Calculation of PICK UP bonus in Slots

Hello guys, i am calculating a slot game, just as a hobby.
And i need small help with formulas.

So, we have a pick up screen with 9 symbols on it. A player must pick up 3 of them, each symbols has some amount of free spins which will reveal after a player chose a symbol. Then all Free spins will be added and it will be a total amount of Free Spins in the bonus game.

I am assuming i need to use Combin() function to determine all possible combinations of 3 symbols, but i don't know what formula i should use to determine what is the average amount of free spins a player will get.

If someone are able to help with this , i will really appreciate that.

Hi Mat, welcome to the forums.

I think we might be missing some more information from you if you want something a bit trickier. If you just want to know the average... add all of the possible outcomes up and divide by the number of possible outcomes. =)

i.e. 1, 2, 3, 4, 5, 6, 7, 8, 9... The average (mean) would be 45/9 = 5.

Quote: Romes

Hi Mat, welcome to the forums.

I think we might be missing some more information from you if you want something a bit trickier. If you just want to know the average... add all of the possible outcomes up and divide by the number of possible outcomes. =)

i.e. 1, 2, 3, 4, 5, 6, 7, 8, 9... The average (mean) would be 45/9 = 5.

Thanks for your replay !

I want to know the average amount of free spins what a player gets from the PICK UP bonus game, to calculate Re-trigger ( N / (1 – M.P) ) and bonus game RTP.

So, basically i just need to add all Free Spins ( hidden in 9 symbols) and divide it on 9, and that's it ?
I thought i need to do something more complicated...

If all you want is the average, then you just need to know what the available options are and divide by the number of options =).

In order to actually extrapolate out every possible scenario, that would be factorials and combination analysis... but that's not what you're asking for (thank goodness). You just simply want to know "When I click on 3 of these, what will the average amount be?"

I will amend and say you need to find the average then multiply it by 3 because you're stating they pick 3 of them.

Example: You're playing this game, 9 symbols appear... behind them are the number of free spins (1, 2, 3, 4, 5, 6, 7, 8, 9). So that means if you pick RANDOMLY you have a fair shot at each one, with the "average" you could pick being 5 (45/9). For your case you need to find the numbers behind the symbols (which they'll show all of them after you're done picking to show you how you did), add those up and divide by 9.

So if your # of free spins is the 3 symbols you pick COMBINED, then "on average" you could expect Avg*3 = 5*3 = 15.

*One last note... Usually it's 'relative' but the symbol amounts/average could change based on your betting level. If you're playing a slot for $1 per spin the average number of free spins could be different than if you're playing for $5 per spin. If they are different based on the level, just re-evaluate the exact same for the different level.

Quote: Romes

If all you want is the average, then you just need to know what the available options are and divide by the number of options =).

....................................................................

*One last note... Usually it's 'relative' but the symbol amounts/average could change based on your betting level. If you're playing a slot for $1 per spin the average number of free spins could be different than if you're playing for $5 per spin. If they are different based on the level, just re-evaluate the exact same for the different level.

Thank you Romes a lot ! That's exactly what i was looking for!

It is quite easy, since you do not need to calculate the probability of each unique number of free spins.

In short: average free games = number of picks * average free games per pick.

To calculate re-initiating:

average free games/(1-p(re-init)*average free games)

Let's say the probability of initiating free spins is 1/100 and the average number of free spins is 15, then the total expected number of free games is:

15/(1-0.01*15) = 17.647

Thanks again for the information, i started calculation and now i have one more small question :

Let's say we have next amount of Symbols and Free spins :

PRIZE (Free Spins) / Symbols:
2 / 4
3 / 3
4 / 1
5 / 1
Total 14 / 9
Avg. Free Spins 4.66667


----------------------
The minimum what can pick up a player is 6 free spins (3 Symbols x 2 free spins)
But the average is 4.66667.

In this case, this calculation is correct too ?

Or maybe i should calculate the average between min and max amount of free spins ?

Quote: Mat23lv

Thanks again for the information, i started calculation and now i have one more small question :

Let's say we have next amount of Symbols and Free spins :

PRIZE (Free Spins) / Symbols:
2 / 4
3 / 3
4 / 1
5 / 1
Total 14 / 9
Avg. Free Spins 4.66667


----------------------
The minimum what can pick up a player is 6 free spins (3 Symbols x 2 free spins)
But the average is 4.66667.

In this case, this calculation is correct too ?

Or maybe i should calculate the average between min and max amount of free spins ?

The average of {2,2,2,2,3,3,3,4,5} is 26/9 or 2.89.

Therefore, the three pick average is 8.67.