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In Pathfinder point buy, ability scores of lower than 7 (before adjustments from race) may not be bought with point buy.

What would be a balanced price for such low ability scores?

I am looking for personal experience from people who have done such an extension, or for a reasonably accepted view in the character optimization community.

Motivation for the question: How likely is to roll elite array or better with 3d6 in order?

In particular, I am not worried about players creating horrible malformed monsters with only threes and eighteens as their ability scores.

The question Is it allowed to buy ability scores lower than 7? addresses whether buying low ability scores is allowed (no), which is not the question here. The answer also argues that allowing buying such scores is a bad idea. My use case is very different - I want to have a method of measuring how good or bad ability scores are, and allowing anyone to buy them is not an issue here.

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The formula is that you have to pay for an ability score the new modifier. So going from 7 to 6 gives you a price of -2, 6 to 5 and 5 to 4 each give you -3, and so on. Dropping an ability score to 3 would give you 16 points.

Score | Mod | Cost  
   10 |   0 |    0
    9 |  -1 |    1
    8 |  -1 |    2
    7 |  -2 |    4
    6 |  -2 |    6
    5 |  -3 |    9
    4 |  -3 |   12
    3 |  -4 |   16

It's uncertain whether those values would be balanced ; while they follow the pattern of ability score costs, nothing says that this pattern won't fall apart outside of the 7-18 range. Furthermore, in any case, this should never be an option available to players as discussed in the answer to this question.

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    \$\begingroup\$ This is better than a pure guess, but I would be surprised such a symmetrical result were true. Do you have play experience or serious character optimization people taking a look at this? \$\endgroup\$ – Thanuir Apr 7 '18 at 18:38
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    \$\begingroup\$ Negative. I'm highly certain that the formula is correct, but as mentioned, nothing says this formula will work outside of the 7-18 range. Especially considering that standard roll is 4L6 and not 3D6. Sorry if I made it sound more confident than I am. \$\endgroup\$ – Bainos Apr 8 '18 at 8:23

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