It's probably just that the term is a bit misleading. In terms of probabilities, I think you mean that each score is **independent**. It's like flipping two coins. The result of the first coin doesn't tell us anything about the result of the second. With a deck, the same outcome can occur like this:

I did, in fact, use the phrase "completely independent" in my post you quoted above, so...yes, I very much meant "independent."

In this case, we have no information on any score in advance: they are all equally a surprise. Do you see what I am saying. I believe what you are chasing is at heart something more specific. It's not to do with the randomness, or per score surprise. Most likely you want the sum of scores to vary. How much by?

Well, again, we're not talking about

*my* interests, but my understanding of others' interests. But I can tell you, right now, explicitly, that I have been told that if there is literally ANY effect--anything WHATSOEVER, no matter how small, no matter how unpredictable--

*causes* later stats to be better if earlier stats were worse, no matter how probabilistic that effect is, it is unacceptable. There needs to be truly, absolutely ZERO impact on probabilities.

Drawing cards without replacement, by definition, generates dependent probabilities. The odds of drawing (say) 4 for your second stat are definitely always changed

*because* of what you drew for your first stat. That's literally what drawing without replacement does, it makes each draw's probabilities depend on which cards have already been removed.

Is it okay to have one player have scores summing to 18 while another's sum to 108? Or is that too much variance? I suspect you'd be tempted here to say - that won't happen - but then, like

@Xetheral's DM, what happens if it does happen? I had one campaign where our bear-barian just had far better stats than everyone else. They overshadowed everyone: adding nothing to the campaign. In my experience, players enjoy variance, but much less variance than the dice allow.

If we are actually talking about

**my** tastes, yes, that much variation is unacceptable. I'm fine with some amount of variation, e.g. with 4e PB, counting racial stats, you have a theoretical total sum spread between 73 and 83 (with 73 requiring a hyperfocused human and the 83 being a very suboptimal option and requiring a non-human).

If we're talking about the tastes I've been

*told* by others, then yes, to the best of my knowledge, it is not only

*okay* to have such variance, it is mandatory that such variance be at least

*possible*. Otherwise, again, people feel their characters are "born lucky," and thus uninteresting.

There are always niches of players a design cannot serve. The goal is to satisfy as well as possible your chosen main audience. Points-buy won't serve those players (it has zero surprise). I believe deck-generations offer the most scope for future-design. For example, we could use fewer than all the cards. Taking the deck above, we could add one 6 and one 1. Players still draw only 18 cards, no replacement. There will be surprise, because until the last card drawn they do not know what cards will be left in the deck.

6, 5, 5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2 ,1 draw 18 cards without replacement, allocating three to each score. Either allocating as drawn, or as desired. Two cards will be left in the deck.

Again, for many, this spoils the "surprise" because the probability of drawing (say) 15 goes up if you previously drew a total of 6 for Strength and a total of 7 for Dex (or whatever order one prefers to draw stats in). You haven't actually made the events independent, by definition.