I have a sneaking suspicion that telling players how many encounters there will be in a session may end up with an improved Dungeons & Dragons experience. D&D began with explorations into a dungeon, where the players went for long as they felt able, then returned home. As this continued, players developed the concept of using all expendable powers and spells in the first encounters …
tl;dr: tell the players on advance how many encounters to expect, so they can budget their resources.