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The probabilities are:

12: 0.4%
13: 1.6%
14: 3.9%
15: 7.8%
16: 12.1%
17: 15.6%
18: 17.2%
19: 15.6%
20: 12.1%
21: 7.8%
22: 3.9%
23: 1.6%
24: 0.4%

Thanks for the replies guys, and the probabilities Antimony!

I think my problem with not being able to figure this out is that the possible outcomes don't pay attention to order.
If order mattered, there would 256 possibilities (4*4*4*4).
There aren't that many in reality cause it doesn't matter which dice is first or last, and I don't know an equation for that.
SOOO I just wrote out all of the 35 possibilities (I think i got all of them..)
Obviously refer to 1's as 3's, 2's as 4's, etc. This was easier for me.
Now you just take 100% chance, divided by 35 possibilities (~2.86) and multiply that by however many are in each row.
Example - 15. 3 * 2.86 = 8.58% chance to get a 15.

12. 1111
13. 1112
14. 1113 1122
15. 1114 1123 1222
16. 1124 1133 2222 1223
17. 1134 1224 1233 2223
18. 1144 1234 2233 2224 1333
19. 2234 1244 2333 1334
20. 2244 1344 2334 3333
21. 2344 1444 3334
22. 2444 3344
23. 3444
24. 4444

Maybe this is the right way of doing it? I should have finished my math before posting *sigh*...

So I have a GM who wanted us to make 'Epic' characters. Very special beings and what not, yet still play by regular class rules.
One way we are special, is that instead of rolling 4D6, dropping the lowest like I have normally seen, he wants us to roll 4D6 and re-roll 1's and 2's (min 12, max 24).
I'm trying to math, but can't quite get the chart right. What I would really like to know, despite how difficult this would really be to figure out, is with 3's, 4's, 5's, and 6's, what is the percentage chance of getting each specific number?
Example, to get a 24, you NEED 4 6's. You have a 25% chance of getting a 6. To get 4 6's, you quarter 25 another 3 times. Rounded up that would be about a .4% chance (I probably didn't do that right..). Whats the chance of getting a 23? 22? 21? etc...
The middle numbers have a much higher chance, due to more combinations being able to reach it.
It's a lot to ask, I know. This is why you need to stay in school :)

P.S. Im (not-so) silently seething in rage at a player who I think used a 'random number generator' and got a 24 and multiple 22's. 5 out of 6 of his stats are above 20.
I happily rolled a 23 and 2 20's in front of the GM with legitimate dice rolling, and i was ecstatic.
That is kind of the purpose of this little side project.. and you know... Didn't something like this kill the cat?

I just wanted to revert back to the whirlwind and its feats for just a second.
Had an awesome idea, not at all possible, but still would make sense.

Z has dodge, mobility, spring attack, and whirlwind. He uses mobility to help against AoO's to get in the middle (15 feet away), whirlwind as part of a spring attack, fleeing back to where he is standing now after his attacks.
Uses the prereq's, and has a blast while doing it.

Z = PC
X = Enemy
0 = Empty Space

x x x
x 0 x
x 0 x
0 0 0
0 Z 0

Maybe if Whirlwind could be used specifically in a spring attack? I can definitely see a two-hander barbarian rushing into the middle of melee, making a single broad sweep attempting to hit all enemies around him, then retreating back before they have time to react. Avoiding their full attacks next turn, hitting more enemies than a simple full attack would, not stopping on a missed enemy as cleave would. Maybe to balance it further, missed enemies may take AoO's as the PC tries to retreat back (I'm aware spring attack normally doesn't take AoO's from the target, but hey, my way could be pretty powerful).

If this ever actually came up, I'd probably allow it, but ONLY because Whirlwind has those prerequisites.

You have to charge as well as a mount

Well with that new ruling, it pretty much changes everything that has been said.

The wording for INA and Strong Jaw both work off the original size of the creature, so they don't stack.

prototype00

Somehow I knew the first reply was going to be about them stacking :)

After reading multiple threads with arguments both ways and never finding an actual developers ruling on it, I just asked my GM if he thinks they stack. He believes a lot in Herolab which i guess has them stacking so he is allowing it (sucks for him).

I am still curious though, and would like to know if it has been ruled and I just couldn't find it.

I think a lot of people overlook the INA description before the size comment though.

Benefit: Choose one of the creature's natural attack forms (not an unarmed strike). The damage for this natural attack increases by one step on the following list, as if the creature's size had increased by one category. Damage dice increase as follows: 1d2, 1d3, 1d4, 1d6, 1d8, 2d6, 3d6, 4d6, 6d6, 8d6, 12d6.

A weapon or attack that deals 1d10 points of damage increases as follows: 1d10, 2d8, 3d8, 4d8, 6d8, 8d8, 12d8.

If you omit the whole half sentance talking about the size category I think A LOT more people would think it stacked. I'm partial to either, I wouldn't whine if my GM said they don't stack, but if I was the GM, I would allow them to stack.

If it increases by one step on the following list, then that damage would be the damage you increase by strong jaw, no? Just my opinion on the matter.

All that aside I as hoping the whole free trip attacks while great cleaving would be verified. If I hit with great cleave, I get that free trip attack, and then move on to great cleave the next guy and possibly trip all as the one standard action great cleave.

Upon further investigation I found a lot of people using the manufactured weapon chart with the 2D4 claws. 2D4 would go to 2D6 as you stated, but a medium 2D6 goes up to 3D6. That seems to make the most sense, and I found it all on my own :P

(Strong Jaw table doesnt have 2D4 for some reason, neither does Improved Natural Attack table)

Thanks for inspiring my research though, and thanks for the calculations. Making a druid and you have definitely convinced me to include a dire tiger form.

4D6 claws with Improved Natural Attack and Strong Jaw :) (2D4 -> 2D6 -> 3D6 -> 4D6)
That should change your damage calculation numbers quite a bit (even without INA)

Basically, I've got this 11th level druid. I have a Stegosaurus animal companion, mainly for the Trip special attack it gets.

"A creature with the trip special attack can attempt to trip its opponent as a free action without provoking an attack of opportunity if it hits with the specified attack. If the attempt fails, the creature is not tripped in return."

Snagged power attack for him early, put a point into int at 4th level, got cleave, improved natural attack, and great cleave.

My Stego, being the badass that he is, deals 2D8 base damage, 3D8 with INA, and 6D8 with Strong Jaw. 8D8 if i want to go so far as to Animal Growth him.

So now we put it all together into a Great cleaving 8D8 damage dealing free action tripping beastmode Stego (with 10-15 feet of reach!)

Am i correct in assuming this all goes together as I have stated? Or is the 'specified attack' it says in the trip description a special kind of attack action? My interpretation is the specified attack is his tail attack which is what he is great cleaving with.

Thanks for reading :)

Dire Tiger: 4 claws 2d4 + STR + static bonuses, bite 2d6 + STR + static bonuses and improved critical.
With strong jaw: 4 claws 2d8 + STR + static bonuses, bite 4d6 + STR + static bonuses and improved critical

2 Things

1. I've been looking and I really want to show my GM where you got the advancement from 2D4 to 2D8. Not under improved natural attack or strong jaw. Where'd you get it?

2. When you wild shape into a dire tiger, you do not get its feats. Thus, no improved critical (99% sure). Not a special ability, just a feat that its bestiary stat block has.