delericho said:
...(I hope that's legible. Also, I hope it's correct.

)...
I applaud your effort in calculation, but these numbers aren't correct. I do however agree the Barb20 vs. TWF F20 isn't a close comparison on TWF vs. THF+PA, though this whole TWF thing is quite a sidebar to the thread topic...except that it leads to an answer...
Anyway, here's the correct #s for the Fighter 20 example.
Str 29
Dex 19
Feats as above. Wields two-bladed sword. Blade 1 is +5 Speed Shock; Blade 2 is +5 Flaming Frost (an interesting combo).
THF with blade 1 has the attack bonus progression:
+36/+36/+31/+26/+21
That's 20 (BAB) +9 (Str) +2 (WF, gWF), +5 (Weapon), with the extra full BAB attack from the Speed enchantment.
Average damage/normal hit = 30
That's 4.5 (sword) +13 (Str) +4 (WS, gWS) +5 (sword enchant) +3.5 (sword xtra)
Average damage/crit hit = 56.5 (sword xtra not doubled)
TWF with both blades has the AB progression:
blade1
+34/+34/+29/+24/+19
Average damage/normal hit = 26
That's 4.5 (sword) +9 (Str) +4 (WS, gWS) +5 (sword enchant) +3.5 (sword xtra)
Average damage/crit hit = 48.5
blade2
+34/+29/+24
Average damage/normal hit = 24.5
That's 4.5 (sword) +4 (Str) +4 (WS, gWS) +5 (sword enchant) +7 (sword xtra)
Average damage/crit hit = 42
Math check
Suppose blade1 is wielded THF-style, and your opponent's AC is 30. Turns out the best PA to go with is 7,
not zero! How did I get 7? Well, here's the
average full attack damage/round against AC 30, PA 0 (no DR).
[(15/20 + 4/20*1/20)*30 + (4/20*19/20)*56.5] x 3 for the +36/+36/+31 attacks
plus
(13/20 + 4/20*3/20)*30 + (4/20*17/20)*56.5 for the +26 attack
plus
(8/20 + 4/20*8/20)*30 + (4/20*12/20)*56.5 for the +21 attack
boop beep beep boop boop...
answer =
151.79
Now, what if you PA-ed for 7?
AB progression = +29/+29/+24/+19/+14
blade1 normal D = 30 + 7*2 = 44
blade1 crid D = 84.5
<full attack D, 30 AC> =
[(15/20 + 4/20*1/20)*44 + (4/20*19/20)*84.5] x 2
+ (11/20 + 4/20*5/20)*44 + (4/20*15/20)*84.5
+ (6/20 + 4/20*10/20)*44 + (4/20*10/20)*84.5
+ (1/20 + 4/20*15/20)*44 + (4/20*5/20)*84.5
=
177.14
OK, clearly 177.14 > 151.79. So PA 7 better than PA 0. What about PA 6? or PA 8? or PA 20?

This is where spreadsheets can help. Mine does every calculation, PA 0-20 (no epic levels, sorry), and is why it's so darn big. But it is exact. Turns out 7 gives the max damage. BTW,
there is no complete analytic formula which generates the optimum PA values... you're much better off doing this tby brute force or by a more elegant dynamic program.
This is all presented to give the reader confidence that the numbers which follow are correct.
And here they are.
Code:
AC THF PA THF+PA TWF PA TWF+PA
10 167.7 20 358.2 224.7 16 303.5
11 167.7 20 349.9 224.7 15 298.1
12 167.7 20 341.5 224.7 14 292.7
13 167.7 20 333.2 224.7 13 287.3
14 167.7 19 323.6 224.7 12 281.9
15 167.7 18 314.0 224.7 11 276.5
16 167.7 17 304.4 224.7 10 271.1
17 167.7 16 294.8 224.7 9 265.7
18 167.7 15 285.2 224.7 8 260.3
19 167.7 14 275.6 224.7 7 254.9
20 167.7 13 266.0 224.7 7 249.6
21 167.7 12 256.4 224.7 6 244.3
22 167.7 11 246.8 223.2 6 239.1
23 167.7 11 237.5 221.6 5 234.0
24 165.9 10 228.3 220.1 5 228.9
25 164.1 10 219.4 218.6 4 223.9
26 162.4 9 210.5 217.1 4 218.9
27 160.6 9 202.0 212.6 3 214.0
28 158.9 8 193.5 208.2 3 209.2
29 155.3 8 185.3 203.7 2 204.4
30 151.8 7 177.1 199.3 1 199.6
31 148.3 7 169.3 194.8 0 194.8
32 144.7 6 161.5 187.4 0 187.4
33 141.2 5 153.7 180.1 0 180.1
34 135.9 4 145.9 172.7 0 172.7
35 130.6 3 138.1 165.3 0 165.3
36 125.3 2 130.3 157.9 0 157.9
37 120.0 1 122.5 145.9 0 145.9
38 114.7 0 114.7 134.1 0 134.1
39 105.7 0 105.7 122.3 0 122.3
40 96.8 0 96.8 112.0 0 112.0
41 88.1 0 88.1 101.7 0 101.7
42 81.0 0 81.0 91.1 0 91.1
43 73.9 0 73.9 80.7 0 80.7
44 66.7 0 66.7 70.5 0 70.5
45 59.5 0 59.5 63.1 0 63.1
46 52.6 0 52.6 55.7 0 55.7
47 47.3 0 47.3 48.1 0 48.1
48 42.0 0 42.0 40.6 0 40.6
49 36.5 0 36.5 33.3 0 33.3
50 31.1 0 31.1 28.9 0 28.9
Comments:
1). Turns out you can power attack with a two bladed sword, even though the off-hand attack gains no benefit.
2). Turns out for low-mid AC for either style, you're better off PAing for at least a little.
3).
A lot of analysis such as this has proven #2, and disproven the oft-stated myth that you should
only PA, and then for max, when you can't hit an opponent except with a 20, or when your opponent clearly has no armor. That's bull.
4). Against ACs 24-47, this character is better off TWF.
5). Ergo, 2 for 1 THF PA trade-off not overpowered.
edit: once again,
free spreadsheet found on the site linked in the signature of my 1st post above