How To Calculate The Expected Value of a Casino Bonus

It's no secret that one of the biggest reasons players sign up with online casinos is to claim their generous bonus offers. However, to inexperienced and uninitiated players picking an online casino bonus is all about its size. In other words, they believe the bigger the bonus, the better the bonus. The reality is that with bonuses bigger is not always better.

What utter nonsense, I sense you thinking. Of course bigger is better. Why else would you choose one bonus offer over another? Well, the answer to that question is if one bonus has a better 'expected value' (EV) compared with another. Expected what, you say? Expected value, which you can use to work out if a bonus is worth your while to claim or not.

What is Expected Value?

Although a widely known concept use by mathematicians and economists, expected value has only recently become a 'thing' in the online casino world, and a good thing too. Expected value is the mean or average of a random variable which, in the context of online casino bonuses, can be used to work out whether a particular bonus will be financially worthwhile to claim or not.

Ideally you always want to see a positive expected value which means that the bonus should be beneficial i.e. give you a positive return when you claim and use it. It's important to note that expected value is not designed to work out probabilities over the short-term because its formula is reliant on a weighted average to deliver an accurate outcome or result.

To put in other words, it is a statisical calculation and repsresnt the average outcome of a series of events, in this case bets on a casino game where every event is based on a random outcome.

How to Calculate Expected Value?

The expected value of any online gambling scenario can be calculated if you have the right variables or values. Plug these values into the special formula and you can determine if the expected value will be positive or negative. The easiest way to demonstrate this is with a two-sided coin flip with values; the odds of that bet paying out + the pay-out of a bet.

To work out the EV of a coin flip for money over time, you can use the following formula:

EV of coin flip = (Odds of heads) x (Pay-out of heads) + (Odds of tails) x (Pay-out of tails)
= (50%) x (£1) + (50%) x (-£1)
= (50p) + (-50p)
= 0

Conclusion: The expected value of this coin flip is zero, meaning you should come out even.

If, however, the pay-outs were different for heads and tails, the EV would be different:

EV of coin flip = (50%) x (£2) + (50%) x (-£3)
= (£1) + (-£1.50p)
= -50p

Conclusion: The expected value is -50p which means you'll likely come out behind and should thus avoid this bet.

Applying Expected Value to Online Casino Bonuses

To work out the expected value of online casino bonus offers you need three key variables:

  • The total bonus
  • The house edge of advantage of the particular casino game you intend to play using the bonus
  • The bonus wagering requirement in currency (instead of percentage).

Next, simply plug these values into the EV online casino formula as featured below.

Take, for example, a Welcome Bonus worth £200 with a wagering requirement of £4,000 (this is calculated by multiplying the wagering requirement (20) by the total bonus size (£200)) that you intend to use to place on Roulette bets with a 2.5% house edge:

EV of bonus = (Total bonus) - (House edge) x (Wagering requirement)
EV of bonus = (£200) - (£100)
EV of bonus = £100

Conclusion: The expected value of this online casino bonus is £100 which means it's worth claiming.

It's important to remember that EV is only an average, which means there is no guarantee that you'll personally win £100 or any other amount. It just means that in the long-term the majority of players that claim this bonus will come out ahead, and is thus worthwhile.

Consider another example, a 100% Match Bonus of up to £300 with a wagering requirement of £10,000 which you use to play an slot machine game with a house edge of 3.5%:

EV of bonus = (£300) - (3.5%) x (£10,000)
EV of bonus = (£300) - (£350)
EV of bonus = -£50

So you stand to lose £50 in trying to play through the bonus.

Conclusion: The expected value of this bonus is- £50 which shows it has an average negative expectation. Is it worth claiming? Probably not but there is always the random possibility that you hti a big win playing this game, and wmanegd to wager through the requirement without losing a large amoutn of your winnings.

Why is the Expected Value of a Bonus Important to Know?

It is important to calculate the expected value of any given online casino bonus so you can calculate how much a bonus offer is likely to cost you in real money when you choose to use it to play certain games.

Online casinos are very clever because they offer players what appear to be very generous bonuses, but which can actually cost you more than you think on the way to fulfilling their particular wagering requirements listed in their bonus terms and conditions.

With the exception of no deposit online casino bonuses which are 100% free to claim, all Welcome / Matching / Sign Up bonuses (for new players) and Reload bonuses (for existing players) require you to make a deposit in order to unlock, claim and use them.

When you start playing, you're actually playing with deposited funds and bonus funds as both contribute to the bonus wagering requirements. This can put you at risk of losing some if not all of your real funds en route to meeting the bonus wagering requirements.

How House Edge Impacts Expected Value

For this reason the games you decide to play can have a big impact on the expected value of a particular bonus. It's not so much about the games themselves, but about their particular house edge, as every casino game under the Sun comes has its own house edge.

Using the expected value casino bonus formulas highlighted above, you can see for yourself how the house edge of one game can make the EV of a particular bonus feasible and the house edge of another game can make the exact same bonus offer unfeasible.

Take for instance the same 100% Sign Up bonus highlighted above worth up to £400 with a wagering requirement of £10,000, and find out what happens when it's EV is calculated if it is used to play Roulette (2.5% house edge) compared with if it used to play Caribbean Stud Poker (5% house edge):

Roulette - 2.5%

EV of bonus = (£400) - (2.5%) x (£10,000)
EV of bonus = (£400) - (£250)
EV of bonus = £150

Conclusion: The expected value of this bonus is £150 which means it's worth claiming.

Caribbean Stud Poker - 5%

EV of bonus = (£400) - (5%) x (£10,000)
EV of bonus = (£400) - (£500)
EV of bonus = -£100

Conclusion: The expected value of this bonus is- £100 which means it's not worth claiming as you will lose this amount in tryign to wager the requirement.