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Okay, i am truly confused about how to advance a monster. For example, the giant crab. He starts off with 3d8 HD and a 14 Con. Now I want to make him Large, as opposed to Medium. Table 2-2 in the Bestiary has be apply +4 Str and Con, -2 to Dex, and +2 Natural armor to his AC. That makes him Large. According to the Crab, Giant entry a large giant crab has 5d8 HD and is CR 4. Will I want a CR 8 creature.
So I try again, this time following the directions on p. 295 of the Bestiary. I want a CR 8 creature. If i read things correctly here's what happens.
1) the crab become Large since its HD is more than doubling
2) the calculation mentioned above take place
3) Now table 2-1 comes into play. Totaling the hp additions between the the CR 2 row and the CR 8 row results in +65 hp. Since the crab's Con has changed I can't seem to wrap my head around how to figure out how many HD the new CR 8 crab should have.
Base version: 3d8+6
Large version: 3d8(?)+24
CR 8 version: nd8+n*4=total hp
How does the +65 come into play? Are these base hp not modified for Con> Or has the Con already been added? My read of the material says,
Note that if the creature increases in size, its Constitution may also increase, as noted on Table 2–2, granting it additional hit points that might offset the need for additional Hit Dice (this also applies to any other Constitution increases).
That seems to say to me that the Con modifier for hp is included in the CR 2 to CR 8 hp calculations.
Usually I am good at math but this seems rather circular to me. Can anyone help?

AvalonXQ |

The Monster Advancement table isn't for changing stats. It's something to compare a changed monster to in order to make sure its values fall within the expected range for its new CR.
What the book is telling you to do is to keep adding racial hit dice to the crab until its values match those for a CR 8 creature.
Your normal CR 2 crab has 3d8+6 = 19 hp. Advance it to around 84 hp.
Since the large crab has a +4 Con mod, it's going to get 8.5 hp per hit dice. So a 10 HD large crab should be perfect.
The 10 HD crab has 10d8+40, or 85 hp. It gets two ability score increases, +7 to a variety of skills, total BAB of +7, etc. Check these numbers to make sure they fit a CR 8 creature okay, and call it a day.