Applying Expected Value Principles to Maximize Free Opportunities

The Mathematical Concept of Expected Value in Sports Betting

Let’s start with the basics. The EV tells you how much you would expect to win or lose by placing the same bet over and over again. A positive EV tells you that you can expect to gain a profit over time, while a negative EV tells you that you should lose more than you win. The simplest way to calculate the EV is using this formula: EV = (Probability of Winning × Profit if Win) − (Probability of Losing × Amount Lost).

The probability of winning is the key to getting this figure right, as this is where you need to work out the real probability rather than relying on the sportsbook’s odds. This can be done most simply by removing the vigorish (vig) or juice that the sportsbook has added. Alternatively, you might carry out your own research to calculate the chances of each outcome occurring, taking into account the most important statistics and factors like previous meetings, current form, and injuries. When adding the profit figure, you need to exclude your stake from the total.

An Example of Using the EV

We can make this clearer by looking at an example. Let’s say that the Los Angeles Lakers are playing the Boston Celtics. The moneyline bet has the Lakers favorites at -180, while the Celtics are underdogs at +150. You work out that the Celtics have a better chance of winning based on current form and availability, so you want to know the EV for a $100 bet.

At +150, the potential profit is $150, while the possible loss is $100.: The implied odds can be worked out as follows: implied odds = 100 / (odds + 100). This gives us a 40% chance of a Celtics win according to the odds. Let’s imagine that you work out that this probability is actually 45%, meaning a 55% probability of losing.

We can now plug the numbers in the EV formula to give us (0.45×$150.00)−(0.55×$100). This leads to EV=$67.50−$55.00, meaning a positive EV of $12.50.

The Use of EV in Other Forms of Gaming

While EV usage is closely linked to sports betting, it’s also moved into other areas of gaming in recent times. If we consider that free spins are still gaining popularity, a casino with free spins gives players a great chance to try new games. Yet, it makes sense to analyze which offers make the most sense.

Since slots have a completely random outcome, the EV formula would normally be simply: Expected Winnings from Free Spins − Expected Loss from Wagering. However, with free spins, the EV formula no longer needs to take into account the risk of loss, as there is no entry cost.

Instead, we need to add in the extra factors from the offer’s terms and conditions. We can start by looking at the total value of the spins multiplied by the return to player (RTP) of the slot. This could give us something like $10 x 0.96 = $9.60, on a $10 offer with a 96% RTP.

Don’t Forget the Wagering Requirements

The next step is to add the wagering requirements. If you need to play through the winnings 20 times, then this gives $9.60 x 20 = $192. You need to gamble $192 to cash out your winnings, but you would expect some losing spins during that process. In this case, we apply this formula: Expected Loss = Total Wagering × House Edge. For example, $192 x 0.04 = $7.68.

We can now combine the different formulas to calculate our EV on the free spins. This would give us $9.60 - $7.68 = $1.92. In this case, we can see a small expected profit.

By looking for offers with a high spin value and low wagering requirements that you can use with high RTP slots, you can effectively work out which casino free spins bonuses are best for getting the highest EV.