There is no one-size fits all approach when it comes to the ideal number of bookmakers. Factors that have an influence on the ideal number of bookmakers are the number of arbitrage opportunities a user wants to have, the amount of risk a user wants to bear, the size of the winnings when placing bets, and the size of the total bankroll.
When more bookmakers are selected the number and the size of the arbitrage opportunities goes up, due to more options to place a bet with the highest available odds. However, more bookmakers means a larger spread of funds, which translates into lower available money to place at an individual bookmaker. Furthermore, when placing bets at different bookmakers, there will be fluctuations in the account balances of the different bookmakers. Some account will be in the plus, due to winnings at that specific bookmaker, while others will be in the minus, due to losses at that specific bookmaker.
To make the differences between accounts not to large, it is advised to never bet more than 25 percent of the starting account balance of one bookmaker at a certain bookmaker at once. This means that when you deposit, for example, €200 to a bookmaker, never bet more than €50 at that bookmaker on one single bet. When the bettor does this the fluctuations in the account balances will be relatively small, which causes that transferring money between bookmaker account will be less often necessary. The reason bettors should not want to transfer money between accounts is because it will cost time and sometimes money in the form of withdrawal and deposits costs. Also, bookmakers make costs every time a user withdraws or deposits money, making them not happy with a customer that constantly does this. Meaning the likelihood off a closed or limited account will get larger when users constantly transfers funds.
Another important factor is the risk a user wants to bear. Even though the aim is to bet on arbitrage opportunities, errors can occur, especially beginners will sometimes make errors when placing bets. Also, sometimes a bookmaker cancels a bet, while the other bookmaker keeps the bet in play. Because of this there is always a small risk. It is advised to always bet a maximum of 2,5 percent of the total bankroll. Because of this errors will be less fatal for the bankroll and funds will be less spread, as will be displayed in the tables below.
Nevertheless, when a higher percentage of the total bankroll is being placed, a higher on average winning per bet will occur. However, due to the lower number of bookmakers, keeping in mind that it is advised to never place more than 25 percent of the available funds at a certain bookmaker, the arbitrage opportunities will likely be smaller and less occurring. Finding a balance between these aspects, keeping also in mind how much a user wants to earn with a single bet, is user dependent. Nonetheless, keeping the 25 percent at a single bookmaker and 2,5 percent of the total bankroll guidelines discussed above in mind there can be something said about the ideal number of bookmakers.
In table 1 a list is presented with total number of bookmakers ranging from 2 to 20, a total bankroll size of €2.000, the total stake at each bookmaker when funds are equally divided, total bet size when keeping in mind the 2,5 percent guideline and average win per bet based on an average arbitrage profit of 2 percent. Note that the bold numbers in total bet size column exceed the 25 percent guideline.
Also note that the total bet size column represents the maximum value of the combined bets on all the bookmakers the bets are placed, but the 25 percent guideline is based on only one bookmaker. The reason for this is mathematical practicality and, even though it does not occur often that more than 99 percent of the stake is placed at one bookmaker, the numbers in the total bet size should give some indication. For example, odds in a two-way bet of 1.15 or lower mostly already require that more than 90 percent of the bet is wagered at one bookmaker.
Table 1 shows that 10 bookmaker is the maximum number of bookmakers keeping the 2,5 percent and 25 percent guidelines in mind. More bookmakers means more and higher opportunities for arbitrage profit, meaning that 10 bookmaker would be the ideal number, keeping in mind the presented guidelines.
However, not every person will agree with the guidelines. For example, they want more risk to get potential higher rewards by increasing their bet size to a maximum of 5 percent of their total bankroll and/or they take less large buffers and play with a maximum bet of 50 percent at one bookmaker. The ideal number of bookmakers changes when these preferences change, as can be seen in tables 2, 3 and 4.
Table 2 indicates that 5 bookmakers are ideal when a players uses a 5 percent maximum bet and keeps the 25 percent guideline as a max bet at one bookmaker. Note that the average arbitrage profit stay at 2 percent, increasing the win per bet to €2. In reality this number will likely get lower when less bookmakers are used, because there are likely less profitable arbitrage opportunities and the opportunities that arise are on average lower than when the user has more bookmakers.
Furthermore, when a player does not mind transferring a lot of funds he could choose to put the maximum bet per bookmaker at 50 percent, while keeping the 2,5 percent total stake per bookmaker. The results in table 3 indicate that 20 bookmakers are in this case ideal.
For players that are looking for greater risk, 5 percent of total bet size, and are willing to transfer funds between account a lot by keeping a 50 percent maximum bet of funds at each bookmaker, 10 bookmakers are ideal, as can been seen in table 4.
As can be argued from the tables above, depending on player preference, the ideal number of bookmakers lies between 5 and 20 bookmakers. Nonetheless, some arbitrage software providers cover up to 80 different bookmaker. The reason for this is because some of their users play with large amounts of cash and they face maximum bet restrictions. That is why they have to divide their funds over more than 20 bookmakers. Furthermore, the more experienced player is likely to have a preference for certain bookmakers and wants to have the option to choose between different ones.
The two guidelines
Guideline 1: Never bet more than 25 percent of the starting account balance of one bookmaker at a certain bookmaker at once.
Guideline 2: Never bet more than 2,5 percent of total funds at once.