RTP in Roulette – Understanding How Returns Work

How to know the RTP?

Other than looking at each game’s advertised RTP, there is an easier way to get a working knowledge of what the RTP of any given game is. The RTP formula is quite simple, and it is represented as:

$\mathrm{RTP}=100\%-\mathrm{house\; edge}$

This is very logical when you come to think about it. But what if you don’t know what the house edge is? Well, we have a way of finding out as well – and this is the formula that defines the house edge:

$\mathrm{House\; Edge}=\left|\frac{(-\mathrm{bet\; amount}\times \mathrm{odds\; of\; loss})+(\mathrm{bet\; payout}\times \mathrm{bet\; amount}\times \mathrm{odds\; of\; win})}{\mathrm{Bet\; Amount}}\right|\times 100\%$

As a result, we need to calibrate what the RTP formula looks like, which is now going to change to this:

$\mathrm{RTP}=100\%-\left(\right|\frac{(-\mathrm{bet\; amount}\times \mathrm{odds\; of\; loss})+(\mathrm{bet\; payout}\times \mathrm{bet\; amount}\times \mathrm{odds\; of\; win})}{\mathrm{Bet\; Amount}}|\times 100\%)$

Great, let’s start putting this knowledge into practice. For example, let’s try to calculate a bet on a dozen European roulette. In this case, we will have to cover 12 numbers out of the 37 total numbers available in this specific version of the game. We have decided to assign a bet value of 5 CAD, and the formula will now look like this:

$\mathrm{RTP}=100\%-\left(\right|\frac{(-5\times 25/37)+(2\times 5\times 12/37)}{5}|\times 100\%)=100\%\left(\right|\frac{(-3.3783)+(-3.2432)}{5}|\times 100\%)$

$\mathrm{RTP}=100\%-\left(\right|-0.027|\times 100\%)=97.3\%$

Voila! The RTP is now determined as 97.30%. In other words, you need only a handful of data points to calculate the RTP yourself, and they include: how many numbers are covered by the bet, the bet’s payout, the bet amount itself, and the total amount of numbers available in the specific version of the game you are playing.

Following this example, you can crunch the RTP of any game and always be confident that you have arrived at the correct value. To illustrate that the RTP would remain the same for European Roulette, no matter what bet type you choose, we have decided to bet 15 CAD on a split bet with a payout of 17:1. Here is what we get as a result:

$\mathrm{RTP}=100\%-\left(\right|\frac{(-15\times 35/37)+(17\times 15\times 2/37)}{15}|\times 100\%)=100\%-\left(\right|\frac{(-14.189)+\left(13.783\right)}{15}|\times 100\%)$

$\mathrm{RTP}=100\%-\left(\right|-0.027|\times 100\%)=97.3\%$

As you can see, even though we have just changed the bet type and bet amount, the RTP remains at the same final metric – 97.30%, which means that the return will remain unchanged for this version. Alright, but what if we tried a different version of the game – American roulette, where we placed a $ 10 CAD bet, with the 11:1 payout, and calculated the 38 total numbers? Here’s what the formula looks like:

$\mathrm{RTP}=100\%-\left(\right|\frac{(-10\times 35/38)+(11\times 10\times 3/38)}{10}|\times 100\%)=100\%-\left(\right|\frac{(-9.2105)+\left(8.6842\right)}{10}|\times 100\%)$

$\mathrm{RTP}=100\%-\left(\right|-0.0526|\times 100\%)=94.74\%$

As you can see, the RTP changed, but that’s mostly to do with the fact that you now have an extra number on the wheel, and that’s that.

Are there exceptions for RTP?

Basket Bet and American Roulette

As it turns out, there are exceptions for calculating RTP in a roulette game. In the case of Basket Bet in American Roulette, the RTP will be slightly different. This bet is formed by 0, 00, 1, 2, and 3. The payout ratio here is 6:1, but the RTP is lower than you would normally expect from this version of the game. We have decided to place a bet worth 5 CAD and recalculate the RTP to see how this is possible:

$\mathrm{RTP}=100\%-\left(\right|\frac{(-5\times 33/38)+(6\times 5\times 5/38)}{5}|\times 100\%)=100\%-\left(\right|\frac{(-4.3421)+\left(3.9473\right)}{5}|\times 100\%)$

$\mathrm{RTP}=100\%-\left(\right|-0.0789|\times 100\%)=92.11\%$

As you can see, the RTP for this type of bet is actually smaller, 92.11%, which will definitely be an interesting observation to make. However, do remember that this is an exception that proves the rule!

Straight-up bets and multipliers in roulette

Another very popular example that demonstrates an exception to the rule is the types of roulette that run multipliers. There are, in fact, pretty huge multipliers found in some versions of the game. In the normal version of roulette, the straight-up bet would pay at a ratio of 35:1, but because of the multipliers that can reach 500x and 2000x, or even greater values in some instances, the house edge will change.

The RTP for straight-up bets will vary from one version to the next, and it can be anything between 19:1 and 29:1. As casinos are also keen to offset these large multipliers, they offer players something that will make it worthwhile for them as well. Developers have therefore figured out a way to offer players an exciting gameplay at the expense of RTP.

Lightning Roulette by Evolution Gaming has a max multiplier of 500x. What does this mean for its straight-up bets? Well, the payout of this type of bet is fixed at 29:1, lower than the usual 35:1.

$\mathrm{RTP}=100\%-\left(\right|\frac{(-10\times 36/37)+(29\times 10\times 1/37)}{10}|\times 100\%)=100\%-\left(\right|\frac{(-9.7297)+\left(7.8378\right)}{10}|\times 100\%)$

$\mathrm{RTP}=100\%-\left(\right|-1.8919|\times 100\%)=81.09\%$

Are you reading this correctly? Yes, you are! The RTP for straight-up bets for multiplier roulettes could be as low as 81.09%. So, you are incentivized to play this type of bet because they could potentially trigger huge multipliers, and the overall RTP of the game is set at 97.10%, but when you look at this exception to the rule, the RTP will be much lower!

Even-money bets and French Roulette

French Roulette can even offer you a boosted RTP thanks to its unique La Partage rule. The rule will make it so that when you bet on even-money bets and lose because of zero, you will be allowed to get half of your money back, thus further reducing the house edge and boosting the potential return the game offers.

Because of this, the actual RTP for a game of French roulette is set at 98.65%. Let’s give it a try with the following formula:

$\mathrm{RTP}=100\%-\left(\right|\frac{(-10\times 18/37)+(1\times 10\times 18/37)+(-10/2\times 1/37)}{10}|\times 100\%)=100\%-\left(\right|\frac{(-4.8648)+\left(4.8648\right)+(-0.1351)}{10}|\times 100\%)$

$\mathrm{RTP}=100\%-\left(\right|0.0135|\times 100\%)=98.65\%$

This is great – it all matches, but it’s important to consider this small but important detail – the higher house edge will only apply to even-money bets in French Roulette, and more than that, on versions of the game that specifically feature the La Partage rule.

In other words, if you are really looking to boost your experience and specifically focus on the best RTP possible, you will need to look up French Roulette, specifically the game version that has the La Partage rule. There are plenty of such excellent roulettes to try, however, including French Roulette Gold, Auto Roulette La Partage by Evolution, and not least – Live French Roulette, developed by Playtech.