Singles Or Doubles Which Makes More Profit

Guest post by DOC from Punters Paradise.

The choice between backing singles or doubles may often come down to personal preference but the Devil is in the detail.

Some background

Back in the long ago, bookmakers were surly beasts who wouldn’t accept anything less than a treble on football bets (or so I’m told!).

In this day and age, with easy access to the Internet for many punters, the increased competition has forced the end of this practice. Punters have the option of checking a wide range of bookies to find the best odds, leading in many cases to the virtual elimination of the bookmakers margin, or ‘overround’ .

“Bookmakers were surly beasts who wouldn’t accept anything less than a treble on football bets.”

That freedom to choose prices from a range of bookmakers, means that even those who bet on a large number of games may only have a single bet with a particular bookmaker at any one time.

“Many betting sites would have strongly advocated betting in single bets, rather than multiples. But is this correct?”

Meanwhile, many betting sites would have strongly advocated betting in single bets, rather than multiples – and certainly staying away from large accumulator bets.

But is this correct? We assume that the bettor is only placing his/her money when they believe they have an ‘edge’ – that is the return being offered is higher than their estimation of the risk. This is the ‘value principle’ that underlies all successful gambling.

However we know that the edge is multiplicative rather than additive – that is, if I have an edge of 20% on two bets (highly optimistic, but indulge me!), then the edge on a double is 44% rather than 40%. So I actually achieve a higher edge on multiple bets. Given that the edge is the average profit I can expect to make on any given bet, we appear to have an answer, yes?

Other things being equal, yes we do – but other things are seldom equal. We also need to account for the fact that I am now staking at longer odds, so will expect less winners. To maintain my risk at reasonable levels I need to reduce my stake size when betting longer odds. And after all, a double bet can be viewed as a single (where I bet that both events happen) with longer odds.

It would seem therefore that there may be some optimum in the middle where the balance of higher risk (for the doubles) is compensated for by the higher expectation. This series of articles sets out to explore this middle ground.

The Approach

“We’ll need to make certain simplifying assumptions, which hopefully will allow us the insight to generalise to more realistic scenarios.”

If we are going to look at a problem like this we’ll need to make certain simplifying assumptions, which hopefully will allow us the insight to generalise to more realistic scenarios.

What I have done here is to examine a wide range of possibilities in several distinct groups. I assumed that the bettor began with a bank of 100 units and had a season of 300 ‘events’, all of which were at the same odds, and all of which had the same edge.

An event was considered as two parallel ‘matches’. For each ‘event’ there were three possibilities – both ‘matches’ won, both lost, or one won and the other lost. I considered on one hand a bettor who bet doubles (using the recommended Kelly stake for this combination of edge and odds), and on the other hand a singles bettor who bet half the recommended Kelly stake (for the single) on each of the two singles.

This constituted a single simulation run, at the end of which I recorded whether the bettors bank (in each of the cases of singles and doubles bettors) had dipped below 80 units, 60 units, 40 units, 20 units or 0 units (i.e. bankrupt). Each simulation run was repeated 1000 times. Finally the above process was repeated for every combination of odds and edge, using the following odds:

• 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 5.0, 10.0

and the following edges

• 1%, 2%, 3%,………19%, 20%

In these articles I’ll look at the risks to your bank when staking singles with various odds and edges. The staking in both cases will be ‘fixed-Kelly’ – that is calculated based on a 100 unit (i.e. starting) bank, not on the current bank as is the case with ‘pure’ Kelly staking.

The results

The graph below shows the risk of dropping below 80 units bank during the course of a ‘season’ when betting with varying edges at odds of 1.4.

e.g. with an edge of 5% there is a 40% risk of the bank dipping below 80 units at least once during the season. We must be careful about drawing too many conclusions from this one graph, and from a limited simulation run (we would prefer 50,000 or 100,000 simulations rather than just 1,000 – to smooth out the ‘noise’ in the graph). However, in part 2 we can note certain things, which we can then keep an eye out for in the other results.

DOC is the owner of the Punters Paradise forum. One of best forums online for serious bettors and those looking to learn how to make a profit, a lot of regulars have very strong statistical skills and there is a lot of conversation around these topics. I have had many of my questions answered there.