Actually the capstone would be roll 2d8, plus another 2d8 and pick the highest set of 2d8.
At 20th level, an investigator can use inspiration on all skill checks—even ones he isn’t trained in—and all ability checks without spending inspiration.
In addition, whenever he uses inspiration on an ability check, attack roll, saving throw, or skill check, he adds 2d6 rather than 1d6 to the result. Some talents can affect this. If using the amazing inspiration investigator talent, he rolls 2d8 instead. If using this with empathy, tenacious inspiration, underworld inspiration, or a similar talent, he rolls two sets of inspiration dice and uses the higher of the two results.
I don't actualy know how that would change things, but an off-the-cuff guess is that you'd average about 12 on your Inspiration (17 for a Half-Elf).
Although it's worth noting that the Empiricist loses that aspect of the capstone:
At 20th level, an empiricist’s powers of reason and deduction become almost superhuman, and he is able to use them in nearly all aspects of life. At 20th level, an empiricist can use inspiration on all skills (even ones he is not trained in) and all ability checks (including initiative checks) without spending inspiration. This ability replaces true inspiration.
furthermore, a half-elf with 1d8+2 is sacrificing a bunch of hitpoints to get that extra +2, and on a d8 class with only light armour that is not necessarily something that is going to sit well with many players. It doesn't matter how good your sense motive is if you die every second combat.
You're sacrificing 1hp/level, or 1 skillpoint/level, and potentially getting +1 to 12 - 22 different skills by level 4 (or more by spending Inspiration), which is easily worth more than 4hp.
But the real draw is that this can cover Attack rolls, Saving throws and even Ability checks. By the time you can get the Combat Inspiration talent (level 9) the Half elf FCB is giving you +2 to Inspiration rolls. +2 to Attacks and saves when you need it is worth a few feats right there.
Then there's the Inspired Weapon property. Adding +2 to attack and +4 to damage on top of your Inspiration makes this a decent combat enhancer as well. At level 9 the average Investigator is looking at ~+3.5 to hit and ~+7 damage, while you're looking at ~+5.5/~+11. If you really want to stack bonuses by level 13 you're doing the "roll 2d8 and take the highest" thing (Amazing/Tenacious Inspiration) and add 3 (FCB) for an average of ~+9/+17. This means you can just throw an Inspiration die on your last attack of the round and it'll probably hit, if it hits you'll get some pretty nice damage, and (unless you're playing a Swashtigator) you can use that hit as a Studied Strike and add even more damage.
The Ability checks part is nice too. That door the Barbarian is struggling to open? Stand aside I got this!
Now obviously the Half-Elf FCB isn't the only part of this, but it's a scaling bonus that applies to a lot if things and stacks with whatever else you've got going on.
Is it the best thing since Sliced Bread? No.
Is it potentially better than 1hp/level? Absolutely.
Either way, given that you can use inspiration for attackrolls, damage, skill checks, initiative, and saving throws. Whatever flavor of investigator, two talents is a minimal investment for the return. Other than iteratives late game, ive found between inspired weaponry and combat inspiration plus studied combat an investigator can murder people about as effectively as a novaing magus.
Actually the capstone would be roll 2d8, plus another 2d8 and pick the highest set of 2d8.
I don't actualy know how that would change things, but an off-the-cuff guess is that you'd average about 12 on your Inspiration (17 for a Half-Elf).
I got bored and decided to work this out.
The odds of rolling each number if you have Amazing Inspiration, Tenacious Inspiration and True Inspiration all acting together is:
2 = 0.024% (1/4096)
3 = 0.195% (8/4096)
4 = 0.695% (27/4096)
5 = 1.563% (64/4096)
6 = 3.052% (125/4096)
7 = 5.274% (216/4096)
8 = 8.375% (343/4096)
9 = 12.5% (512/4096)
10 = 13.013% (553/4096)
11 = 13.477% (552/4096)
12 = 12.573% (515/4096)
13 = 10.938% (448/4096)
14 = 8.716% (357/4096)
15 = 6.055% (248/4096)
16 = 3.101% (127/4096)
(to the nearest thousandth of a percernt)
And the average roll is ~10.725.
That's actually not as good as I thought, Tenacious Inspiration is only giving you ~+1.7 there (although it is making those low rolls EXTREMELY unlikely).
You can also see that you'd roll 9-12 around 52% of the time.
EDIT:
yeah but with an inspired weapon that turns into +10/11 to hit +20/22 to damage. Pretty beefy
Oh it's still great, I just expected it to be slightly better (approximately 1 better to be precise, I was expecting ~11.8 average), but hey that's why you check I guess ... or that's why I check, I dunno if anyone else cared that much =P
Heh, as soon as you ask who wants to be responsible we all stop responding, typical right =P