Hi, this is my first time on the forums and I am having a very hard time with some math questions. I have tried searching the web for my particular question but most sites are concerned with the sums of 2 six-sides dice not target numbers. What I mean by target numbers is I am trying to figure out what the probability of rolling "at least" one 1, 2, 3, etc. on multiple dice. The reason I am doing this is because I am trying to build an excel sheet to help me make better decisions with a table top game I play called "Heavy Gear Blitz". I very fun game, everyone should check it out.
One of the facets of the game is when you roll a double/triple/etc. six instead of getting a six, you get six plus how many other sixes you have rolled. For example, on four dice I rolled a 6, 6, 6, 4. I would then have the final score of 8 because of my first six and then +1 for every six after it. This really puts the math a bit beyond me. I have gotten a bit of the target number math done, but I am really not sure if I have it right or not.
This is what I do:
3 six-sides dice being rolled
chances of not rolling at least a 6 on the first die = (5/6)
chances of not rolling at least a 6 on the second die = (5/6)
chances of not rolling at least a 6 on the third die = (5/6)
I then multiple all the results together = .5787 or 57.87%
I want to find out the result of rolling a 6 so I then subtract the number I found from 1 = .4213 or 42.13%
I hope this is all right. I am not really sure how to do the math for what I was talking about early with "at least" rolling a "7". Thank you for your time and any help you can give!