Maximizing goal probability is an important objective in probabilistic planning, yet algorithms for its optimal solution are severely underexplored. There is scant evidence of what the empirical state of the art actually is. Focusing on heuristic search, we close this gap with a comprehensive empirical analysis of known and adapted algorithms. We explore both, the general case where there may be 0-reward cycles, and the practically relevant special case of acyclic planning, like planning with a limited action-cost budget. We consider three different algorithmic objectives. We design suitable termination criteria, search algorithm variants, dead-end pruning methods using classical planning heuristics, and node selection strategies. Our evaluation on more than 1000 benchmark instances from the IPPC, resource-constrained planning, and simulated penetration testing reveals the behavior of heuristic search, and exhibits several improvements to the state of the art.