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
15

January 1, 2016 at 1:01 pm

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MarkCorrigan 15 January 4, 2016 at 5:01 pm

Interesting… Yeah, I’ve always used the FBs on horses – they let you anyway.

There’s a banner on the left hand side of the home page with a link to the acca bonuses in January.

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Coco Popo 0 January 4, 2016 at 5:03 pm

Thanks Mark,

I may have missed this, but what’s EV? and how’s it calculated?
For WH, is the limit making 1 Acca per day, or is it 1 Acca finishing per day?

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MarkCorrigan 15 January 4, 2016 at 5:09 pm

EV is expected value.

The limit is 1 acca finishing per day, so you can place several in one day as long as they all finish on different days.

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Coco Popo 0 January 4, 2016 at 7:15 pm

The exchange odds you mention and use to calculate the implied probability, are they the back or lay odds? Can you elaborate on what this shows as opposed to the bookies odds?

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Tony 13 January 4, 2016 at 7:32 pm

Thank you to all those who have contributed to this thread, particularly you Mr Corrigan!

Would you be willing to share any results stats that you have on these acca bets? I am curious to see what the return is over a decent sample size of wagers. I completely understand if you would rather not. Thanks again

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JeremyUsbourne 0 January 4, 2016 at 8:01 pm

Bookmaker odds are (almost) always worse than the exchanges – this discrepancy is their ‘edge’ and how they are able to make money. As their is no house edge on exchanges (no need to consider commission) we can assume that the exchange odds are representative of probability as this is how the free market has valued the various outcomes.

I do not know Mark’s methodology but it is my belief that the average of the back and lay odds on bettfair is the most accurate representation of probability, but given they are generally different by 0.02 the effect on the accas EV is basically negligible between just using back or lay odds, assuming the market is tightly matched.

EDIT: Unbelievable that *bet_fair is censored from forum posts, hope Smarkets are paying Matt a lot!

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tennispunter 2 January 4, 2016 at 8:25 pm

Hi Mark

Many thanks for your response which was very helpful.

Two more questions if I may :
1) How do you calculate the 0.3163
‘And, of course, the probability that more than one leg loses:
Pr(Loses) = 0.3163’
and
2) Why the reduction factor of 0.9 – is this simply to lose a little and void being banned?

My thanks to you in advance for your assistance. Maths is not my strongest point as you can probably tell.

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swindonraf 0 January 5, 2016 at 8:56 am

So if I was to start my 6 fold acca today with a £25 bet at 1.2 for example

Would I lay the whole amount as in a qualifying bet so if that first bet lost I’ve only lost a minimal amount (.50-1.50)

Then don’t bother laying anymore and just hope that the other 5 come in to get the refund

But if it wins do I lay on the second bet the amount to cover the initial £25 bet again + the extra £6 that I have lost from laying the first one?

Also rather than laying I’m sure doing a double chance at another bookies gives you the same outcome as laying but with the added bonus of extra mug brownie points with that bookie

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dangerzone14 16 January 5, 2016 at 10:26 am

wish I was as intelligent as the people who can work this stuff out. I understand the maths of expected value but I don’t understand the statement that if our first 5 legs win, we get a free bet on the 6th leg at high odds.

The way I have thought about it is that if five legs win then we are guaranteed our money back so for example if we stuck a tenner on the acca then we get a tenner back regardless if the first 5 win. How then does it effectively become a free bet for the last leg?

I’m assuming we lay off the last leg (the high odds selection).

If the high odds team wins, we get the winnings from the acca – our lay liability
If the high odds team loses we get our lay stake as profit

Obviously the second option is definite profit seeing as we get our tenner outlay back from the acca. But what about the first option? Is our winnings from an acca guaranteed to be higher than a liability?

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MarkCorrigan 15 January 5, 2016 at 3:04 pm

Everything you write seems to be correct… IF the first 5 legs win, we now have a risk free bet on our 6th leg – if the leg loses, we get our stake back and if it wins… well, the acca wins. This is almost similar to the bet365 situation where we get our money back if the bet loses (albeit we have it as a free bet in this case). Therefore, we would want to choose high odds and lay off to secure a high profit.

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MarkCorrigan 15 January 5, 2016 at 3:07 pm

This is certainly one strategy for tackling the accas… Lay as you go along until one leg loses and then hope you get the free bet.

There’s ultimately several strategies and it really depends on your preferences (the example you give, underlaying, overlaying, not laying at all…).

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mike j 11 January 5, 2016 at 6:39 pm

Think ive finally got my head around the lay method.

dangerzone 14 you wrote:
‘if the high odds team wins, we get the winnings from the acca – our lay liability
If the high odds team loses we get our lay stake as profit

Obviously the second option is definite profit seeing as we get our tenner outlay back from the acca. But what about the first option? Is our winnings from an acca guaranteed to be higher than a liability?’

Yes it is in an example i just worked out, lets say the final game has lay odds of 5.0. You need to lay a stake which would cover all your previous bets to make sure you dont lose money, however for a £10 acca, you would get £9 back from the free bet if the lay bet wins. So if the lay stake required to cover our previous bets was £23 @5.0 =liability of £92. we can instead lay £14 @5.0 = liability £56 (we get £9 if the lay bet wins so no need to stake it as it will just increase liability)

Am trying my best to explain it, i know that probably looks like a jumbled mess, took me a while to get my head round it

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stick 0 January 5, 2016 at 10:00 pm

First post … So be gentle !!! I am new to all this, I am still in my first month and have been greatly helped by all on this forum.All the info and advice is helping get over/avoid newbie errors and that’s great when you are starting out. Anyhow have challenged myself to understand the Acca Insurance.?. I have chosen to lay off each leg as that seems easier and have hopefully been able to calculate lay stakes for each leg correctly.My brain however,cannot get around how to calculate the last bet. So,for example on a five leg Acca I have ‘won’ the first 4 legs and have layed off each leg. I am now, outstanding £10 on Acca and say £30 on lay bets.i could win £80 if Acca wins with a tenner refund if it loses. My last leg odds are 4. How do I calculate (formula?) what to lay to even up profit?
Many Thanks

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MarkCorrigan 15 January 5, 2016 at 10:22 pm

Hi Stick, I don’t think your example makes sense… You say that you have lost £30 in lays up until the final leg, but you will only win £80 if the acca wins. If the final leg odds are 4, then the previous 4 legs must equate to odds of 2 for this to be the case. The value of your bet having reached the final leg will be 75% chance of a free £10 bet + 25% chance of £80 = at most £27.50 (less than your £30 loss up to that point).

I’ll change the example a little. Just suppose you have lost £L up to the final leg. The amount you have lost up to that point is a sunk cost so won’t influence your decision thereafter.

The final leg’s odds are 4. If it loses, you currently get the £10 free bet and, if it wins, you’ll get the £80 winnings. How much to lay to even this up…? Let x be the amount you lay and assume 80% extraction.

If it loses you get: 0.80*10 + x = 8 + x
If it wins you get: 80 – (4-1)*x = 80 – 3x

Equate these and solve for x: 8 + x = 80 – 3x
Giving x = £18. So in this case you would lay £18 at odds of 4, securing you a profit of 26 – 10 – L = £16 – L.

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RyanB 14 January 5, 2016 at 10:27 pm

^ Brings me back to the good old GCSE Math days!

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