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Calculating fixed odds

posted in: Fixed-odds gambling

Fixed-odds gambling is a form of gambling against odds offered by a bookmaker, an individual, or on a bet exchange.

It is customary with fixed-odds gambling to know the expected odds at the time of the placement of the wager (the “live price”), however this category also accommodates wagers whose price is determined only after the race or game has taken place (the “starting price”). It is ideal for a bookmaker to price up a book such that the net outcome will always be in his favour, i.e. the sum of all possible outcomes will be in excess of 100%. The amount of the sums wagered in excess of 100% represent profit to the bookmaker in the event of a balanced book. This excess is known commonly as an overround. In the case of an imbalanced book, the bookmaker will have to pay out more winnings than what is staked, or he will earn more than mathematically expected. This may happen since there is no way for a bookmaker to know the true probabilities for the outcome of competitions left to human effort, and the fixed odds therefore being compiled on the basis of his personal view and knowledge.

With the advent of internet and bet exchange betting, the possibility of fixed-odds arbitrage actions and Dutch books against bookmakers and exchanges has expanded significantly. Betting exchanges in particular act like a stock exchange, allowing the odds to be set in the course of trading between individual bettors, usually leading to quoted odds that are reasonably close to the “true odds.”

In making a bet where your expected value is positive, you are said to be getting “the best of it”. For example, if you were to bet \$1 at 10 to 1 odds (you could win \$10) on the outcome of a coin flip, you would be getting “the best of it” and you should always make the bet. However if someone offered you odds of 10 to 1 that a card chosen at random from a regular 52 card deck would be the ace of spades, then you would be getting “the worst of it” because the chance is only 1 in 52 that the ace will be chosen. It is mathematically incorrect to make a bet where you are getting “the worst of it.”

When making a bet where you must put more at stake than you stand to win, you are laying the odds or laying the bet. So, for example, if you bet \$1000 that it will rain tomorrow, and if you win you will only win \$200 but if you lose you will lose your entire \$1000, then you are laying a bet. It is possible that you could be getting “the best of it” or “the worst of it” when you lay a bet; the fact that you are laying a bet does not necessarily mean you are getting “the worst of it”. A lay bet is a bet that something won’t happen, so if you lay \$50 on a horse then you are betting the horse won’t win.