Betting Bonus Expected Value – What is It and How to Use It to Make Money?

You must have seen those advertisements with betting bonuses such as ones by Bet-at-home or Bet365 and you must have wondered – is this for real? Are these brands actually giving money away? There must be some catch, right?

In this article we’ll look into that and tell you what are the exact mathematics of betting bonuses so you can make up your mind if you want to use them or not. It’s all very simple.

What is the Expected Value (EV)?

If you would play some game in which you’re expected to get back 95% of your investment with a bank of €100, you’d be expected to get €95 back, right?

Let that sink in for a bit. Whatever game you’re playing at a sportsbook or a casino, there is always a house edge. Betting odds, for example, are a bit worse than they should be if the sportsbook would be totally fair.

On two-sided events with 50-50 probability, you’d expect to see odds 2.00 – 2.00 on both sides, but in reality they will be closer to 1.90 – 1.90, which means there’s an inherent house edge built into those odds.

Expected Value Example

Let’s now take the Bet-at-home bonus as an example.

You get a 50% bonus on your first deposit, and the bonus can go up to €200. This means you have to deposit €400 of your own money to get €200 in bonuses.

Once you do that, you must place bets worth 4x your deposit and bonus. That would be €2400, and you must place all those bets on tickets with odds 1.70 or greater.

Now, the question is – if you were forced to bet €2400 on tickets with odds 1.70 or greater, how much would you win or lose? Well, if the 1.70 was a fair price and if it was indeed representing the probability of 1 / 1.7 = 58.82 then you’d break even.

But since Bet-at-home’s house edge is usually around 8%, you are expected to lose 8% of your money through vigorish. Take note, here we haven’t even begun to talk about you making good or bad betting predictions. We’re just examining the playing field and the rules.

If the house edge is 8% and you’re forced to bet €2400, you’re expected to lose €192.

The welcome bonus by Bet-at-home is €200, which means that it has a positive expected value (EV) of €8. That may not sound like much, but this is amazing – most casino and sportsbook bonuses have a negative expected value. When you find one with a positive value, it means you’re actually getting a very good deal.

How to Calculate EV for Other Games

In all cases, the EV calculation is the same.

You need to take a look at the house edge first. For example, in European Roulette it’s 2.70%. If you’re forced to make 1000 bets worth €1 on that game, you’re expected to lose 2.70% of your €1000, which is €27. After that, take a look at what the bonus value is. If it’s more than €27, you’re profitable.

This is a simple calculation that will always tell you if the bonus is worth pursuing or not. The key number to find here is the house edge, which isn’t always so straightforward. But once you do have it, you can calculate EV.