boochaka Joined: Jan 22, 2010
• Posts: 9
April 15th, 2010 at 10:38:06 AM permalink
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.

Wizard Joined: Oct 14, 2009
• Posts: 24506
April 15th, 2010 at 2:38:00 PM permalink
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.
It's not whether you win or lose; it's whether or not you had a good bet.
boochaka Joined: Jan 22, 2010
• Posts: 9
April 16th, 2010 at 5:06:30 AM permalink
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.
boochaka Joined: Jan 22, 2010
• Posts: 9
May 12th, 2010 at 7:33:11 AM permalink
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!
jass Joined: Sep 18, 2012
• Posts: 3
September 18th, 2012 at 5:13:20 AM permalink
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)?
CrystalMath Joined: May 10, 2011
• Posts: 1907
September 20th, 2012 at 9:22:44 PM permalink
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)).
I heart Crystal Math.
24Bingo Joined: Jul 4, 2012
• Posts: 1348
September 20th, 2012 at 9:34:54 PM permalink
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.
The trick to poker is learning not to beat yourself up for your mistakes too much, and certainly not too little, but just the right amount.
CrystalMath Joined: May 10, 2011
• Posts: 1907
September 20th, 2012 at 9:40:38 PM permalink
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
I heart Crystal Math.
jass Joined: Sep 18, 2012
• Posts: 3
September 21st, 2012 at 2:53:52 PM permalink
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))?
MathExtremist Joined: Aug 31, 2010
• Posts: 6526
September 21st, 2012 at 3:18:34 PM permalink
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.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563