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The Math Behind Betting Odds & Gambling

The Math Behind Betting Odds & Gambling

The criticality of understanding the mathematics at play behind Betting Odds & Gambling cannot be overstated. Any enthusiast or professional gambler worth his salt knows that Betting Odds describes the chances favouring the event and those not favouring the event. Probability, though similar, states the likelihood of a particular event’s occurrence.

The Math Behind Betting Odds & Gambling

Therefore, it pays to know that all the probabilities and odds around outcomes are computed using equations and mathematics is your new best friend in the gambling arena. An ideal world where odds are an accurate The Math Behind Betting Odds & Gamblingdepiction of the probability of the outcome would let the player gain a significant upper hand at winning the bet. However, this is where the margin of bookmakers comes into play. Their margins are ingeniously built-in to the system of calculating odds and thus a winning bet gets harder to accomplish. Some player overcomes this bias by the application of probability statistics in their gameplay.

The most important concept to comprehend to get the math behind Betting Odds & Gambling right is the type of different Odds and their conversion to probability. These include:

Fractional Betting Odds & Gambling

Fractional Betting Odds & Gambling are among the most popular odds in the world, primarily used by the UK and Irish bookmakers. A listing of 6/1 (called as six-to-one) implies that you win £6 for every £1 wagered (in addition to getting that wagered £1 back).

Decimal Betting Odds & Gambling

Decimal Betting Odds & Gambling are easier to comprehend and the number implies the amount a player wins in total for every £1 bet. As an example, if the odds of Donald Trump in the presidential election are 3.00, and a player bets £50 on this wager, then, he could make a total return of £150 (including the initial £50 wager).

American Betting Odds & Gambling

American Betting Odds & Gambling, which are popular in the US, employ negative and positive signs with the numbers to imply favourites and underdogs in the contest. The odds for favourites, coming with a minus (-) sign, shows the amount players need to wager to win £100. Similarly, the odds for underdogs, coming with a plus (+) sign, shows the amount players win for every £100 bet.

Odds to Probability Conversion

Both odds and probability together with critical analysis constitute the game plan of using probability statistics to place that winning bet. Odds conversion can get complicated with a plethora of formats used by bookmakers, like American, Decimal or Fractional Odds format. Instead of a peculiar formula to convert each kind of Odds into corresponding Probability, we can use a simple rule of thumb to convert any type of Odd into Probability:              

Probability of any Outcome = Stake / Total Payout


Where Stake = The amount placed as a bet

 Calculating using a few examples:

  • For fractional odds (2/3), the probability is computed as P = 3/(3+2) = 0.60, there is a 60% probability of the event occurring
  • For decimal odds (2.5), the probability is computed as P = 1/2.5 = 0.40, there is a 40% probability of the event occurring
  • For American odds -250, the probability is computed as P = 250/(100+250) = 0.7143, there is a 71.43% probability of the event occurring

A point worth noting in this whole exercise is that Betting Odds & Gambling are never a constant figure. They keep changing as more and more bets arrive at the bookmaker, and thus, the probability estimations of the bookmaker are time variant. Complicating the whole process is the fact that different bookmakers display different odds for the same event and that too by large margins, which implies that the odds derived by bookmakers aren’t always accurate.

It makes economic sense to back winners only when the odds are a true reflection of their winning chances. Therefore, the biggest value in a Betting Odds & Gambling environment is when the player’s calculated probability of any outcome turns out to be higher than the one assessed by the bookmaker. Going all out to wager in such a situation greatly improves the chances of winning the bet.

The House Wins, Always Wins

It is sufficiently clear that the odds showed by bookmakers never truly reflect the chances of an event taking place or not taking place. This is due to the fact that bookmarkers add their own operating margin to these odds, which ensures that the payout received by the winning player is always lesser than what he must have received if bookmaker’s odds had shown the true probabilities.

This whole analysis implies that bookmakers need to know the most accurate probability of an outcome so as to set it for customers in a way that makes them a hefty profit, irrespective of the outcome of the event. 

Calculation of Bookmakers Over-round

Consider this real-life example:

The figures display the probability for a Cricket World Cup match

Australia: -250 (probability = 71.53%)

New Zealand: +200 (probability = 33.23)

Upon close examination, you will see that the sum of these 2 probabilities is not 100% (which according to the law of probability, it should be) and is equal to 104.76 (=71.53 + 33.23). This has proved that the odds displayed by the bookmaker are not fair odds. In the number which shows the sum of the two probabilities, the percentage above 100% is 4.76%, which constitutes the bookmaker’s profit if his bookie accepts the wagers in a certain proportion. Essentially, you are taking the risk of losing £104.76 in order to certainly get back £100, and this difference is the profit of the bookmaker, no matter who wins or loses. What a brilliant in-built advantage!

Betting Odds & Gambling must be evaluated critically without blind reliance on the bookmaker’s display. In a similar way, the betting opportunity must be seen as valuable only if the probability calculated for an outcome is more than that approximated by the bookmaker.

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Post Name : The Math Behind Betting Odds & Gambling

Posted On : 01/07/2019

Author : Cameron Riddell