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Author: Pete Timestamp:- 11/5/2003 10:17:52 PM Subject: The Mathematics of betting
Message: Consider a 9 horse field. Assume that each horse had an equal chance and that a bookie betting on the race rated the race the same and decided he would bet to exactly 100%. In that case he would offer odds of 8/1 for each runner and 2/1 the place.
Now consider another 9 horse field. This time the runners are rated this way but the bookie still bets to 100%..... 6/4, 4/1, 13/2, 10/1, 15/1, 16/1, 33/1, 66/1, 100/1. What are the correct place odds here?
I believe I have the correct answer but I would like to canvass the opinions of those serious forumites out there and see what answers they come up with.
After that I think I can engender some thoughtful discussion and also show where the punter can exploit a mathematical advantage.
I shall return in a few days time and hopefully take this further.
Message: mathematically, a place bet has 3 times as much chance of being successful as a win bet (provided they pay a 3rd div), so the shorter the odds the better the value the place bet is in relation to the win bet.
i dont take short odds, but am always amazed how many people take $1.50 the win, instead of $1.30 or even $1.20 the place. i would take neither, but if people cant help themselves the $1.30 is much greater value for the risk involved.
Author: Pete Timestamp:- 13/5/2003 9:06:12 PM Subject: Re: The Mathematics of betting
Message: Ok, as the originator of this thread, it was pleasing to see 24 responses at the time of reply. There was however only one correct answer: that being Nick who got exactly the same answers as me. The notion that place odds equal 1/4 the win odds is wrong. There is no quick formula that connects the win odds and the place odds. The correlation depends on the way the win odds fall. As the favourite gets shorter, the place odds as a fraction get shorter. So herein lies a mathematical advantage. If a bookie bets each way any runner then the place odds of a quarter the win price, represent value, especially in the shorter range of odds. With computerised bookies these days it may be hard to find such a situation, but it certainly does occur. The place odds must add up to 300% before the bookie breaks even on the place portion of his book. In my original book, my win prices added up to 100% and if you took a quarter of these odds then your percentage for the place would be 252%, a losing book. The correct prices the place are as Nick said or in terms of conventional odds, 2/11, 6/10, 11/10, 15/8, 3/1, 13/4, 15/2, 15/1, 25/1. Certainly, it raises a point about mathematical advantages.
Author: Gary Still Timestamp:- 13/5/2003 6:27:33 PM Subject: Re: The Mathematics of betting
Message: You are correct Smallie. My error. $ Clark is asking what price the punter should attach to each horse, to determine whether a quarter of the win odds are value or not in respect of each runner. $ I don't have the patience to do the math, but intuitively I'd be rating the 4/1 second fave at about 7/10 the place. I'll take even money all day on that one!
Author: Mr Small Timestamp:- 13/5/2003 5:48:27 PM Subject: Re: The Mathematics of betting
Message: Yeah, that's fine Speedy, I understand all that. I didn't know that it was called arbitraging. Is this word commonly used for this tactic - not being a smart arse - just want to know?
My point, particularly to Gary, is that Pete wrote a question about fair place odds, then Gary strayed from the point, suggesting that there is no need to get place dividends to equal 300% and you can bet this way and that way to make a profit.
if the fav is $1.25 win (80%), that's $1.06 place (94%). from there u only need an 20% extra for 100%, but 206% for 300%.
get the idea?
say there's another 8 horses in the race, each at 2.5%, or $40. place divs of $10.75 (9.3%)
8 times 9.3% = 74%
94% + 74% = 168%. that leaves 132% shortfall from the 300%.
this is an extreme example that wouldn't happen on race day, but i used it to highlight the concept of arbitraging. u place e/w bets on every runner in appropraite amounts and no matter who runs 1,2,3 u win.
now the tricky part is 1. finding a heavily over bet fav 2. finding a bookie that offers e/w betting and favourable %s.
Author: Mr Small Timestamp:- 13/5/2003 2:49:44 PM Subject: Re: The Mathematics of betting
It DOES automatically follow that the figures must add up to 300% for 3 places. 100% for each place.
At fair place odds (which was what Pete asked for) and for the bookmaker to pay out $100 on each runner, he would hold $84.74 on the 6/4 horse then, $62.90, $47.62, $34.60, $24.70, $23.31, $12.07, $6.23 and $4.15.
If any of these horses place, the bookmaker must pay out $100. If you add the figures above, you will see that the bookie holds $300. If any 3 horses place, he pays out $300 and breaks even, ie fair odds.
If you add the percentages of the place tote odds and add their take-out, it will also come to 300%.
I don't mean to be rude, but I'm not sure why you find this difficult to accept.
Author: Da G Show Timestamp:- 13/5/2003 2:16:43 PM Subject: Re: The Mathematics of betting
Message: Mr Gable (Pete),
This is bookmaking 101!
The win odds percentage adds up neatly to 100%. In theory you could back every horse to finish square!
The anomaly is that the place odds percentage adds up to only 251%. what are known as "losing figures" (by 49%) for eachway bookies.
How to profit? back all the chances e/w and hope the fave runs a place at worst. If the fave runs a place you won't be too badly off even with your worst way. In theory a nice way to punt - betting eachway where there is a short price fave with low percentages and 10 or less runners, but.......
Here's my question for you - Find me these races regularly (realistically where the win market is around 115%) and the bookies that will bet eachway on them!
It does happen, but most of them tend to have computers with betting software that tells them the percentages or they can tell by just looking at the market that it's no good for e/w betting. They are out there but they're usually small cash bookies that are going the same way as the dinosaur!
Author: Gary Still Timestamp:- 13/5/2003 2:05:44 PM Subject: Re: The Mathematics of betting
Message: I don't understand why anyone is TRYING to make the figures add up to 300%? $ Just because the win percentage is 100%, it doesn't automatically follow that the place must be 300%. $ The bookie calculates all place returns by dividing the win price by 4. Some of you have already done that and achieved a figure of around 250%. $ What this means is that if you outlayed $250 for the PLACE, in the right proportions on each runner, your return irrespective of the result, would be $300. You cannot lose.
Author: Mr Small Timestamp:- 13/5/2003 1:51:58 PM Subject: Re: The Mathematics of betting
What's this arbitrage you are talking about?
I've never known anyone to buy a ticket from a bookmaker and then sell it for a small profit.
I've read about a few punters doing it but have never seen it practised.
In stock market terms, an arbitrageur is someone who captures a tiny percentage gain by buying a stock at say $2.00 then selling it to a buyer he's already hooked up with, for $2.02. He keeps $20 for every thousand shares traded.
Why would anyone wnat to do this at a race track?
There's been a lot of writings about maths and overs and unders and barriers and track bias and .... etc. How 'bout this? Pick a horse to win and bet on the bloody thing!
Author: Mr Small Timestamp:- 13/5/2003 12:38:05 PM Subject: Re: The Mathematics of betting
Message: You're a genius!
I tried to cheat but it didn't work. My figures didn't add up to 300%.
The reason I tried to cheat is that otherwise I'd have to work out every exacta combination and add that to every trio combination. As you say, thousands of calculations.
I tried it another way. There are 3.6 black marbles and 5.4 white marbles (ie, 9 places to be filled), what are the chances of me not picking a black marble in 3 tries (black representing the 6/4 shot), then subtracting that answer from 1.
I liked the theory, but again, no 300% and the figures didn't look right anyway.
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