I play a card game called Hearthstone and need the ability to do fast calculations on the fly. There is one type of probability that I can't seem to wrap my head around.
An example in-game would be the following: I have a spell card that shoots out 2 missiles. There are 2 enemies and I want to hit 1 of them. That means I have a 1/2 chance of hitting the one I want. However, I have 2 spell cards in my hand. What is a trick/fast way to calculate my chances of hitting the enemy at least once?
Another example: The opponent is running 2 cards in his deck that counter me - we'll call them Card(A). I know the odds of him having this card at the moment is 40%. However, there are also 2 other cards that counter me - we'll call them Card(B). The odds of him having Card(B) is also 40%.
As you can see, there's a 40% chance of having Card(A) and a 40% chance of having Card(B). Both will counter me so I need to know the chances of him having both Card(A) and Card(B).
There are a lot of situations in this game where there is a specific outcome and multiple events that have a probability to lead to that outcome such as the ones I referenced above. I need a quick way to calculate this on the fly.
An example of being able to calculate things on the fly is the odds of something happening back to back. For example, if I have two 1/2 chances, but I need them both to hit after each other it's simple. You just go 1/2 * 1/2 = 1/4 to figure out your odds. I need something quick and simple like this for the examples I listed.
I'm not very good at math. I've looked online, but all the solutions I've found are too advanced for me to understand. They usually have probability trees, formulas, or equations that I'm not able to understand since I don't have a formal education in mathematical probability.
If someone could explain this to me in a way that I can understand and am able to calculate and replicate with speed while I play I would be very grateful as this has been a question I've been looking to solve for far too long and it's very frustrating.
Thank you in advance