Single Bets or Accumulators ?

In this lesson we will talk about single bets or accumulators, the differences, the odds of single bets or accumulators and why bookmakers encourage bettors to place accumulators.
It is a fundamental lesson because we will see why an expert bettor never bets in accumulators or at least only rarely and for leisure, never for profit.

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The different types of games

Modern bets can be divided into single bets, accumulators, and betting systems.
A single bet provides for a single event to be predicted: when the event occurs, the bet is called a winner.
The accumulators  have one or more events to predict (max 20) simultaneously. To be successful, all the forecasts of which it is composed must be correct.
A betting system , finally, allows betting on multiple events as in an accumulator but, unlike this, you can get a win even if not all the bets are correct. The famous double and triple systems are part of the betting systems. We will talk more about it in a dedicated chapter.

Single bets: winning odds

Before continuing, it is necessary to remember the definition of classical probability: the ratio between the number of favourable cases and the number of possible cases, whether they are equitable .
We have seen that in the case of sports betting, the probability of an event is suggested by the odds. Apparently very low odds are attributed to high success rates and vice versa. We have also seen, however, that this value is influenced by bookmakers’ advantage and psychological tricks.

Single bets, precisely because they require the occurrence of a single event, represent the most suitable types of bets to apply positive progression strategies that aim at high profits.

Accumulators: calculation of the probability of winning

As already mentioned, a bet is defined as an accumulator when it is composed of several events and, in order to win, all events must occur. The events are independent of each other, that is, the occurrence of one does not affect the occurrence of the other.
The probability of multiple independent events is given by the intersection of the probabilities of the individual events, that is, by their product.


We calculate the probability of success of the following accumulator formed by 2 events:

  • Inter Milan, probability of event X: 1/3 = 0.33 = 33.33%
  • Juventus – Rome , event probability Over 1.5: 1/2 = 0.50 = 50%
  • Probability of winning the accumulator = 0.33 * 0.50 = 0.165 = 16.5%

Let’s see how the probability changes when a third event is added:

  • Inter Milan, probability of event X: 1/3 = 0.33 = 33.33%
  • Juventus – Rome , event probability Over 1.5: 1/2 = 0.50 = 50%
  • Naples – Chievo Verona , event probability DC 1X: 1/2 = 0.50 = 50%
  • Probability of multiple wins = 0.33 * 0.50 * 0.50 = 0.08 = 8%

The calculations just mentioned are a bit inaccurate because they do not take into account some fundamental factors that are included in the calculation of the odds, such as the performance and the shape of the team.
To understand better, with the classic probability all 1-x-2 events of the Inter Milan match referred to above have a 33.33% probability of occurring, but we know that it would not be exact that if Inter were at the top of the standings and Milan back from 4 consecutive defeats.
Let’s see how to have a more accurate calculation of the probability of winning an accumulator.

Accumulators: calculation of the probability of winning

In order to have a more accurate calculation of the probability of winning by an accumulator, we also take into consideration the odds cleared of  bookmaker’s percentage. To speed up, we will calculate the probability of the first accumulator, the two-event probability.

Let’s assume that the bookmaker suggests the following odds:

  • Inter Milan:  1  (2.10)  X  (3.25)  2  (3.70)
  • Juventus – Rome: Under 1.5 (1.62) Over 1.5 (2.15)

The percentage is 5% on the first and 8% on the second. The odds without this advantage would be the following:

  • Inter Milan:  1  (2.17)  X  (3.44)  2  (4.00)
  • Juventus – Rome: Under 1.5 (1.75) Over 1.5 (2.38)

We will calculate the probability of individual events as the average between the probability given by the betting odds and that given by the classical probability:

  • Inter Milan – event probability 1: (1/3 + 1 / 2.17) / 2 = (0.33 + 0.46) / 2 = 39.5%
  • Inter Milan – event probability X: (1/3 + 1 / 3.44) / 2 = (0.33 + 0.29) / 2 = 31%
  • Inter Milan – event probability 2: (1/3 + 1 / 4.00) / 2 = (0.33 + 0.25) / 2 = 29.5%
  • Juventus – Roma , probability of Under-15 event: (1/2 + 1 / 1.75) / 2 = 0.54 = 54%
  • Juventus – Rome , event probability Over 1.5: (1/2 + 1 / 2.38) = 0.46 = 46%

Now we can proceed with the calculation of the probability of success of our accumulator:

  • Inter Milan – event probability X: 0.31 = 31%
  • Juventus – Rome – probability of event Over 1.5: 0.46 = 46%
  • Probability of multiple wins = 0.31 * 0.46 = 14%

If instead of betting on Inter Milan’s X, we bet on 1, the probability would change to:

  • Inter Milan – probability of event 1: 0.395 = 39.5%
  • Juventus – Rome – probability of event Over 1.5: 0.46 = 46%
  • Probability of multiple wins = 0.395 * 0.46 = 18%

And if we bet only on the events considered, according to the odds, more probably (respectively 1 and Under 1.5), the probability of winning of the multiple would change in:

  • Inter Milan – probability of event 1: 0.395 = 39.5%
  • Juventus – Roma – probability of Under-15 event: 0.54 = 54%
  • Probability of multiple wins = 0.395 * 0.54 = 21.3%

As we can see, despite the most accurate calculation, the probability of winning the accumulator remains very low compared to the probability of winning the games taken individually (and therefore played in single).

Why do bookmakers prefer accumulators?

Bookmakers have two advantages in preferring accumulators:

  1. The first advantage is that as the number of events increases, the probability of success of the bet immediately decreases, as seen above.
  2. The second advantage is that as the total odds increase (and therefore also the number of events) the percentage of total odds increases.
  3. Many bookmakers offer a multiple bonus when the accumulator reaches a high level. More than a bonus, it is a small “discount” that bookmakers make to bettors in relation to the very high percentage of book breaking achieved.

Summing up, so now it is clear why experienced bettors prefer to place single bets, applying the different strategies including particular high-profit progressions.

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