We apply the two-pluyer game assumprio~ls of 1i111ited search horizon and cornn~itnrent to nroves i constant time, to .single-agent heuristic search problems. We present a varicrtion of nrinimcr lookuhead search, and an analog to ulphu-betu pruning rlrot signijicantly improves the efficiency c. the algorithm. Paradoxically. the search horizon reachuble with this algorithm increases wir. increusing branching facior. hl addition. we present a new algorithm, called Real-Time-A ', fo interleaving planning and execution. We prove that the ulgorithm makes locally optimal decision and is guaranteed to find a solution. We also present a learning version of this algorithm thrr improves its performance over successive problen~ solving trials by learning more accurate heuristi values, and prove that the learned values converge to their exact values along every optimal path These algorithms ef/ectively solve significanrly larger problems rhan have previously beerr solvabk using heuristic evaluation functions.