(usually with out) to reach the limit, to reach the maximum.
He maxed out his odds of dating Rebecca
The highest limit
The greatest value of a set or other mathematical structure, especially the global maximum or a local maximum of a function
An upper bound of a set which is also an element of that set
The largest value of a batch or sample or the upper bound of a probability distribution
A 147 break; the highest possible break
A score of 180 with three darts
A scoring shot for 6 runs