Calculate RTP of slot with bonus games

Question

I'm working on a mini slot machine for a browser game. To not screw up the economy of the game I try to get an RTP (return to player) of around 97%.

My basic game has an RTP of 92% there is a chance of 1 on 100 to activate the bonus game, which has an RTP of 150%.

Now I want to calculate the overall RTP but I'm a little lost in how to calculate this, can you guys point me in the direction on how to calculate this?

Answer 1

If you are saying that $99$ times out of $100$ there will be a RTP of 92 and $1$ time out of $100$ there will be a RTP of 150%, then the total RTP can be calculated using a weighted average.

$$\Big(\frac{99}{100}\times0.92\Big)+\Big(\frac{1}{100}\times1.50\Big)$$ Alternately $$\frac{99\times0.92+1\times1.50}{100}=92.58\%$$

If you are saying that the bonus offers a 150% return in addition to the 92% return $1$ out of $100$ times, then the calculation would be

$$\frac{100\times0.92+1\times1.50}{100}=93.5\%$$

Answer 2

Think about it this way: From 100 games he will win 92 points from the base game plus will activate the bonus game once, yielding 1.5 points extra (on average). Thus:

$$RTP=\frac{92+1.5}{100}=93.5\%$$