#Estimate which entity is more likely to have a higher sum (Probability).
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Example simulation of 2 rolls per entity with p=0.21 q=0.28 n=35 m=40:
Entity 1 rolls 0.23. e_1 stays 0.
Entity 2 rolls 0.27. e_2 = m = 40.
Entity 1 rolls 0.2. e_1 = n = 35.
Entity 2 rolls 0.19. e_2 = m + m = 80.
max(e_1, e_2) = e_2 = 80
Don't answer I am preparing a better formulated question. Just testing out markdown syntax: $a_i \in\mathbb N$