State is = remaining amounts of soup A and B. But if , that's way too many states. observation: all serving amounts are multiples of . Divide everything by .
State becomes . 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 , A almost certainly empties first. When , the probability is so close to that the difference is below (the required precision). Return directly for large .