From a standpoint of probability, and assuming true randomness, the former rolls indeed don't have any effect. (See the Monty Hall problem for an example people commonly get wrong.)

However, the game's generation of random numbers is not truly random. Therefore, it is possible for a combination that is possible with true randomness to not actually be possible under the game's PRNG. In particular, for results that are extremely unlikely (especially if less than 1 over the PRNG's period), most such results are not possible. For those few unlikely results that actually possible with the game's PRNG, those results will be more likely than expected.

To put it another way, given a long enough sequence of random numbers, there are sequences that simply can't be generated by the PRNG. Another example of this would be games like Solitaire and Freecell; the common computer versions, I believe, simply can't generate all possible deck shuffles, so there are games that simply can't be generated.

Remember, we're not talking about true randomness here; we are talking about the behavior of the game's pseudo-random number generator.

If this is true, then 18s would be quite rare. With 3d6, the chance of rolling an 18 is 1/216, or about .46%. With 4d6, the chance is apparently 21/1296 (I looked it up), which is about 1.6%. (Note that this is the chance for any given stat.)

Also, if what you say is true, the chance of a Paladin rolling 18 Charisma will be about the same as that of a Human Fighter rolling the same.

Edit: I think I may try simulating some of these observations (in C or Rust) and reporting my results here. A computer simulation is not bound by the mistakes of human thought (provided, of course, that the code doesn't have a bug in it).

I just did a bit of simulation here.

The PRNG I used is the one found in POSIX.1-2001 (according to the linux manpage for rand(3)). Note that I used 32-bit integers because that's what the game likely uses (note that the Enhanced Editions might (or might not) differ in this respect) and because it is feasible to loop through the entire PRNG cycle.

I then multiplied each one by 6 and divided by 32768 to get a number in the 0 to 5 range, and then looked at streaks of 5s (because the game likely adds 1 to the value to get a number in the 1 to 6 range when rolling a d6).

The results:
It turns out that, in the entire 2^32 cycle, there are only 2 streaks of 12 6s. There are none of 13 or more.

Therefore, at least for this particular PRNG, which is likely not too dissimilar to the one actually used in the game, rolling 18 6s in a row (and hence rolling all 18s via the 3d6 method) is not possible.

Next step, which is more complicated, is to see what happens with the 4d6 drop lowest method; is there a sequence that gives you all 18s?

For reference, here is the C code that actually appears in the manpage I mentioned:

static unsigned long next = 1;

/* RAND_MAX assumed to be 32767 */
int myrand(void) {
next = next * 1103515245 + 12345;
return((unsigned)(next/65536) % 32768);
}

void mysrand(unsigned int seed) {
next = seed;
}

Something crossed my mind so I'll mention it.
This would affect the investigation of whats possible in the RNG if you or someone else decides to look more seriously at it.

When does the game roll the d100 for str?

I don't know. I actually didn't think about that.

However, I do know that, once it's determined, it doesn't change unless you re-roll or use the Alt-8 cheat. Lowering (or raising) a stat away from 18 and raising (or lowering) it back will not cause exceptional strength to be re-rolled.

A related question: For non-fighter-types and halfling fighters, is exceptional Strength rolled (and then ignored, of course) at all? My guess is that it is rolled for halfling fighters, but not for non-fighter-types.

I was thinking about that too.

It probably comes down to which was easier for the engine to handle when they coded it, or what they thought would be easier.. Be it not rolling for non fighters, or rolling for all and just ignoring said value.

I just hope your Godlike character won't get killed by bandits on your way to Friendly Arm Inn.