I am very confused by this. So far as I know, you're allowed to guess and attack blindliy.
We're discussing Gygax's AD&D rules. Pages 60 and 70 of the DMG seem to make it pretty clear that, if an invisible creature is not detected in some way, then no attack is permitted.
The idea of "guessing" as a viable element of an action declaration is a more recent development in the rules.
Okay, so we have in the rules that an invisible creature can be attacked if the other side saw it turn invisible, but at a -4 penalty. Why is that? He can't see the invisible creature. It's because he can GUESS where the creature is, having seen it become invisible.
The last sentence is not a correct account of the relevant AD&D rules.
The reason the character can attack the invisible creature whom s/he saw turn invisible is because s/he KNOWS where the creature is.
Page 70 of the DMG says:
Invisible opponents are always at an advantage. They con only be attacked if they are attacking or otherwise detected somehow. These opponents always cause the attacker to attack at a -4 on “to hit” rolls because of the invisibility. They can never be attacked from flank or rear positions unless the attacker can see them (thus they are, in fact, visible!).
This passage tells us a few things. First,
detecting an invisible creature is a broader concept than
seeing an invisible creature. If you can see it, it's not invisible at all (it is, in fact, visible!). Second, if you can detect but not see it, then it is still invisible, gets bonuses, but can be attacked. Third, if you can't detect it, you can't attack it.
Then, going back to p 60, we have:
Once detected, the invisible creature will be kept track of thereafter, as the detector will be able to note the cause. Any attacks incur the -4 penalty of attacking on invisible opponent, of course, and the invisible creature likewise is entitled to +4 on saving throws.
That is, if an invisible creature is detected, it will be
kept track of.
Finally, why is it the case that "if the party is observed doing so [ie turning invisible], there is no reason why an opponent cannot attack with the standard penalty (-4) for inability to see the target"? I think its' pretty clear that this is, likewise, because the opponent who saw the creature turn invisible can keep track of it.
How do you keep track of an invisible creature? Still on p 60, we are told that "[t]his is explainable as the observer's ability to note a minor disturbance in the air - a shimmering or haze - or by keen hearing, and/or keen sense of smell."
It's not
guesswork.