I wanted to expand on this post without derailing the original thread:
To expand on this, in my own game I want to know who is mapping, who is probing with the 10' pole, who is checking for secret doors as they go, who is looking ahead and who is looking behind. Mapping, probing and checking for secret doors all slow movement from late-D&D standard to 1e speeds, which enables wandering monster checks.
This suggests you need, ideally, a party of at least 5, and possibly 6, in order to cover all bases: one for each role mentioned (I rule that probing walls and floor with a pole divides your attention sufficiently that you can't really focus on the more distant path ahead); except for searching for secret doors, which requires one elf or two non-elves to cover each wall using early edition rules.
If you have less, you have choices to make in terms of what areas you leave uncovered, or if you want to slow your speed by having certain characters duplicate roles. So for a three person team, assuming you always want someone watching the van and rear at all times, only one person is available to map, check for secret doors, and probe for traps; covering all of those roles will triple or quadruple your wandering monster checks, so there are real decisions to make.
To be clear on the searching for secret doors role, for most people this requires that they inspect, prod, and tap on walls. Based on a passage in the 1e DMG, which I don't care to look up, I let elves search by just concentrating, as long as they walk within, say, 5 feet or so (although I have some setting specific limitations on this).
It becomes particularly interesting if you run an edition where the action economy (what you can do in a round/on your turn) is an important factor in combat. The mapper needs both hands to map, and cannot carry a weapon or a light source; the same goes for the person with the pole, unless he is using a polearm, which will probably be shorter and has other issues in confined spaces; stowing writing implements and drawing weapons is a real issue. Non-elf secret-door searchers can likely carry a weapon and tap on walls with it, but they likely can't wear a helm that muffles sound (great helms, armets, etc., basically the more protective helms), since they need to hear the sound of the tapping.
