There is no info on the hydra traits "multiple heads", so i'm trying to reverse engineer it, here are my thoughs.

**Effective attack CR 8:**

 - Five attacks (1 per head), 10 damage each for an average of 50 damage.
 - +8 bonus to hit
 - Average damage is CR 7, but the bonus to hit scale it to CR 8

**Effective defense CR 10:**

Keeping in mind that regeneration effects are calculated for 3 rounds, I'm guessing that the game expects a 3 round combat, so the hydra is expected to take, at least, 1/3 of its life each round: 57 (172/3)

> **Multiple heads** 
>
>Whenever the hydra takes **25 or more damage in a single turn, one of its heads dies**. If all its heads die, the hydra dies. **At the end of its turn, it grows two heads for each of its heads that died since its last turn**, unless it has taken fire  damage since its last turn. The hydra **regains 10 hit points for each head regrown** in this way.

My interpretation of this is that each time the hydra receives 25 damage it lose a head, because we're assuming that the hydra lose 57 health each round, 2 heads dies and 2 heads grows back. Therefor the hydra is regenerating 20 hp each round.

 - 20 hp each round per 3 rounds = 60 hp. 172+60 = 232 effective hp
 - AC 15
 - Average hp is CR 11, AC reduces this to CR 10

**This ends with an average CR 9, not a CR 8.** 

Things to keep in mind:

 - Maybe its CR is a result of playtest.
 - The multiple heads traits is ignored.
 - My calculations of how much hp it loses each round doesn't include the hp regeneration. That would be 77 (232/3), or 3-4 heads dead each round.

My bet is that the hydra is expected to lose more than 2 heads each round, therefor the hydra lose attack power each round, so the Multiple heads is ignored, to some degree.

**Are my calculations correct? How the trait "Multiple heads" is calculated?**