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I asked over at the RPG stack exchange and they sent me here.

I am working on making a RPG and am trying to understand the statistics of the core mechanic so I can determine how effective leveling and bonuses will be.

Right now the core mechanic is a skill die based mechanic where you roll a d4, d6, d8 or d10 based on your skill opposed by either a DC set by the story teller (1-10) or the result of another die via an opposed roll.

I am experimenting with rolling two dice and picking the higher of the two, however I don't know how to make a statistical model for this. So if I rolled a 5 and a 4 on two six sided dice I would pick the 5 and ignore the 4. I don't know how this would change the probabilities.

I am finding this especially difficult due to the fact that I am planning on using exploding dice. (Exploding dice is a term for when you roll the highest number on a die and roll the die again, adding the number you previously rolled to the die. This can continue indefinitely.)

I would very much appreciate some help on coming up with a formula for this. I want to set up an excel sheet to compare different bonus methods so I would really like something where I can put the formula in and tweak it instead of just probabilities listed.

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    for the first question: http://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.432850.html2012-10-26

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