(HEADNOTE: Gary, I was nearly done with writing this as your post appeared, so forgive me if it doesn't directly address your further detailed and illuminating re-response. I hope this provides some response back, but will have to think about yours first before adequately replying. Meanwhile, I'll just finish this, and hope this works to some satisfaction….)
It's highly unlikely what I'm ruminating about hasn't been discussed on this board before—I'm so new here, it's just impossible to go over every previous post for however many decades.
But what I'm wondering about, is the nature of the D3 game itself (specifically, the California D3, which does use an algorithm; and, here, I'm only going to talk about singles plays, not doubles).
I posit that the game picks a First number. Then it picks a Second number, and a Third number.
I posit that the game always picks a different First number. Always, and without exception. But the order of the game's picking isn't revealed in the actual result (e.g., result 234 might mean the game chose the 2 as First, or the 3, or the 4: you just don't know, though).
But to expand: it seems evident the game goes ahead and picks different Second numbers, and Third numbers, all the time. So let's just assume for the moment, for the sake of argument, that it does.
So, you can easily still get a repeat number: 234 can reappear as 324, with the Firsts, Seconds, and Thirds mixed up. Proof this is probably the case? The fact that you occasionally do get full repeat numbers like this, but for the most part (?—does it ever happen?) you never get three repeats or more.
If Firsts, Seconds, and Thirds never repeat, then one can go on to say—converting the game's choices now spatially—you will never get a repeated digit from one level of play to the next.
And so, taking the exactly last two California D3 plays from today
F S T
0 2 9 E (b)
5 9 7 D (a)
What we see visually could be the order of Firsts, Seconds, and Thirds: F(a)(b) = 5/0, S(a)(b) = 9/2, T(a)(b) = 7/9. One could mix these up a few different ways, too; but I'm saying what it would not be is F(a)(b) v S(a)(b) v T(a)(b) ≠ 9/9. (I hope I'm using my symbols right there!)
How would this help? Well, if you knew that digit position X of a play couldn't (by definition) be beside, below, nor above itself, that could very well help to strategize[sic.] play.
(It all becomes like a grand Sudoku game—surely that comparison's been made in the past?)
Taking the plays above on face value for the sake of an example (i.e., assuming they are presented visually as well as in reality as First, Second, Third digit placements—this would be perilous in actual strategies, because the true identity of F/S/T placements is unclear), then we would know…
Above F(b), i.e., F(c), you couldn't have another digit 0. This would affect the choice of S(c), because it would be dependent upon what digit appears in F(c) - but we already know, that S(c) can't be digit 2. And so on to T(c), which we already know can't be digit 9.
One would simply have to rearrange the play into correct order F/S/T... but how does one do this? I think there are ways. I even think the pool for each set, F/S/T - beyond its own natural selection (i.e., by definition, they can't all be digits 0-9 at once) - are limited by the current play/s of the game. The more you limit the pools, then filter them through their possible positioning... the more you shrink the possible 120 boxes of play down to viable, playable sets.
... er, right?