Profiting From Accumulator Offers Part 2

Following on from Part 1 I will detail two ways to lay off an accumulator so that we can reduce variance. Naturally a small chunk of our expected value (EV) will be sacrificed since we will be laying up to £100 on average. Both of the methods have their merits and it is mostly a matter of preference which you prefer.

Lay sequentially

This is the best way to lay off an accumulator while keeping the qualifying loss low for each outcome. It also has a better EV than the lay at start method. The process involves considering the lay bet as a whole (ignoring the refund), and attempting to equalise profit/loss after each leg since the potential payout stays the same but the probability of the accumulator winning increases. That probably doesn’t make much sense right now so here’s an example involving five hypothetical selections with a £25 stake:

Match 1: Back 1.3, Lay 1.32

Match 2: Back 1.2, Lay 1.25

Match 3: Back 1.5, Lay 1.52

Match 4: Back 1.4, Lay 1.43

Match 5: Back 1.3, Lay 1.33

Total: Back 4.26, Lay 4.77

When the first match of the acca has started we know that if it loses that we won’t receive a payout at bookmaker even if the other matches win. We can thus treat it as a single bet with back odds of 4.26 and lay odds of 4.77 and try to equalise profit and loss like a normal matched bet. This gives a required lay bet of £22.42 and a loss of £3.02 if we have 2% commission (it really helps to use Smarkets so that you don’t lose too much to commission). If the match loses then we don’t need to lay anymore bets and then we can hope the rest of our bets win so that we can receive a free bet. We will have lost our £25 at the bookmaker and gained £21.98 at the exchange.

If match 1 wins however we can move onto the next match but also consider the rest of the accumulator as a single bet. In other words we still have a Back bet at 4.26 but our lay odds are 4.77/1.32 = 3.61. The required lay bet to equalise profit is £29.67 but instead of a loss we make a profit of £4.07 since we are backing a higher price than we are laying. If the match loses then again we don’t need to lay anymore bets and we simply hope that the rest of the matches win. Our cumulative net loss will be +4.07 – 0.32*22.42 = -£3.10 for the sequence WLWWW. The ‘0.32*22.42’ comes from the fact that we have lost our liability from the first match winning.

If match 2 wins however we can repeat the process. We’ll still be backing at 4.26 but our lay bet is now 4.77/(1.32*1.25) = 2.89. The required lay bet to equalise profit is £37.11 with a profit of £11.36. Our cumulative net loss so far will be +11.36 – 0.32*22.42 – 0.25*29.67 = -£3.23 assuming match 3 loses i.e. WWLWW. 0.25*29.67 is the liability we lost from selection 2 winning.

Match 3 wins: We’ll still be backing at 4.26 but our lay bet is now 4.77/(1.32*1.25*1.52) = 1.90. The required lay bet to equalise profit is £56.65 with a profit of £30.52. If selection 4 loses the Our net loss will be +30.52 – 0.32*22.42 – 0.25*29.67 – 0.52*37.11 = -£3.37 i.e. sequence WWWLW.

Match 4 wins: We’ll still be backing at 4.26 but our lay bet is now 4.77/(1.32*1.25*1.52*1.43) = 1.33 (i.e. the lay odds of selection 5). The required lay bet to equalise profit is £81.30 with a profit of £54.67. If selection 5 loses then the net loss is +54.67 – 0.32*22.42 – 0.25*29.67 – 0.52*37.11 – 0.43*56.65  = -£3.58 for the sequence WWWWL. If selection 5 wins however we lose our lay bet so our profit will be 3.26*25 – 0.32*22.42 – 0.25*29.67 – 0.52*37.11 – 0.43*56.65 – 0.33*81.30 = -£3.58 i.e. the same as the last match losing.

If you’re wondering why the loss gets larger after each match it is because I ignored the effect of increasing commission to make the calculations simpler. If you work through the problem with a hypothetical 0% commission each time you should find that the loss is more or less constant. If you want the loss to be constant and to be able to find these matches more easily I would recommend signing up to OddsMonkey since they have accumulator calculators and matchers to make the process far easier.

EV Comparison to No Lay Method

The approximate probability of each sequence occuring is:

LWWWW = (1-1/1.32)*(1/1.25)*(1/1.52)*(1/1.43)*(1/1.33) = 6.7%

WLWWW = (1/1.32)*(1-1/1.25)*(1/1.52)*(1/1.43)*(1/1.33) = 5.2%

WWLWW = (1/1.32)*(1/1.25)*(1-1/1.52)*(1/1.43)*(1/1.33) = 10.9%

WWWLW = (1/1.32)*(1/1.25)*(1/1.52)*(1-1/1.43)*(1/1.33) = 9.0%

WWWWL = (1/1.32)*(1/1.25)*(1/1.52)*(1/1.43)*(1-1/1.33) = 6.9%

Total: 38.7%

If we average the net loss after each leg the total EV will be around:

EV = 20*0.387 – 3.26 = £4.48

In Part 1 we derived a formula for the EV of the no lay method. The total overround for this accumulator is 1 – 3.26/3.77 = 13.5%. This is ignoring the back-lay spread for the sake of argument. Hence the EV is:

EV = 4*(X-0.8 – X-1) – OR*(X-1)/X = EV = 4*(4.77 -0.8 – 4.77 -1) – 0.135*(4.77-1)/4.77 =  £0.2 per £1 bet

Hence the EV for the full £25 bet is £5. As you can see we lose £0.52 or about 10% of our EV to commission in this example.

There are however obvious drawbacks to this method:

  • Since you are laying after each match you need to find matches that finish one after another so that you have the opportunity to lay. That can make finding matches harder and chew into your free time.
  • Any odds movement mean that you will need to recalculate your lay stake each time.
  • The calculations are tedious, even with a matched betting calculator, which is why I recommend that if you are to use this method you sign up to OddsMonkey so that you don’t waste too much time.
Lay At Start

This method is an alternative to the lay sequential method for those with time constraints. Its main downside is that 30-40% of the time when 1 leg loses we will lose more than a simple qualifying loss of around £3 as we did with the lay sequential method.

The most basic way of doing the lay at start method is to simply lay each of the bets as if we were doing a normal single matched bet to equalise our profit/loss. If we use the same hypothetical matches from the past section that means for match 1 we lay £25.00:

And for match 2:

And repeat for the rest of the matches. I have tabulated the required lay stakes, lay win profit and liability for each of the matches:

Match Lay Stake Lay stake*0.98 (i.e. profit if lay win) Liability
1 25.00 24.50 8.00
2 24.39 23.90 6.10
3 25.00 24.50 13.00
4 24.82 24.32 10.67
5 24.81 24.31 8.19

The average profit from each lay win (selection lose) is £24.31, the average liability is £9.19 and the average lay odds are 1.37. This means our average profit is:

All five selections win: +3.26*25 – 5*9.19 = +£35.55, Probability: 20.72%

4 wins 1 loss: -25 +24.31 – 4*9.19 + 25*0.8 = -£17.45, Probability: 38.33%

3 wins 2 losses: -25 + 2*24.31 – 3*9.19 = -£3.95, Probability: 28.37%

2 wins 3 losses: -25 + 3*24.31 – 2*9.19 = +£29.55, Probability: 10.50%

1 win 4 losses: -25 + 4*24.31 – 9.19 = +£63.05, Probability: 1.94%

5 losses: -25 + 5*24.31 = +£96.55, Probability: 0.14%

The EV is thus: +35.55*0.2072 – 17.45*0.3833 – 3.95*0.2837 + 0.105*29.55 + 63.05*0.0194 + 96.55*0.0014 = £4.02.


Notice how we give away nearly twice as much EV with the lay at start method compared to the lay sequential method (52p vs 98p). This is simply due to the fact that on average we will pay more commission with the lay at start method as the method allows us to win several times on the exchange. This is in contrast to the lay sequential method where we can only win once at the exchange, and more often than not this will be when we’re laying at lower stakes towards the beginning rather than the large amount required for the last leg.

Out of the two lay methods I personally prefer the lay sequential method as we don’t sacrifice that much EV and at the same time it smooths out variance better as we don’t have to worry about losing most of our stake if 4 wins and 1 loss occurs. This is dependent on the football schedule though as its benefits can away its drawbacks if we have to place an accumulator over several days in order to find good close odds. Some bookmakers e.g. SportingBet don’t even allow accumulators spread over several days for their offers so in that case you will be forced to use the lay at start method.

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