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In the 4th edition, when using point-buy system to set ability scores, players can only choose to put "8" in one ability. What is the reason for this? Why don't the rules allow for an "8" to be put in multiple slots?

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It is mostly to avoid min-maxing.

Say you have a build where you only care about two ability scores, considering the rest to be dump stats. With only one ability score allowed at 8, you can reach the following array:

Str 17 (+3) 12 points  
Dex 16 (+3)  9 points  
Con 11 (+0)  1 point  
Int 10 (+0) 
Wis 10 (+0)
Cha  8 (-1)

With all ability scores allowed to be lowered to 8, you could scrape together the following array:

Str 18 (+4) 16 points
Dex 17 (+3) 12 points
Con  8 (-1) -2 points
Int  8 (-1) -2 points
Wis  8 (-1) -2 points
Cha  8 (-1)

Maybe not a huge difference, and this is an extreme example, but in everyday use I imagine that there would be a very high temptation to lower two or more ability scores down to 8, to get just a bit more oomph to the stats you consider important. Allowing only one ability score at 8 removes that temptation, making more rounded characters (the chance that you'll raise that 10 to a 12, is greater than raising the potential 8 to a 12).

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    \$\begingroup\$ +1, Might want to note that this array is prior to adding any racial bonuses, and perhaps include the change in modifiers, since that's what matters. \$\endgroup\$ – DCShannon Mar 28 '15 at 1:36
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I've always assumed it was to prevent excessive optimization, as Rubberduck has pointed out.

I'd just like to add an additional example, based on your character's defenses.


Each of your non-AC defenses (NADs) is determined by the higher of two ability scores: strength or constitution for fortitude, dexterity or intelligence for reflex, and wisdom or charisma for will.

This means, that unless your build needs two ability scores from the same pair (str and dex for instance, as in Rubberduck's answer), you'll usually only increase one of the abilities from each pair, and leave the other low. If you could leave all three low ability scores at 8, instead of two at 10 and one at 8, then your defenses would increase above their intended values.

For example (not including whatever racial bonuses you might have):

One Ability Score at 8

Str    10    (+0)    0 points
Con    13    (+1)    3 points
Dex    10    (+0)    0 points
Int    16    (+3)    9 points
Wis    16    (+3)    9 points
Cha     9    (-1)    1 point

Fort   11    Ref   13    Will   13

Three Ability Scores at 8

Str     8    (-1)    0 points
Con    14    (+2)    5 points
Dex     8    (-1)    0 points
Int    17    (+3)   12 points
Wis    16    (+3)    9 points
Cha     8    (-1)    0 points

Fort   12    Ref   13    Will   13

That's not a huge difference at level 1, but once you can add to a couple scores and factor in a racial bonus, you've got a +1 or +2 to a couple different NADS.

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