Collectibles Math
April 2nd, 2020 at 12:26:45 AM
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Hello,
I am designing a slot game and i would like to implement a bonus that gets triggered after a certain amount of special items is collected throughout a single session , or after a certain amount of wins. I was thinking how to calculate the RTP of the bonus, in particular what i find problems with is the calculating the probability of the bonus getting triggered. My idea is the following:
Let us say we need to collect 10 keys and the probability of a 1 key appearing on any position on the screen is 0,008, on 2 - 0,004 and on 3 - 0,001 (For example if the symbol key is not on the reels, but if it appears is drawn on every spin)
So I was thinking to proceed like this :
On the first spin the user plays the odds are like this having 1 key - 0,008, 2 keys - 0,004, 3 keys - 0,001 - 0 keys -0,987
on the second spin : 1 key- 0,008*0,987*2; 2 keys - 0,008^2+0,004*0,987*2; 3 keys - 0,008*0,004*2 +0,001*0,987*2; 4 keys 0,008*0,001*2 + 0,004^2; 0 keys - 0,987^2
and so on... turning into a some kind of a markov chain with certain probabilities of transfering into states. Do you think this is a valid approach, to calculate the final probability of ending up in the state of 10 keys. Moreover i have no idea how many times i have to perform this kind of "iteration", as if i cant tell how many spins the player will do.
My other idea was to gift a key every time the player scored a win. If the overall probability of the game for getting a win is 0,08, than the probability of getting a bonus should be the binomial, am i right, going like (0,08)^10*(0,92)^(n-10) where n is number the game played by the user so far, but still here comes the question of how many games the player will choose to perform.
I wolud be very thankful for all kind of insight or ideas on the topic :)))
Thanks :)
I am designing a slot game and i would like to implement a bonus that gets triggered after a certain amount of special items is collected throughout a single session , or after a certain amount of wins. I was thinking how to calculate the RTP of the bonus, in particular what i find problems with is the calculating the probability of the bonus getting triggered. My idea is the following:
Let us say we need to collect 10 keys and the probability of a 1 key appearing on any position on the screen is 0,008, on 2 - 0,004 and on 3 - 0,001 (For example if the symbol key is not on the reels, but if it appears is drawn on every spin)
So I was thinking to proceed like this :
On the first spin the user plays the odds are like this having 1 key - 0,008, 2 keys - 0,004, 3 keys - 0,001 - 0 keys -0,987
on the second spin : 1 key- 0,008*0,987*2; 2 keys - 0,008^2+0,004*0,987*2; 3 keys - 0,008*0,004*2 +0,001*0,987*2; 4 keys 0,008*0,001*2 + 0,004^2; 0 keys - 0,987^2
and so on... turning into a some kind of a markov chain with certain probabilities of transfering into states. Do you think this is a valid approach, to calculate the final probability of ending up in the state of 10 keys. Moreover i have no idea how many times i have to perform this kind of "iteration", as if i cant tell how many spins the player will do.
My other idea was to gift a key every time the player scored a win. If the overall probability of the game for getting a win is 0,08, than the probability of getting a bonus should be the binomial, am i right, going like (0,08)^10*(0,92)^(n-10) where n is number the game played by the user so far, but still here comes the question of how many games the player will choose to perform.
I wolud be very thankful for all kind of insight or ideas on the topic :)))
Thanks :)
Last edited by: spinswizard on Apr 2, 2020
