For example, the bookmaker offers fixed odds on a win, a draw or a loss for team sports events. An odds indicates the ratio of the stake to the possible profit: for example, "pay 2.50 for 1 euro stake". The bookmakers can change variable odds at any time. However, bets that have been placed retain the agreed odds that applied when the bet was placed.
The multiplication of the odds with the bet gives the possible profit.
The bookmaker may be taking large risks as he is dealing in probabilities and often large bets. To limit the risk, bookmakers offer bets on all possible outcomes so that they ideally make their profit through arbitrage. To avoid high risk of loss on unbalanced bets, the bookmaker may, for example, limit the size of the bets or reinsure on international betting exchanges. As a rule, however, the bookmaker operates an extremely profitable business.
The bookmaker has an advantage over the bettor because he does not have to predict the correct outcome for his winnings. His task is to correctly estimate the percentage of bets for the various betting outcomes and to calculate the odds based on this. By looking at his "books", the bookmaker can constantly see how the bets placed are distributed in percentage terms. He can adjust the odds at any time. Similar to election projections, he then arrives at very precise statements regarding the betting predictions of the bettors with very small random samples. Large bookmaking companies work with extensive statistical material and methods.
With "fair odds", the bookmaker would have to pay out all the money of the losers to the winners. Of course, however, the real odds are below this, resulting in the bookmaker's profit: the bookmaker margin. The "counterpart" to this - the payout ratio - is between 50% and 60% at the German ODDSET. With many other (especially private) bookmakers, payout ratios of over 90% are not uncommon. The payout ratio can be calculated on the basis of the odds offered, assuming that it is the same for each outcome. This is done by adding the reciprocals of the odds. The payout ratio is the reciprocal of this sum (harmonic mean), for example 1 for a payout of 100%. In a 2-way bet, for two players of equal value, both are offered the odds of 1.95 to win. 1/1.95 + 1/1.95 = 0.5128 + 0.5128 = 1.02564 → 1/1.02564 = 0.975 = 97,5 %. This means there is a very small bookmaker margin of 2.5% in these odds. If only 1.80 is offered for the two players, that means a margin of 10%.