Hello all.

I am working on a game idea that I have but I am stuck on a part where I need to know the probability of an outcome so that I can properly balance the game before actual playtesting. I have tried to do some learning of probability formulas from Google and YouTube, but I'm having trouble making it applicable to this particular problem. I was hoping someone here might be able to help me understand what formula to use so that I can continue designing and testing this idea.

Ok, so on to the scenario:

Thanks a lot for your time! All help is greatly appreciated!

I am working on a game idea that I have but I am stuck on a part where I need to know the probability of an outcome so that I can properly balance the game before actual playtesting. I have tried to do some learning of probability formulas from Google and YouTube, but I'm having trouble making it applicable to this particular problem. I was hoping someone here might be able to help me understand what formula to use so that I can continue designing and testing this idea.

Ok, so on to the scenario:

With that information, what is the average value of a 'set up' drawn from the deck with the break point being 4? What about if it was 5? What is a good formula to use to figure this type of problem out?There is a deck of cards with 80 total cards. 26 of those cards are 'Stars' (more in those below**). The remaining 54 cards 2-10 in six different suits.

During each 'set up' players keep drawing from the deck until the total value of 4 or more is reached (possibly 5, depending on what the averages wind up being) and then they stop. This is called the 'break point'. I'm wanting to know what the average 'set up' value is.

**The Stars are what throw a bit of a kink in the math. If only a single Star is a part of the 'set up' its value is just 1. However, as more are drawn before hitting the 'break point' (currently 4, as mentioned above) their total value increases in triangular fashion. 1/3/6.

So, as an example: If two 3's are drawn the total 'set up' value is 6 because the first drawn 3 didn't meet the break point threshold of 4+ and then a second card was drawn, which happened to be a 3.

Another example is: If two Stars are drawn first and then a 10 is drawn, the total encounter value is 13. That's because the first Star is value 1, the second Star turns their total value into 3, and then a third card is drawn (because they are under the break point) which happens to be 10 in this scenario.

Thanks a lot for your time! All help is greatly appreciated!

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