Justin Alexander (thealexandrian.net) makes a really good point about the Caves of Chaos with respect to new players: When you enter the valley with the caves, you're effectively presented with 12 choices (assuming you see all of the cave entrances). There are few adventures where you're so clearly presented with so many choices right at the very beginning and that's one of the reasons I continue salvaging it and using it in play.
I would argue that the majority of those are false choices. At least 3 of those choices - temple, bugbears, minotaur - lead to TPKs if the party is just 1st level with starting equipment, since they are basically designed with 2nd to 3rd level characters in mind. Even the hobgoblins and orcs are likely to to send starting characters tumbling back in confusion with high loses, and the gnolls certainly will. And one of those choices isn't actually apparent, because it isn't actually a visible entrance.
But more to the point, none of them are real choices because the party has no way of having information on what cave that they want to enter. If the choices is not at all informed, then it's not a choice. I could number the entrances from 1 to 12 and randomly assign a lair to the entrance the party used, and it would be no less a choice than what is presented - that is to say zero choice is not less than zero choice. Giving players the illusion of choice is not the same as giving them multiple paths through the challenge. The difference is that when players have the illusion of choice, they still aren't actually crafting their own narrative.
'Go left' or 'Go right' isn't a real choice. There has to be some quality to the choice that makes choosing that choice mean something. "Assault the front gate" versus "Sneak in the back" is a choice and which is correct might depend on the capabilities of the characters, which means that the players might have some reason to believe they are or aren't making the right choice.
Finally, at least in my small sample set, Gygax correctly assumes that player psychology will lead them away from seeking out the more distant and inaccessible entrances - that also have the most difficult foes. The two groups I played with looked at it, and both said, "What is the closet entrance?" and more or less coin flipped 'left' versus 'right' with one choosing the goblins and the other the kobolds - both of which are clearly intended as the targets of the players initial assaults and are the only lairs you can likely assault without platemail and 2nd level fighters.
By contrast with random meaningless 'left versus right' choices, my own campaigns first adventure began with a natural disaster - a tidal wave inundating a city. To prepare to run this I had to imagine all the possible things that a player might do to respond to this information, beginning with the obvious 'run away', but including things like 'climb atop a building', 'find a sturdy building to shelter in', 'get in a one of the large vessels in the harbor and ride it out', 'get in a small boat and ride it out', and 'do nothing'. Those are actual choices being made based on information that lead to different sorts of outcomes, and then those outcomes in turn lead to different situations - split parties, moral choices (engage in looting versus try to rescue people), and so forth.
Real choices in terms of the situation provided by 'Caves of Chaos' aren't 'What's behind door #3?'. They are things like, rouse the keep's army to attack the caves, side with the cultists in the caves versus the keep, deprive the inhabitants of the lair of provisions, negotiate a peace treaty, assassinate the leaders by stealth, and so on and so forth. But neither the players nor the DM are provided the tools (or reasons) to actually have choice in the scenario. As presented it's a clear kick the doors down, kill the things, and take their stuff scenario. The complexity or subtlety encouraged (or erroneously assumed) with respect to the dungeon by modules like U2 or U3 are not found in the text.
