Is the +3 bonus too much?

[Malcadon]

...similar to OD&D. I would use that system, and house-rule STR as follows:

STR bonuses or penalties to damage only on melee or hand-hurled weapons, also adjustment to open doors roll
3-6: -1
7-14: 0
15-18: +1

Much of the combat rules in OD&D are holdovers from the Chainmail combat system. Two of the three combat systems used in that book, used 2d6 for attack rolls, with every "+1" being more significant then the standard d20 D&D attack roll.

That's one way to go too, which I've also considered. It would also balance with DEX, which gives only a 'to hit' bonus.

I totally agree!

[greyarea]

Maybe strength should only give a damage bonus. No "to hit" bonus. Raw strength is not accuracy.

Agreed that raw strength isn't accuracy, but the reasoning for the bonus "to hit" isn't that, it is breaking down the opponent's defenses.

As mentioned in the DMG:

[Black Wyvern]

I prefer:

3 = -2
4-6 = -1
7-14 = 0
15-17 = +1
18 = +2

Which I use for my S&W games but for Core games I use the classic -3 to +3 and really think both work pretty well. I use 3d6 in order so the standard array ends up with more bumps. I also use difficulty based varying d6 for ability checks and use a lot of them so the actual score has weight without needing bonuses to back it up.

[Blood axe]

Greyarea- I agree its abstract. But you could still change it if it fits your game.

[Gilliadson]

What I have not seen touched on here is that the To Hit modifier for DEX is for missile attacks in which case there is no damage adjustment from STR. The to hit modifier for STR is for Mele only.

[Eldrad]

Remember if you roll 3d6 an 18 is a 1 in 216 chance.

[Black Wyvern]

1 in 216 to roll it naturally, but the rules also allow for modification of prime requisites. Which, though the math is well beyond me, observation would seem to indicate better than 1 in 20 characters are able to get a PR up to 18 depending on how closely the DM reads the description of the rule. Thieves are more likely than others.