Suppose I throw N dice, and my opponent throws M dice.
What are the odds that I threw more sixes than he did?
2026-04-01 00:38:46.1775003926
Odds when throwing an unequal number of dice
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$\textbf{Hint:}$ Assuming the die is unbiased, the probability of getting k or more sixes in N throws is $$ \sum_{i=k}^{N} { N \choose i}\Big( \frac{1}{6} \Big) ^{i} \Big( \frac{5}{6} \Big) ^{N-i} $$