WH Acca Insurance: Example

Hi all, there’s been plenty of discussion and scepticism of the ACCA insurance offers being profitable. I have decided to share an ACCA with Will Hill that I am placing today. If you’re not familiar with the T&Cs, please read them, but we are looking for 6 football legs and there is no odds requirement. If one leg loses, we get our stake back as a free bet. Finally, this month they are offering a 10% bonus on odds for 6 leg ACCAs… The first odds are from WH, and the second odds are on the exchange.

1. New Saints (Welsh) at 1.25 / 1.25
2. Arsenal at 1.30 / 1.30
3. Dunfermline at 1.22 / 1.23
4. Juventus at 1.17 / 1.18
5. Barcelona at 1.22 / 1.23
6. Atletico Madrid at 1.20 / 1.21

Using the exchange odds to calculate implied probabilities, we see that the probability that our ACCA wins is:
Pr(Wins) = 0.2849

The probability that exactly one leg loses and we get our stake back:
Pr(One loses) = 0.3988

And, of course, the probability that more than one leg loses:
Pr(Loses) = 0.3163

The maximum stake is £50 for the insurance. Our value of staking £50 is therefore (the 1.10 factor accounts for a 10% bonus; the 0.90 factor accounts for extraction rate which could be decreased if you like):

Value of £50 bet = 0.2849*3.396*1.10*50 + 0.3988*0.90*50 + 0.3163*0 = £71.16

In other words, we are paying £50 for £71.16 in expected value! Our expected profit is therefore £21.16. My approach is to never lay these as we lose out to commission in the long-run and I place frequently enough to even out (law of large numbers etc. etc.).

If you want to lay off an accumulator, like the one given above, you will need to ensure that none of the legs overlap – this allows you to treat each leg as an individual qualifying bet which you can continually lay off until one legs loses and you then have a free shot at a free bet.

I hope this helps!

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MarkCorrigan
16

January 1, 2016 at 1:01 pm

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Andy 3 January 6, 2016 at 4:48 pm

Never pick odds that high if looking to lay each leg. Evens is as high as I would go.

Also you would underlay the last leg.

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78naD 4 January 6, 2016 at 4:58 pm

Mike you’re essentially gambling a bit on the last leg there, is it?

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MarkCorrigan 16 January 6, 2016 at 4:59 pm

@Andy
I disagree. If you return to basics, you effectively maximise your value by maximising the probability that you achieve the free bet (one leg loses).

If the first 5 legs are all of odds 1.25, it is optimal for leg 6 to also be 1.25.

If the first 5 legs are all of odds 1.10, it is optimal for the final leg to have odds as high as possible (as long as they’re close to exchange odds).

Regardless of whether you choose to lay every leg or not, it is always best to maximise value.

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mike j 13 January 6, 2016 at 5:07 pm

Thanks Andy, just ran the numbers through with last leg being at odd similar to others, worked a treat, think am ready now.

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Andy 3 January 6, 2016 at 5:17 pm

Finding 5 close back/lay odds all around 1.1 and all playing at different times is very unlikely. So because of that reason the laying each leg method only really works at odds lower than evens for each leg.

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tennispunter 2 January 7, 2016 at 8:14 pm

Hi Dekoder

You were kind enough to share a spreadsheet that appears to replicate Mark Corrigans formula (see start of thread).

The maths all seems to add up however the one piece of logic that is not included in any of the calculations is the reference to ‘P of less than 5 winning’

This number is 0.3163. I guess I don’t understand why this figure is even needed if it’s not actually being used in the body of the formula

Any chance you can shed some light on this for an ignoramus like me?

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MarkCorrigan 16 January 7, 2016 at 8:19 pm

Hi @Tennispunter, The probability that less than 5 win is included in the initial post for completeness. If this event occurs, the value is zero, so isn’t actually relevant as such (you would always multiple by £0 and the term disappears).

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swindonraf 0 January 8, 2016 at 6:37 pm

Does anyone know how many days these accas can be spread over?

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tennispunter 2 January 8, 2016 at 9:20 pm

Hi Mark

Thank you for your response (January 7, 2016 at 8:19 pm) as regards my plea for help iro your formula.

I finally get it, well in the sense that I can calculate the expected return with differing odds and offers that crop up from time to time.

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Pickle 61 January 8, 2016 at 9:51 pm

As many as you want but only one can finish per day to qualify for the refund. Well thats as close as ive come to getting one up. My fourth leg scored a winner 3 mins and 6 seconds into 3 mins of injury time and i had Liverpool as my last leg. Luckily i spotted the double change on Exeter was @ 2.5 so i think them not winning was a slightly better result for me.

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JDUBU 8 January 8, 2016 at 9:57 pm

Hi mike what have you gone for?i really want to try this tomorrow 🙂

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mincing_lad 0 January 9, 2016 at 5:36 am

In your experience do the odds deviate much between BM and exchanges on odds that low. i.e is it always worth checking the exchange odds to work out the true probability. Or when the BM odds are 1.25 or less do you assume that exchange odds will be the same or +/- 0.02 that it would not make any difference to the EV?

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swindonraf 0 January 9, 2016 at 8:37 am

@MarkCorrigan
I have another cunning plan…

I’m spreading my accas over today and tomorrow so I can get the lowest odds and plenty of space between the 6 games

I am also doing the same 6 games on 3 different bookies (£50,£25,£25)

So I will just lay as if I’ve done a £100 bet

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JDUBU 8 January 9, 2016 at 10:50 am

Hey Swindon is there any chance you could share your acca so i could give it a shot too and try get my head around it?as i really want to try this 🙂

Thank you

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swindonraf 0 January 9, 2016 at 11:02 am

sat:
everton
man utd
real madrid
sun:
rangers
celtic
olympiacos

using the dominator spreadsheet from the other thread

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