Stats Wiz... anyone?

Folks, I'm trying to work out the probability of getting a feature on a game with the following reel composition

Reel Total Symbols # Feature Symbols
R1 187 6
R2 172 5
R3 168 3
R4 190 3
R5 182 4

I need three or more Feature Symbols to show in the window (which has 5 vertical reels and 3 visible symbols) to be awarded a feature. Only 1 feature symbol can be displayed on any one reel at any one time.

What would be the odds of getting a feature? And (more importantly) how do you calculate that?

Thanks in advance

Quote: p13man

Folks, I'm trying to work out the probability of getting a feature on a game with the following reel composition

Reel Total Symbols # Feature Symbols
R1 187 6
R2 172 5
R3 168 3
R4 190 3
R5 182 4

I need three or more Feature Symbols to show in the window (which has 5 vertical reels and 3 visible symbols) to be awarded a feature. Only 1 feature symbol can be displayed on any one reel at any one time.

What would be the odds of getting a feature? And (more importantly) how do you calculate that?

Thanks in advance

For your example, I get a probability of about 0.0029395577 that three or more Feature Symbols will appear scattered on the screen.

To calculate this, I first find the probability for each reel that a Feature Symbol will appear. On reel 1, for example, there are 6 Feature Symbols out a total of 187 symbols. So, the probability that a Feature Symbol will appear in a particular row of reel 1 is 6 / 187. But since to count the Feature Symbol can be in either of the three rows, so the probability that a Feature Symbol will appear anywhere on reel 1 is 3 * 6 / 187 = 18 / 187. And the probability that a Feature Symbol will not appear on reel 1 is 169 / 187.

Let p1 represent 18 / 187, and n1 represent 169 / 187. Likewise, call the probabilities that a Feature Symbol will appear in reels 2-5 p2, p3, p4, and p5. And let n2, n3, n4, and n5 be the probabilities that a Feature Symbol will not appear in reels 2-5.

The probability of getting five Feature Symbols would then be: p1 * p2 * p3 * p4 * p5.

And the probability of getting exactly four Feature Symbols would be: n1*p2*p3*p4*p5 + p1*n2*p3*p4*p5 + p1*p2*n3*p4*p5 + p1*p2*p3*n4*p5 + p1*p2*p3*p4*n5.

Finding the probability for three Feature Symbols is just a little more complicated. It's: n1*n2*p3*p4*p5 + n1*p2*n3*p4*p5 + n1*p2*p3*n4*p5 + n1*p2*p3*p4*n5 + p1*n2*n3*p4*p5 + p1*n2*p3*n4*p5 + p1*n2*p3*p4*n5 + p1*p2*n3*n4*p5 + p1*p2*n3*p4*n5 + p1*p2*p3*n4*n5 .

And then the probability of getting the feature would be the sum of the three expressions above.

As a check on my calculation, I would also find the probabilities of getting two, one, and zero Feature Symbols. The sum of the six probabilities must equal 1:

Feature Symbols	Probability
0	0.6947149638
1	0.2632733807
2	0.0390720977
3	0.0028373092
4	0.0001008440
5	0.0000014045
Sum	1

Oh boy, this forum just keeps paying out! That is a work of genius. Thank you so much for taking the time to work this out and share. And thank you for explaining your process in such great detail. I can now reproduce your work and calculate the feature odds for any slot. The really interesting point for me is that the average number of spins before a feature drops in is 340. This seems like quite a high number and suggests that the game play is determined by virtual reels and not the actual (visible) reels...

Quote: p13man

Oh boy, this forum just keeps paying out! That is a work of genius. Thank you so much for taking the time to work this out and share. And thank you for explaining your process in such great detail. I can now reproduce your work and calculate the feature odds for any slot. The really interesting point for me is that the average number of spins before a feature drops in is 340. This seems like quite a high number and suggests that the game play is determined by virtual reels and not the actual (visible) reels...

I’m not a slots player, but I thought that the wheels had different weightings so that different symbols are not equally likely to come up.

Quote: p13man

Oh boy, this forum just keeps paying out! That is a work of genius. Thank you so much for taking the time to work this out and share. And thank you for explaining your process in such great detail. I can now reproduce your work and calculate the feature odds for any slot. The really interesting point for me is that the average number of spins before a feature drops in is 340. This seems like quite a high number and suggests that the game play is determined by virtual reels and not the actual (visible) reels...

p13man,

But ChesterDog calculated the probability of hitting the feature as 0.0029395577. That means that it'll hit on average once every 1/0.0029395577 = 340.2 spins... which is what you expected.

Hope this helps!

Dog Hand

Quote: p13man

...the average number of spins before a feature drops in is 340. This seems like quite a high number...

Sometimes the feature is quite a large contribution to the RTP (say 50-75% comes from natural line wins and 25-40% comes from features). Also some machines have a rarer feature but it pays out more when it hits. This means sometimes people keep playing as they hope the feature will pay big when it hits (although sometimes you're unlucky and have a low win). The bigger wins tend to be from features, while line wins tend to be smaller valued prizes to keep you going.