How to calculate probability for scatter wins

I am not very good at probabilities; can anyone please help me on how to calculate probabilities for scatter wins?

What is a scatter win?

Quote: NJ

I am not very good at probabilities; can anyone please help me on how to calculate probabilities for scatter wins?

For an example on how to calculate scatter wins, please refer to the Wizard's new article about deconstructing the video slot called Hexbreaker.

In the table called "Hexbreaker Symbol Distribution" you can see how many scatter symbols are on each reel; they are 3, 2, 2, 2, 3 for reels 1-5 respectively. After play is initiated a scatter symbol might appear above, on, or below the center line for each reel, which means that the reels could have stopped at any of 9, 6, 6, 6, 9 places on reels 1-5 respectively. Each reel has 64 places to stop, so for a scatter symbol NOT to appear, the reels would have stopped at any of 55, 59, 59, 59, 55 places, respectively.

The number of ways to get a total of 5 scatters is this product: (9)(6)(6)(6)(9), which is 17,496, and the total number of ways the reels can stop is this product (64)(64)(64)(64)(64), which is 1,073,741,824. So the probability of getting 5 scatters is 17,496/1,073,741,824 or 0.000016, which agrees with the corresponding probability in the Wizard's table called "Hexbreaker - Scatter Pay."

As a further example, here's the probability of getting 4 scatters: [(55)(6)(6)(6)(9) + (9)(59)(6)(6)(9) + (9)(6)(59)(6)(9) + (9)(6)(6)(59)(9) + (9)(6)(6)(6)(55)] / [(64)(64)(64)(64)(64)]. There are five terms in the numerator because a scatter would not have appeared either on reel 1, 2, 3, 4, or 5. The corresponding expression for 3 scatters would have 10 terms in the numerator because scatters either would not have appeared on reels 1&2, 1&3, 1&4, 1&5, 2&3, 2&4, 2&5, 3&4, 3&5, or 4&5.

This explanation should get you started on your scatter calculations.