LeetCode 808 Soup Servings - The Observation

State is $(a, b)$ = remaining amounts of soup A and B. But if $n = 10^9$, that's way too many states. observation: all serving amounts are multiples of $25$. Divide everything by $25$.

State becomes $(a/25, b/25)$. Another observation: soup A is served more on average (100+75+50+25)/4 = 62.5 vs (0+25+50+75)/4 = 37.5. For large $n$, A almost certainly empties first. When $n > 4800$, the probability is so close to $1$ that the difference is below $10^{-5}$ (the required precision). Return $1.0$ directly for large $n$.