The relationship between bookmaker and bettor is based around the odds priced up by the former, and the opinion of the latter regarding the accuracy of that calculation.
The most readily used example is a fair coin toss. The expectation that either a head or tail will result from a single toss is equal, with an implied probability of 0.5, and if this expectation were to be converted to decimal odds, the fair price for a head or tail would be 2.0.
Of course, a bookmaker intent on making profit would price this market up at shorter odds than 2.0 to ensure that any bet made would, in the long term, be favourable to the book. A price of 1.87 on both would have an implied probability of 0.535 for each of the two possible outcomes.
The margin - learn how to calculate betting margins here - for such a simple market is derived from the sum of the implied probabilities. In the case of the example above, this would be 1.07 and the margin would typically be quoted as 7%.
The larger the margin, the easier task the bookmaker has to ensure their prices are not longer than the true chance of an event happening, which would present a long term value opportunity for the bettor.
Therefore, a bookmaker who consistently applies low margins to their markets, such as Pinnacle should be the preferred bookmaker, as they are more likely to present value betting opportunities in sporting markets, where, unlike a coin toss, the odds are influenced by numerous variables.
How likely is a run of profitable bets?
If betting with a low margin book is the first step to a profitable approach, the most visible sign that a series of bets have passed the value test, is a profitable yield.
However, bettors should look at how likely it is that a run of bets will produce a profit or loss based on the implied true probabilities.
If we again use the artificial example of a series of coin tosses, where we are certain of the true probability, we can calculate the likelihood that a particular run of bets will be profitable or not.
The outcome of ten such true even money bets can range from ten consecutive losing bets all the way through to a full house of winners.
It is more likely that the outcome of ten such trials will include a mix of successful and unsuccessful wagers and the most likely outcome is an even split of wins and losses. In simulations or by the use of a binomial calculator, this particular outcome has a probability of occurring nearly 0.25.
The outcome of each trial is independent of the previous outcome and the bookmaker will use the margin to offer an unfavourable price for each toss.
If, for example the price for each outcome was set at 1.87 - a margin of 7% - five successes from 10 bets would produce a return of 9.35 units if 1 unit level stakes were wagered on each of the ten bets.
Overall, a yield of 0.65 units lost from the ten units staked.
How the margin affects your returns
We can use this simple example to illustrate the importance of understanding the effect the bookmaker’s margin has on returns. If each event had been priced at 1.95, the margin would have only been 2.5% compared to the previous 7% and although a loss would still have been made from only picking five winners from ten bets, this loss would have fallen from 0.65 units to 0.25.
To make a profit from such a series of poor value wagers, six or more successes are required. And again either by simulations or with the online calculator there is just under a 0.21 probability that exactly six wins fall in ten trials, and a yield of 1.22 units are made at 1.87 or 1.7 units at the more generous price of 1.95.
Of course, seven wins and greater will also produce a positive return from these ten bets and the cumulative probability for each number of wins of six or greater totals nearly 0.38.
Therefore, because of how we have set up this artificial scenario, we know that each individual wager is priced to represent poor value for the bettor. Yet there is not an insignificant chance that six or more wins will occur in ten bets and a profit will be made.
Keep records to identify the difference between luck & skill
Real life betting sequences will involve a variety of prices and stakes, but the key to a successful approach will include identifying prices, which may not fully reflect your estimation of the actual chances of an outcome occurring.
Therefore, keeping a record of your estimation of the true probability of your bet being successful, alongside the implied probability from the bookmaker’s odds, is a good habit to develop.
Not only can you compare the two values, but it also allows for relatively simple spreadsheet based simulations, along the lines of the coin toss scenario, to be created to examine the part in which luck and skill may have played in the short term to your current yield.
A knowledgeable bettor will often think in probabilistic terms, not only for individual outcomes, but also in the profit or loss scenario from a sequence of such bets.