Just to remind you, the 12 card method allows a single switch, so a single 18
somewhere is always possible.
Out of curiosity, if I came to your game and said "I like to come up with my character concept ahead of time, so I'll use your method but I want to pick the card combination. If it matters, I won't start out with an 18 in any stat."
Would you allow it? Why or why not?
If I use that method (I haven't started using it yet, but it is my intention to use it next time I DM a campaign), then the whole point is that the group make their PCs together, starting with these semi-random stats. I also intend the character creation to be done in this order:-
1.) Choose race. At least half the PCs must be human, no more than half can be non-human, no more than one PC can be 'uncommon' (half-elf, half-orc, gnome, human looking 'other', like variant tiefling or aasimar), no other races allowed.
2.) Choose background.
3.) Determine stats, using the 12 card single switch method, with the players communicating during the process so that if they
want to have a balanced party, they can.
4.) Go away and have a week to design their PC's, with steps 1, 2 and 3 now set in stone.
The idea is to create a more 'realistic' group, one that would reflect the population more accurately, while still skewing the bell curve to be 'heroic'.
I'm tired of parties that look like a zoo. You have a world which is largely human/elf/dwarf/halfling by a large proportion, of humans being by far the largest of those. Meanwhile, the party turns up. Although they are from this world so our expectation should be mainly human, the rest mainly dwarf/elf/halfling, the actual party consists of dragonborn/devil-like tiefling/bugbear/warforged/genasi/tabaxi, and then they wonder why there is never any room at the inn!
I'm also tired of point-buy destroying the assumption of a bell curve. Instead of most results being around the middle (and I'm okay with the 'middle' being skewed higher to reflect 'heroic' PCs), scores are either 8 or 15 before racial. I'm tired of looking at the Str/Dex scores and the entire party, without exception, has either Str 16/Dex 8 or Str 8/Dex 16.
So I chose my method to combat all of those faults. Usually, players choose a race that gives a racial bonus to the prime stat of the class. That results in a PC population that has no wizards that are not elves, tieflings or gnomes, no barbarians that are not dragonborn, half-orc or mountain dwarf, no clerics that aren't wood elves or hill dwarves. Yet surely every population that worships gods has clerics!
I've chosen a method that is likely to get, say, a dwarven wizard or an elven barbarian, simply because fate has made their best stat Int or Str. The order which the steps are taken (race, background, stats) is because that's how actual people come into being! You can't help what race you are, your background might be affected by race but might not, but is beyond your control, and high Str or Int is equally possible in all populations (before racial adjustments). However, your class is not random; you choose your class bearing in mind your natural aptitudes, so although an Int 8 person
can be a wizard, other classes seem a better fit. This is why stats are determined after race and background but before class is chosen.
Because the players are all doing the first three steps as a group, they can go for a balanced party if they want. But what if someone dies and needs to be replaced? What if a new player joins later? In a normal game, the existing party roster is usually borne in mind when the new PC is being created. This would be difficult to achieve with only a single 12 card single switch. Which is why these later additions would deal the first six cards randomly one to each stat in order, but could then look at the six cards remaining in hand and choose where to assign them. The order would be unchanged re: race/background/stats/class.
All that said, I haven't put this into practice yet. The last time I DMed a campaign I told everyone what the (semi-)random stat generation system was, and then told them that if at the end of the entire stat generation process they didn't like what they got then they could use point-buy instead. This is just like rolling for hit points each level, but taking the set hit points if the roll was worse; I do this too.
Would you have walked away from
that one? Your wife was disappointed at being forced to play those low rolls; would she have been okay if her friend would've been allowed to keep her high rolls but your wife could throw her rolled scores away and use point-buy instead? Would her friend have felt guilty enough to throw her high scores away and use point-buy if there wasn't such a huge discrepancy between the scores she and your wife rolled?