Variance And Expected Value

You'll hear us talking about variance lots.

The thing about casino offers is that the result is not guaranteed.

Often you will make a profit from a casino offer.  However, sometimes, you might make nothing, and sometimes you will even lose a little bit of money.

Imagine you completed a casino offer three times.

One time you might make a £5 profit, another time £20 profit, and another time you lose £4.  You've made a profit overall, but your results were completely different each time.

This change in results is variance.

You might be thinking, doesn't variance mean it's luck whether I make a profit or not?

And the answer is no! With casino offers, we can calculate an offer’s Expected Value. Expected Value is the amount of money that we expect to get back, on average, when we complete an offer.

If an offer has a positive expected value (+EV) then we have a mathematical edge and would expect to make a profit on average.

If an offer has negative expected value (-EV), then we would expect to lose money on average.

Because of variance, your profit or loss from completing an offer is going to vary from the EV.

Imagine an offer with £3 EV and you complete it 4 times.

Your results might be +£10, +£5, £0, -£3. Twice you didn't make a profit. But overall you made £12 profit, equal to £3 profit per offer.

The £3 value indicates what you should be making in the long term, on average.

If you attempted an offer 100 times, you’d expect the variance to balance out and a profit of about £300 overall (so £3 profit per offer on average).

If you consistently do +EV offers over time, there is an extremely strong chance that you will achieve a profit. Sometimes you will make money. Sometimes you will lose money.

Over the long term, the profits should far outweigh the losses, and your overall profit should be close to your EV.

You can find a detailed guide on how EV is calculated in our casino guides section, but for now, don't worry about this.

Casino offers are a great way to make some money over time.

However, you will go through periods of bad variance, where you don’t make much profit, or even lose a bit of money.

Bad variance can be frustrating, but remember that everyone experiences it.  It is a completely normal part of casino offers.

You are only doing offers that are +EV.  Focus on completing these offers, and don’t worry about any bad variance. It's long term results that matter.

Consider a scenario where you toss a coin once.  If it lands on heads you win £6, and if it lands on tails you lose £5.  It is a 50/50 scenario, and we win more if its heads than we lose if its tails.  So this would be +EV.

Variance means that there is a 50% chance that we make money and a 50% chance that we lose money. This doesn’t seem like a great proposition.

But what if we were to repeat this a second time?

There would now be a 75% that heads happens at least once, giving us a profit, and a 25% chance that it is tails both times.

So by increasing the number of times that we toss the coin, we have reduced the chance of making a loss from 50% to 25%.

This is a very basic example, but the same principle applies to casino offers.

Imagine we have a casino promotion that requires us to play £10 on blackjack. Our variance, and the chance of making a loss, would be much lower playing 10 x £1 hands, rather than a single £10 hand.

This applies to all casino games. To reduce your variance, you should do smaller bets and a higher number of game rounds to complete offers.