Mathematics and Betting Thread

[MahoganyVic]

Probably a stupid question, but how do you work out the odds of getting a winner if have several horses in the race/ event.

Eg Looking at the British Open golf odds on betfair, is there a quick way to calculate the rough odds of having an English winner?

[doubleup]

for every player 1/betfair odds added up eg

player 1 betfair 10

player 2 10

player 3 10


1/10 + 1/10 + 1/10 = 3/10 = .3 probability

to get back to betfair odds 1/.3 = 3.33

[MahoganyVic]

Cheers

[Omm]

Tal kindly put this link up on TFT to help those of us who need it, big thank you to doobs for spending the time to start it in the first place. No doubt this will be a massive help for a lot of us.

I have a question about EV in sports betting. I really wanted to know how important or relevant it is? I was reading an article which gave an explanation of how to work it out:

1. Find the decimal odds for each outcome (win, lose, draw)
2. Calculate the potential winnings for each outcome by multiplying your stake by the decimal, and then subtract the stake.
3. Divide 1 by the odds of an outcome to calculate the probability of that outcome
4. Substitute this information into the above formula.

For example, when Manchester United (1.263) play Wigan (13.500), with a draw at 6.500, a bet of $10 on Wigan to win would provide potential winnings of $125, with the probability of that happening at 0.074 or 7.4%.

The probability of this outcome not occurring is the sum of Man Utd and a draw, or 0.792 + 0.154 = 0.946. The amount lost per bet is the initial wager – $10. Therefore the complete formula looks like:

(0.074 x $125) – (0.946 x $10) = -$0.20

The EV is negative for this bet, suggesting that you will lose an average of $0.20 for every $10 staked.


From that I ran a few examples myself and it seems that the odds have to be evens on both sides for the EV to be positive. So for example If I bet on NFL where the prices are generally 10/11 or 1.91. Using the equation above my EV is negative showing I will lose on average £0.47 for every £10 staked.

So how does that compare to the reality of the situation, is it really a case that in the long run on this type of bet am expected to lose? Does that reflect on whether I should place the bet or not? Is there a need to be aware of the EV of bets?

[doubleup]

Each books individual odds are going to show a decent % in the books favour.  But you should be taking the best odds from the whole market.  If the best odds still show a high -ev, it might be wise to swerve that kind of bet unless you are fairly certain that the odds are wrong.

[Doobs]

Bump.  Free bet stuff is in the 2nd post in this thread.

[Doobs]

Bumped for discussion of arbing thread bets, including using golf to arb those bets, including the issues we have doing so with HilliamBills

[GreekWay]

Only just seen this. Great post Doobs.

Some important eye-openers. Really helpful. I always hated advanced maths but you make them look really easy.

Thank you very much Sir.

[Simon Galloway]

For dirty each ways, I thought the easiest maths (and the choice of nits) was to just calculate the cost of unloading the win part (and unload the win part) and compare your remaining place only bet (after factoring in the disposal cost) with betfair place market?

[Doobs]

I never got round to doing the dirty each way bit, sorry.

May as well answer this whilst here

Looking ahead to tomorrow's Cheltenham action, Ladbrokes are taking on Annie Power but vowing to refund stakes as a free bet if Willie Mullins' mare wins the race they sponsor, the World Hurdle.

Annie Power is the big-race favourite at 6/4 at present, although Ladbrokes say they will go up with 9/4 in the morning.

The money-back offer will go live at 0900 GMT with a maximum of £25 to be refunded.

The firm's David Williams said: "Annie Power is the stand out horse on day three and we're dangling an enormous carrot with this money back pledge framed around her winning.

"We're thrilled to bits that the showdown with Big Buck's is on in what we believe is the clash of the week and we fully expect this offer to trigger the busiest build-up to the racing we've seen all week across all our key channels."

Annie Power's main rival is four-time winner Big Buck's, about whom Boylesports are currently offering 4/1.

So if they go for a refund offer which of the two is worth it? Backing Annie Power or Big Bucks?

Discuss.

I believe that is a question for the expert Mr. Doobs. Smiley

Here is the maths behind the shall I back Big Bucks or Annie Power question under the Ladbrokes offer.

Ladbrokes are offering 9/4 Annie Power or 3/1 Big Bucks but with a refund if Annie Power wins.

Assuming you can bet £25 on each.

The expected return from the Annie Power bet can be calculated as follows. 

If Annie Power wins, you get £25 x 13/4 as a return ie £81.25.  Assuming Betfair is the true odds, the chance of that happening is 1/2.65.   
81.25/2.65 = £30.66

The expected return from the big Bucks bet can be calculated as follows.

They only offer 3/1 on Big Bucks, so if it wins you get £100.   Assuming Betfair is the true odds, the chance of that happening is 1/5.15.   
81.25/5.15 = £19.42. 
You also get your £25 back as a free bet if Annie Power wins.  I assume free bets aren't really worth £25, as you usually lose a bit when you place them.  This applies if you arb or just find a nice bet.  Assuming we lose 10% of the value which is fairly typical.
So free bet is worth chance of Annie Power winning x £25 x 0.9 = 22.5/2.65 = £8.49.
So total value of Big Bucks bet is £19.42 + £8.49 = £27.91.

So to me it is absolutely clear the best plan is to just back Annie Power at 9/4.  That also is much simpler, as you don't have to use a free bet, set up an arb etc.

[doubleup]

I never got round to doing the dirty each way bit, sorry.

you were overawed by the power of excel

https://docs.google.com/file/d/0Byg8Wbbo5p2ucDN2WVdueENUYzA/edit?pli=1

[Doobs]

I really have a couple of time issues at the minute.  Friday I tend to play poker late, and my kids can be up as early as 6 in the morning with the brighter mornings.  I rarely get woken after 7.  People can look back and see what time I put the Hills bets up and it must generally be 2 or 3 in the morning.  

I can put up free bets by scanning the Hills prices in things I know well, and checking against Betfair.  I can probably do this in 10 or 15 minutes and put something sensible up.

I realise this isn't ideal, but if I was to look for the very best Hills bet it will genuinely take me much longer than that.  

I think together with the free bet and doing the top thing I can make a fiver or so from each free bet.  The extra I can get from doing a much better scan of Hills is going to gain much less than the initial fiver or so, and the gain can't be much more than a pound or two.  On the arbbing thing, I have no tools for arbbing, so say I wanted to arb a golfer, I'd probably have to look through at least 3 golf tournaments a week (maybe 500 golfers) to find the best bet.  That seems a big undertaking to me, even if I could cut some out quickly.  If I was to add in some football scores, the work I would have to go through to get that extra pound or two seems like a lot of work to make very little gain.

I appreciate I may be able to google around and take somebody else's Hills arb of the week for the best way to use a free bet that week, but that isn't something I am comfortable with or a route I want TfT to take.

I am not sure why I am the only one who gets the you don't want to do it like that treatment.  When somebody puts up a Scottish footballer to score anytime, nobody ever suggests that we back a golfer and lay it off on Betfair instead.  It doesn't seem to cross people's minds apart from with the free bets.

Anybody any thoughts?

[TightEnd]

I've no complaints about the maths or the free bets

The issue is whether to embrace variance (we currently put a free bet on something "at a price") or reduce it (we lay off on betfair exactly what we back with the free bet)

I think the weakness we have is that the selection of the item for the free bet is often rushed, sometimes last minute panicky and often doesn't have the same level of thought or written research as some of the original bets.

This isn't a criticism of doobs, it applies to tikay's time management and the reluctance (it seems) for a range of people to put forward ideas for free bets in good time

At the end of the day though with a higher variance approach you are going to get low returns for long spells with the free bets at 10-1+ shots.

I do think the selection of some of those can be improved, or more process driven (ie not last minute "it has to be used today, what on?"). I think this is sonour's point


On arbbing, doobs is saying it "seems a big undertaking to me" whilst arrboy says its virtually no work at all to guarantee turning a free bet into cash at a 95% rate. I've no idea which applies but I suspect with tikay (no offence meant) its got to mean misclick potential, more demands on his time and probably more thread admin

[arbboy]

I very rarely encounter free bets where the stake isn't refunded as the vast majority of my business is done on bf.  My only real experience of them is when opening new accounts with firms and because of the crazy ladbrokes promo on the chelsea v man u game when i ended up with 60 £25 freebets which i had 7 days to use and i just wanted the least swingy way to effectively convert them back to cash.  I didn't find it an issue finding numerous big prices at ladbrokes which i could lay at shorter prices on bf to convert these back into cash. 

The other option was to have £1500 invested in 20/1-100/1 shots and just roll with it and potentially iron out £1500 in real cash effectively on events i didn't especially have a view on but i was forced to invest due to the 7 day expiry date of the free bets.  I wouldn't have backed any of the selections with my own cash if i didn't have the free bets as i had no strong view on the events.  Therefore i just saw it as a manner to convert free bets into cash with the least potential variance as i had made plenty of cash already out of the promotion.

[doubleup]

The thing is though that a "perfect" arb bet should be a perfect bet to keep.  Arbing is just a tool to reduce variance that comes at a cost.

The solution might be to have a process for time pressure situations eg look at the correct score market for the TV high liquid matches.  Or even just do a shout out in the thread for bets at 10s+ same price in liquid betfair markets.