TRPG Dice Idea

 In Tabletop Role-Playing Games(TRPGs), probabilities are often represented in terms of dice, e.g. 2d10, 2d6, etc. If the resulting sum is greater than some other number determined by the 'difficulty' of the task or the 'stat' of the player character, then the check is a success. Well, in real life, probabilities are represented as a sum of probability amplitudes of Feynman Diagrams. What if we develop a similar system for TRPGs? Of course calculating the amplitudes is not easy, especially for people who are not physics majors. But we can still examine the typical form of $\Gamma$. The final probability $\Gamma$ must be unitless. Hence it has factors of mass ratios (e.g. $m_1 / m_2$) and often some power of $\pi$ in the denominator. Now, we can leave $\pi$, just for fun, and replace the mass ratios with stat ratios (e.g. $\text{STR} / \text{Difficulty}$).

Now all of this is great, but now you need a computer to actually play the game, and perhaps not having phsical dice is not as satisfying......