Expected value of free spins on slot.

How is the average return of a free spin combination on a slot calculated?

I've been searching all around your site, and other info I have, and until now I have no clue.
The closer I have reached, is the example and calculations you made on the Atkins Diet Slot you designed,
but I can't yet see the formulas used there.

I want to calculate the EV of a combination like the one in Atkins diet,
and how can I calculate other with less or more spins / winning multipliers.
And knowing the EV of all the other combinations.

I hope I made myself clear, and appreciate your help with this.

Thanks in advance.

The simple formula is [number free spins]*[average return from each free spin].

In the Atkins Diet machine the number of free spins is not obvious. You start with 10, but free spins can earn more free spins, infinitely. In that case, the expected final number of spins is n/(1-n*p), where n is the number of free spins earned per bonus, and p is the probability of the bonus per spin. In the the Atkin's case, the bonus probability is 0.011185, so the expected number of free spins per bonus is 10/(1-0.011185*10) = 11.259335.

Quote: Wizard

The simple formula is [number free spins]*[average return from each free spin].

In the Atkins Diet machine the number of free spins is not obvious. You start with 10, but free spins can earn more free spins, infinitely. In that case, the expected final number of spins is n/(1-n*p), where n is the number of free spins earned per bonus, and p is the probability of the bonus per spin. In the the Atkin's case, the bonus probability is 0.011185, so the expected number of free spins per bonus is 10/(1-0.011185*10) = 11.259335.

Thanks, I will try with that and return here if I get stuck.

How the [average return from each free spin] is calculated?

It is (total number of hits) * Sum (EV) / Total Slot combinations ?

or Sum ( Return of each combination * P(comb) ) / Game Total Hits ?

I'm kindda confused here, because I can't make my way to get the numbers on the Atkins Diet machine,
and I want to understand how this work.

Thanks Again!

My question is about different number of free spins when you have different number of scatter symbols visible. In the Atkins Diet machine, for each number of visible scatter symbols (3, 4 or 5), the player is granted with the same number of free spins (10 free spins).
How can we calculate the expected number of free spins if for example:
for 3 scatter symbols you win 5 free spins (probability to get 3 scatter symbols is p_3)
for 4 scatter symbols you win 7 free spins (probability to get 4 scatter symbols is p_4)
for 5 scatter symbols you win 9 free spins (probability to get 5 scatter symbols is p_5)?

Quote: jass

My question is about different number of free spins when you have different number of scatter symbols visible. In the Atkins Diet machine, for each number of visible scatter symbols (3, 4 or 5), the player is granted with the same number of free spins (10 free spins).
How can we calculate the expected number of free spins if for example:
for 3 scatter symbols you win 5 free spins (probability to get 3 scatter symbols is p_3)
for 4 scatter symbols you win 7 free spins (probability to get 4 scatter symbols is p_4)
for 5 scatter symbols you win 9 free spins (probability to get 5 scatter symbols is p_5)?

The expected number of free spins for 3 scatter symbols is 5/(1- (p_3*5 + p_4*7 + p_5*9)).

Quote: boochaka

How the [average return from each free spin] is calculated?

It is (total number of hits) * Sum (EV) / Total Slot combinations ?

or Sum ( Return of each combination * P(comb) ) / Game Total Hits ?

I'm not totally sure what you mean by "game total hits," but these sound to me like they'd be the same number.

Quote: 24Bingo

Quote: boochaka

How the [average return from each free spin] is calculated?

It is (total number of hits) * Sum (EV) / Total Slot combinations ?

or Sum ( Return of each combination * P(comb) ) / Game Total Hits ?

I'm not totally sure what you mean by "game total hits," but these sound to me like they'd be the same number.

I think I know what he's getting at. I glossed over this post.

Anyhow, the return of a slot game, which is the same calculation used for the free games is: Sum (Return of each combination * P(comb)).

P(comb) = hits(comb)/total slot combinations

Using this formula I can calculate expected number of free spins for 3, 4 and 5 scatter symbols, separately.
But, how can I calculate the expected number of free spins for the game?
Is it (5+7+9)/(1-(p_3*5+p_4*7+p_5*9))?

Quote: jass

Using this formula I can calculate expected number of free spins for 3, 4 and 5 scatter symbols, separately.
But, how can I calculate the expected number of free spins for the game?
Is it (5+7+9)/(1-(p_3*5+p_4*7+p_5*9))?

No. The prior formula gives you the expected # spins starting from the given feature trigger, so just weight each number by the odds of each trigger.

But I typically wouldn't do that aggregation without computing the individual results first. I'd recommend keeping things broken out and computing RTP based on each individual feature trigger.