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House Rules: Rolling Ability Scores

I don't know if 5e uses the same D20 attribute bonuses but what I did in D20 was to give the players a certain number of total bonus points. So they may start with +12. They assign those to the attributes. Then roll a single d6. If it is odd then the first attribute number will be odd. Look up that attribute bonus and take the attribute rating that is odd for that bonus. The next attribute will be even and alternates all the rest.
It is SOOOOO much faster and it gives the players a lot more control. You can set the total bonus based on whatever you want them to average to. You could have +16 for truly powerful characters or +5 for normal modern characters.
 

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A method my group has used for over 20 years across various editions is a standard 6x 4d6 dropping the lowest. If the set does not contain at least one 15 or higher then discard the set and roll again. Once a valid set is established, decide whether or not to keep it. If that is discarded then you must use the next valid set rolled. In exceptional circumstances, the DM may allow you to discard another qualifying set but that is reserved for exceptional bad luck.

Low scores (or their potential) is part of the game and whilst no-one I know would actively choose to have a low score, the times we have had to deal with them have led to some of the best roleplaying experiences we have had. As examples, one of my characters using my second set scored two 18's, two 16's, a 13 and a 3. This was clearly always going to be an exceptional character with a huge flaw. With the type of fighter I wanted to play that flaw was going to be intelligence (even moreso as an optional rule at the time only allowed fighters to go that low). The roleplay of various situations was great fun and to this day that character is one of a handful amongst the group that are remembered and brought up in (usually drunken) conversations, although often its for the way he actually died. A current example in our new 5E game is a wizard with great stats except for a low charisma. She roleplays this as a massive social ineptitude perfectly and social situations often provide great entertainment for the whole group based on this.

Based on this, I believe that rerolling 1's (making anything below 8 impossible and anything below 10 unlikely) is actually robbing yourself of the potential entertainment to be gained from roleplaying the overall situation. Of course if more than one stat is particularly low this has a greater impact and affects survivabilty but a single low stat can actually help build the character and the personality
 

Low scores (or their potential) is part of the game and whilst no-one I know would actively choose to have a low score, the times we have had to deal with them have led to some of the best roleplaying experiences we have had...

The roleplay of various situations was great fun and to this day that character is one of a handful amongst the group that are remembered and brought up in (usually drunken) conversations, although often its for the way he actually died...

Based on this, I believe that rerolling 1's (making anything below 8 impossible and anything below 10 unlikely) is actually robbing yourself of the potential entertainment to be gained from roleplaying the overall situation. Of course if more than one stat is particularly low this has a greater impact and affects survivabilty but a single low stat can actually help build the character and the personality

How did you explain my thoughts so perfectly? Excellently put. Although it must be asked... How did that character die?
 

I still need to play 5e to be absolutely sure, but I'm inclined to think that I'll be switching to the 'standard' house rule I've been using for ability scores for the past few years:

Each player can choose which of three methods to use. You can only choose "Random Roll" if you're rolling in front of the group, and once the first die falls you can't change your mind.

Method #1: Random Roll

4d6-drop-lowest. Reroll is the net modifier is 0 or lower, or if your highest score is 13 or less. (That is, standard as per 3.5e.)

Method #2: Standard Array

The array is 16/15/13/12/10/8. Arrange as desired.

Method #3: Point buy

28-point buy, using the 3.5e costs:

9 -> 1 point
10 -> 2 points
11 -> 3 points
12 -> 4 points
13 -> 5 points
14 -> 6 points
15 -> 8 points
16 -> 10 points
17 -> 13 points
18 -> 16 points

(I did strongly consider using the 5e point values but extending the table up to an 18, but at length decided against - I know how the random roll stacks up against these costs; I don't for the 5e costs, though it won't be very different.)
 

How did you explain my thoughts so perfectly? Excellently put. Although it must be asked... How did that character die?

He was an elf and actually had 19 dex (one of the 18s plus 1 racial). The party had triggered a trap and the dungeon appeared to be collapsing forcing the party to make a speedy exit. The route out had a makeshift plank system spanning a pit trap. The DM had ruled that you could walk carefully across the plank or run if you made a successful dex check (old style roll lower than dex). He was bringing up the rear, last man to leave. The party made their way across the pit carefully which presented an opportunity to close the gap (about 60' I think it was) up to them. Attempt to run across, dex check (needed 19 or lower) rolled a 20 so slipped off. DM allowed a second dex check to try to straddle the plank rather than fall down the pit... rolled another 20. The character was skilled at acrobatics (I forget the actual skill name from that edition, tumbling was it?) so the DM allowed another dex check at -4 (so had to roll 15 or lower now) to use the plank as a spring to somersault out of the pit, rolled 17. Fell down the pit, took just enough damage to fall unconcious and bled to death while the rest of the party fled. We calculated later that he had around a 1 in 15000 chance (3 failed checks plus enough damage) of not making it out of there but still died.
 

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