# Profiting From Accumulator Offers Part 1

Many bookies nowadays offer a free bet if one of your selections in a fivefold accumulator (“acca”) lets you down. This is seemingly hard to profit from as there’s no clear way to lay off an acca and it feels hard to qualify for the free bet as it requires precisely four of your selections to win and one to lose. However, in this two part series I hope to show that you can in fact make a profit, and make it ‘risk free’ by laying it off on the exchange.

__No lay method__

We shall start with my favourite method of profiting from accumulators – The straight up punting method. The problem with laying accumulators is that unlike with a standard free bet offer where we are laying once (see Matched Betting), we have to lay several times which means that its not only a hassle but it can also eat into our expected value (EV). This can be quite significant as a typical no lay EV per £25 offer is around £5. Paying £1 or more in commission means we are effectively giving away up to 20% of our long term profits for the sake of smoothing out variance – A judgement you will need to make. Another benefit that I’ve noticed is that a lot of the time the exchange odds for short priced favourites move in our favour if we take odds early. The odds can obviously also drift, however in my experience more often than not they will stay the stay or shorten a bit which means we’ve effectively reduced the bookmaker’s edge.

The no lay method requires a leap of faith to get started. You need to accept that exchange odds represent true odds. That is to say a selection at odds of 2.00 will win 50% of the time, a selection of 3.00 will win 33% of the time etc. This isn’t to say that one can’t find value on the exchange for a given selection, however over time if you placed bets at random on the exchange you will break even minus commission in the long run. In short the reason for this is due to Wisdom of Crowds.

Naturally, the EV of these offers varies with the odds of the accumulator and the closeness of these odds to those on betfair. High odds are bad since not only does our accumulator not win very often but we get a free bet less often as well, which is where the value lies. Counterintuitively an accumulator with too low odds is also bad since we reach a point where we don’t receive a refund very often and our payout is low when we win.

__Calculating the EV of the no lay method__

For the moment let’s assume that we’re taking accumulator odds, X, with zero overround i.e. if we bet on this selection long term we will neither make nor lose money.

For a fivefold accumulator the average odds per selection will be X^{0.2}, or since decimal odds are the inverse of probability written in decimal P(1W) = X^{-0.2}. There are five ways that four of our selections will win and one will lose:

WWWWL

WWWLW

WWLWW

WLWWW

LWWWW

The probability of a loss is one minus the probability of a win i.e. 1-X^{-0.2}. We can now calculate the probability of four wins and one lose in no particular order:

P(4W1L) = 5*X^{-0.8}*(1-X^{-0.2}) = 5*(X^{-0.8} – X^{-1})

Since we know the EV of all combination of wins and losses is zero from having perfect odds we only need to consider the refund value for 4W1L to calculate the EV. If for the sake of argument we say we can extract 80% of the free bet value e.g. a £25 free bet nets us £20 profit then the EV is simply:

EV = 0.8*5*(X^{-0.8} – X^{-1}) = 4*(X^{-0.8} – X^{-1}) per £1

With a bit of calculus we get that the maximum EV is at X = 1.25^{5} ≈ 3, which is the same for all refund amounts as the function is only scaled in the y direction.

Virtually all the time however we don’t get perfect odds due to bookmaker overround. We can look at our EV from the overround and then add this to the EV from the refund to find our true EV.

As an example if the bookmaker payout to Betfair payout is 0.95 then naturally we would expect to lose 5% of our money over time. In other words the EV from the overround is -0.05. Hence our total EV is:

EV = 4*(X^{-0.8} – X^{-1}) – OR per £1

Where ‘OR’ is the overround. To show the effect of this I have created a graph showing the EV per £10 stake vs the Betfair odds of the accumulator:

The main point to note is that the bookie payout to BF payout ratio is more important than having odds close to the optimum at around 3.00. For example, accumulator odds at 10.00 with 0% overround has the same expected value as accumulator odds at 6.00 with 5% total overround. In this case a 5% increase in overround is equivalent to a 67% increase in the odds of the accumulator winning!

The only bookmaker I’m aware of that will allow you to do this offer at odds as low as 3.00 are SportingBet. Another good bookmaker for high EV is GentingBet although they have a minimum odds requirement of 6.00. They often have very good odds with minimal overround. I’ve often found potential accumulators at odds 11 which have odds of around 11.25-11.5 on Betfair. I try to keep the odds as close to 6.00 however as variance increases exponentially with lowering probability.

__Suggested Starting Bankroll__

In general the maximum refund for these offer is a £25 free bet and generally you will be forced to take odds around 6.00, with an average total overround of about 15% as a worst case scenario. With this in mind I wrote a quick simulation in Octave/Matlab to see what the expected drawdown of this would be. A thousand trials were run each consisting of a thousand bets. The code is shown below:

clear() clc() for j = 1:1000 for i = 2:1001 x(1) = 0; a(i) = rand(); if a(i) < 0.145 x(i) = x(i-1) + 125; %Win elseif a(i) > 0.145 && a(i) < 0.485 x(i) = x(i-1) + 20 - 25; %Refund elseif a(i) > 0.485 x(i) = x(i-1) - 25; %Two or more losses endif endfor lowest(j) = min(x); j endfor bust = min(lowest);

Here are the results:

Max Loss > £200 | Max Loss > £500 | Max Loss > £1000 | Max Loss > £1500 | Max Loss > £2000 | Max Loss of all 1000 trials (£) |
---|---|---|---|---|---|

522 | 204 | 49 | 13 | 4 | 2325 |

If we assume we want the chance of losing our starting bankroll to be less than 1% then the suggested starting bankroll is around £1600.

Visit Part 2 where I shall detail ways of laying off accumulators and their expected value compared to not laying them off.

__Suggested Bookmakers__

SportingBet – Stake back up to £25 if one leg in a fivefold or greater accumulator doesn’t win. **No minimum odds**. They even even allow live bets! The only drawback is that all legs must finish on the same day. This can sometimes be a pain if not many big league matches are on as you’ll have to make a choice between taking poor odds or no odds.

GentingBet – Stake back up to £20 if one leg in a fivefold or greater accumulator doesn’t win. Min odds of 3 legs must be 1.50 and total accumulator odds of 6.00.

Dafabet – Stake back up to £30 if one leg in a sixfold or greater accumulator doesn’t win. Min odds of each leg is 1.20.

21Bet – Stake back up to £25 if one leg in a fivefold or greater accumulator doesn’t win. Min odds of each leg is 1.33.

Betmclean – Stake back up to £25 if one leg in a fivefold or greater accumulator doesn’t win. Min odds of each leg is 1.2. Main leagues only e.g. Serie A, La liga, Bundesliga, English Premier league etc.

Mintbet – Stake back up to £25 if one leg in a fivefold or greater accumulator doesn’t win. Min odds of 1.5 per leg.