first. Lets say it didn't win but a horse priced $10 wins. We can then determine our horses chance of running second. We know it didn't win the race and a 10% chance did so that means we are 0.90/4 = 22.5% chance of running second. A horse paying $20 (5%) runs in second. We now have a 0.85/4= 21.25% chance of running third.

In the above example its close to your 22% for each place. But here is the problem. Lets say a $5 horse wins (1/5 = 20%) leaving us a 0.8/4 = 20 % chance of running second and lets assume a $6 chance actually ran 2nd. this leaves us with a (0.8-.16)/4= 16% chance of running third.

We can do the above again with our $2.50 chance. If the horse which ran first was a $10 horse and the horse which ran 2nd was a $20 horse then our $2.50 horse has a 0.85/2.5 = 34% chance of running third. If the first horse was a $5 horse and the 2nd horse was a $6 horse then we had a (0.8-0.16)/2.5 = 25.6% chance of running third. In these instances its much higher then your 22%.


I hope my maths above is correct but it should give you the basis of the idea of determining how to correctly price a place chance. What you need to do is run every permutation of the field with the horse your pricing not running a place. This gives you a semi accurate price. I say semi accurate as I am assuming the win prices are the correct % chances of a horse winning. Some horses are those types which either win or don't run a place and this will screw this pricing. Also you are going to get some fav-longshot bias affecting the prices which you may need to account for.

Understanding how to correctly determine a horses place chances is very important if you want to bet/lay in the place markets.

So in summary as I know the examples above are heavy reading your horses chance of running third for a $1.50 chance depends on

a) its win chance
b) the odds of the chance which ran first
c) the odds of the chance which ran second.

I am happy to discuss further if you need more help with this.

If you give me a race with 7 horses or less that you have looked at (provide all win odds at time of looking) I can go through the working to determine the place price of your selected horse that you would intend to back or lay.

[UselessBettor]

My maths below is wrong. thats what I get for doing it so late.

Sorry very tired while trying to type this out. Below is the correct maths for determining it. I had the divide the wrong way around.

It should read:

Lets use my $4 priced horse first. Lets say it didn't win but a horse priced $10 wins. We can then determine our horses chance of running second. We know it didn't win the race and a 10% chance did so that means we are 0.2/0.90 = 22.2% chance of running second. A horse paying $20 (5%) runs in second. We now have a 0.2/0.85= 23.5% chance of running third.

Lets say a $5 horse wins (1/5 = 20%) leaving us a 0.2/0.8 = 25 % chance of running second and lets assume a $6 chance actually ran 2nd. this leaves us with a 0.2/(0.8-.16)= 31% chance of running third.

We can do the above again with our $2.50 chance. If the horse which ran first was a $10 horse and the horse which ran 2nd was a $20 horse then our $2.50 horse has a 0.4/0.85 = 47% chance of running third. If the first horse was a $5 horse and the 2nd horse was a $6 horse then we had a 0.4/(0.8-0.16) = 62.5% chance of running third. In these instances its much higher then your 22%.

[Chrome Prince]

Thanks UB, seems I am making life more difficult than need be for myself.
I understand, the odds of placing first are determined by the win odds and then divide the remaining odds for second and third.
I had not considered this aspect.
However, the further permutations are not known until the race is over.
Also, I need to find out the odds of running third.
According to your examples, I'm always going to be ahead of 33.33%.
I need it to run third less than 33.33% of the time.

But as always, the details are overkill. I have approached it wrong from the beginning.
I can simply lay the field with Betfair and back the field with the bookie.
This reflects that I cannot win!

Although the odds say I can win more than lose.

Example:
I back the field and lay the field.
4 out of 7 runners I breakeven.
First and second, I win $5.00 as per my example.
Third, I lose $10.00

Result breakeven :(

[UselessBettor]

However, the further permutations are not known until the race is
over.

I'll re-read what you posted below and answer when I have more time but just quickly in response to the quote above what you want to do it work out all the permutations based on the win odds just prior to jump. Having every single permutation allows you to determine the place odds. The place odds though are going to depend on the "odds" shape of the race. Lots of long shots or lots of evenly priced horses will result in different place percentages (as it should).

I use the above approach semi-successfully at the moment on betfair. Its up over 150 units in profit so far based on backtesting and up 35.19 units in real time testing (not much $$$ on small bets though). I adjust for horses which win more then place and make slight adjustments for overbet/underbet. I then add a buffer for betting and a buffer for laying. Its surprising how many "value" place bets you end up with.

[UselessBettor]

Although the odds say I can win more than lose.

Example:
I back the field and lay the field.
4 out of 7 runners I breakeven.
First and second, I win $5.00 as per my example.
Third, I lose $10.00

Result breakeven http://www.propun.com.au/racing_forums/images/smilies/frown.gif

I couldn't help myself and had to do a real example.

Canterbury Race 5 today. I hade to use tote odds (tatts) as I can't find any bookie prices anywhere.

Tatts Odds :
2 - 4.40
4 - 1.80
5 - 2.10
6 - 3.80
7 - 2.50
8 - 3.90
9 - 4.90

Betfair odds from the betfair advantage tool (lay odds as I assume your laying)

2 - 3.30
4 - 2.04
5 - 1.54
6 - 2.46
7 - 2.00
8 - 3
9 - 4.10

Ok lets assume you backed the entire field with 10 units each.

I assume you layed the field for $10 each runner.

Result was 4,8,7

Lets do it horse by horse.

2 - Breakeven.
4 - Gain of $8 from tatts and loss of $10.40 on betfair
5 - Breakeven
6 - Breakeven
7 - Gain of $15 on tatts and loss of $10 on betfair.
8 - Loss of $10 and loss of $20 on betfair.
9 - Breakeven

I'll adjust for commission so betfair gain of $40 - 10.40 -10 - 20 = a loss of 40c.

Tatts Gain = 8+15-10-40 = -27

In the case above you have made a loss of 27 units. Are my maths wrong ?

Here is another one so lets see if it profits. Morphetville R2:

In this case I'll assume you get best of the three totes for place odds:

2 - 11
3 - 2.1
4 - 3
6 - 1.9
7 - 9.1
8 - 2

Layed at :

2 - 9.6
3 - 1.6
4 - 1.87
6 - 1.2
7 - 9
8 - 1.48

Result was 6-4-3

2 - Breakeven
3 - Loss of $10 and loss of $6.00 on betfair
4 - Profit of $20 and loss of $8.70 on betfair
6 - Profit of $9 and loss of $2 on betfair
7 - Breakeven
8 - Breakeven

Result for betfair is 30-6-8.70-2 = 13.30 * 0.95 = 12.63
Result for Totes is 20 + 9 -40 = Loss of $11

This means you made $1.63 and that was on the best available odds. Lets use NSW divs instead as they seemed to be the higher few opn avg:

2 - 11
3 - 2.1
4 - 2.90
6 - 1.4
7 - 9.1
8 - 1.5

Based on these odds :

2 - Breakeven
3 - Loss of $10 and loss of $6.00 on betfair
4 - Profit of $19 and loss of $8.70 on betfair
6 - Profit of $4 and loss of $2 on betfair
7 - Breakeven
8 - Breakeven

Result for betfair same at : 12.63
Result for NSW is -40 + 19 + 4 = -17

Its going to be a hard slog to get the equivalent of best tote odds for placings with most bookies on all meetings meaning your very restricted and even then you might just edge a profit but is it worth the risk ?

[UselessBettor]

You would learn much more by correctly determining the place price and backing value and laying short priced selections on the place markets.

[moeee]

You must consider the Odds of the rest of the Field.

Picture that the Favourite was BlackCaviar.
Your $1.50 a place horse has virtually zero chance of winning.
Therefore the whole 66% place chance is divided up between 2nd and 3rd position.

If your horse was substantially better than the rest of the also rans, then it could be divided up as 50% and 16%
If it were of equal ability of say 2 other runners, then it could be divided as perhaps 33% and 33%.

[Chrome Prince]

Canterbury Race 5 today. I hade to use tote odds (tatts) as I can't find any bookie prices anywhere.

Tatts Odds :
2 - 4.40
4 - 1.80
5 - 2.10
6 - 3.80
7 - 2.50
8 - 3.90
9 - 4.90

Betfair odds from the betfair advantage tool (lay odds as I assume your laying)

2 - 3.30
4 - 2.04
5 - 1.54
6 - 2.46
7 - 2.00
8 - 3
9 - 4.10

You could have arbed 2, 5, 6, 8, & 9.
Surely those BAT odds aren't accurate?

[Chrome Prince]

Just checked the results site, yes those prices are correct.
Getting matched could be a problem, but BINGO!

[woof43]

You must consider the Odds of the rest of the Field.

Picture that the Favourite was BlackCaviar.
Your $1.50 a place horse has virtually zero chance of winning.
Therefore the whole 66% place chance is divided up between 2nd and 3rd position.

If your horse was substantially better than the rest of the also rans, then it could be divided up as 50% and 16%
If it were of equal ability of say 2 other runners, then it could be divided as perhaps 33% and 33%.

Just noticed your post Moeee,

in 2006 i posted this in a win efficiency thread

"The whole point about playing our handicapping game (and a lot of the "game of life") is being forced to make decisions even when faced with incomplete or conflicting information. And a person that is better at determining those probabilities and expectations in the handicapping domain, especially with uncertain information, gets paid more money in the long haul."

What was your bankroll then? I'd say your understanding is a lot better now.