In the Arms and Equipment Guide a young, untrained wyvern costs 3,000 GP. It costs another 3,000 GP to, instead, buy one that's trained. I want to train it myself. How do I do this? How much freedom will I have to determine the wyvern's feats? How loyal will this wyvern be?
[RPG] How to train a wyvern
dnd-3.5emount
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[The following is based on my experiences in 3.5e, but from what I know about Pathfinder it should be trivially adapted. Also, I apologize in advance for what I'm certain will be a post filled with incorrect terminology -- I've been playing 4e for quite some time now, and it's been even longer since I last sat down with 3.5e.]
If you think Diplomacy is broken at level 5, just wait until you get to the Epic levels! This is where we were when my DM decided to address it.
They way he approached it was to completely ditch the static DC list -- static DCs make sense for climbing ladders (which don't typically get harder as you get higher in level), but they don't make sense at all when you're dealing with more and more experienced and powerful individuals; just like AC and other such things, as the CR goes up so, too, must the DC.
So he sat down and took the table of Diplomacy skill DCs and turned them into situational modifiers. I think he started with "Neutral" granting a +4 (reasoning being that changing people's minds is not easy, even if they don't dislike/distrust you), and then each step toward Hostile added an additional +2, while each step toward Friendly added a -2.
The resulting modifier was then used on the NPC's own opposed Diplomacy roll. Thus the table of Diplomacy DCs that is so trivial for PCs to game was gone, replaced by opposed checks to modify a character's attitude.
But he went even further. Between each stage on the "trust continuum" (i.e. Friendly, Neutral, Hostile, etc.), the DM added a "half step"; a successful Diplomacy check would move the NPC's attitude half a step, not a full step, thus requiring 2 successes to effect a change in the character's attitude. (When an NPC is on one of these "half steps", his/her attitude is the one "rounded" toward neutral; thus an NPC is effectively Neutral across 3 distinct "steps", but 2 "steps" for all others.)
Finally, he added one more thing: Continued successful/failed checks could move an NPC further than the ends of the "attitude spectrum", although no further mechanical advantages were earned. What it did do was make it less likely for the NPC's attitude to be changed later, by simply keeping track of how many "steps" would need to be adjusted.
These were the mechanical changes he house-ruled into Diplomacy. He also required certain role-play elements to also be met before a Diplomacy check could even be attempted -- the Halfling Bard walking up to the dragon and rolling an impressive 34 Diplomacy is just wasted effort if said dragon isn't even listening! There were also common-sense limitations imposed: a dragon who's entire life is centered around accumulating his horde is not going to just give it up, no matter how many Diplomacy successes the Bard accumulates!
Giant in the Playground's Increasing Size, Effective Size, Unarmed Damage, Reach thread is of some limited utility.
Minmaxboard's Grappling Handbook, Hulkamania is runnin' wild, is of somewhat more use.
From your current position, I suggest the following.
Option 1: Sorcerer
No, really. Enlarge Person as a spell gives you +5 to your grapple modifier. It comes in a cheap wand at your level. Babau Slime increases your grapple damage with a bunch of acid (scales with caster level, buy a higher CL wand). Fearsome Grapple is a level 2 spell, so 4500gp, i.e. 'you can afford it', and adds +4 to your grapple mod. Another level 2 is Balor Nimbus, 6d6 to anyone grappling you per round. Corrosive Grasp creates multiple touch attacks, so you do normal grapple damage and it sets off the touch attack for +1d8 acid each time. Fist of Stone gives +6 enh to strength and a natural slam attack, but only for a minute. Of course, timing all this short-duration buffing requires an ambush on your part, so why not buy a wand of Chameleon to help hide, or Invisibility for sneaking around.
You'll also have an Octopus familiar from Stormwrack, for another +3 to grappling.
Sorcerer avoids having to make use magic device checks to use the wands - if you have a friendly arcane caster willing to sneak along with you and buff you for your grappling ambush, then you can forgo this option entirely.
Option 2: Warblade
Non Tome of Battle classes count as half initiator level for determining eligibility for maneuvers. So a level in Warblade with your 11 other levels counts as a 6th level Warblade, meaning you can select 3rd level maneuvers. A 3rd level maneuver (it's a stance) is Crushing Weight of the Mountain. It gives you the Constrict ability. Other than a Soulmeld, this is one of very few ways to get Constrict in the game without changing shape. Constrict is amazing, because ANY TIME YOU ROLL A GRAPPLE CHECK, even to /enter/ a grapple, to do unarmed damage, when they try to escape, WHATEVER, you get to do Constrict damage. Yes, in addition to your unarmed strike, yes, in addition to entering the grapple damage, yes every time they try to escape. You just squeeze the life right out of them. Crusader provides a better chassis, and also has Crushing Weight of the Mountain, but warblade has access to Iron Heart Surge which is very barbarian.
Option 3: Totemist
At level 2 in Totemist from Magic of Incarnum, you grow an extra pair of arms and add your essentia x 2 + 4 to your grapple mod. At this level, with the Expanded Soulmeld Capacity (Totem) feat, that's +12 to grapple. Also grants extra natural attacks from the arm, and other stuff from other soulmelds (short-range teleport, Spell Resistance, Natural Armour, Fire Resistance, etc).
Doesn't really do much for you this level, though. A good choice to take after you've dipped the low-hanging fruits in Warblade and/or Sorcerer.
Feat: Scorpion's Grasp
From Sandstorm, this feat lets you basically have improved grab for unarmed strikes and one-handed weapon attacks. It lets you punch someone, grab them, succeed on a grapple attempt, punch them again, and still have the rest of your actions free to punch people. The best part of Improved Grab, however, which is grappling at a -20 to count as not grappled and building a big ball of weak enemies that you carry around with you and use as a melee weapon, is sadly absent.
Feat: Snatch
Requires claws or bite, MMII. Gives Improved Grab, and the ability to fling creatures 3 sizes smaller than you far, far away. Totally awesome.
Feat: Open Lesser Chakra (Arms)
Combined with a level in Totemist to get access to Kraken Mantle, binding the Mantle to your newly opened Arms slot will give you +2 to grapple per Essentia placed in (max 3, for +6 to grapple untyped).
Item: Gloves of Titan's Grip
From MiC, 3/day activate to get +8 Enhancement to Grapple for 7 rounds. Strength boosts are usually enhancement, but nothing really enhancements grapple except Grip of Iron, so this is great. Totally great. Buy it.
Item: Scorpion Claws
From Sandstorm. Exotic weapon that grants +4 to grapple checks. Well worth it, possibly even if you're not proficient.
Notes
Scaled Horror prestige class from Savage Species requires the 'Aquatic' or 'Reptilian' subtypes. You could make an argument that as a Dragon Disciple, you're kind of doing that. If so, it picks up Improved Grab at first level. Warblade -> Scaled Horror would be a great power boost.
Black Blood Cultist from Champions of Ruin is normally great for grapplers, but you're too high level and it overlaps with Dragon Disciple, also your alignment is wrong. Avoid it entirely.
Psychic Warrior is a great class for grapplers, but at this level you get too little benefit and too few power points to be of any use. The two key powers are Grip of Iron and Expansion, but they both want Augmentation to be great. There are more Wizard/Sorc spells that benefit grappling than there are powers, so even if you grabbed some Dorjes, it wouldn't be as worth it as a Sorc dip. Check the second link for more spells/powers that help out grappling.
Aberration Blood - This feat sets you up for Inhuman Reach, a natural reach increaser. It also adds +2 to grapples. At this level, it's probably sub-par.
Best Answer
TL;DR
In dnd-3.5e riders needn't bother training most intelligent creatures that can serve as mounts.1 Instead, a rider makes Diplomacy skill checks to negotiate with the intelligent mount about what the mount will do while the rider's aboard. An intelligent mount's loyalty is gained through role-playing as one would gain the loyalty of any NPC. And, as an NPC, an intelligent mount has whatever feats the DM gives it.
Training a wyvern
The Arms and Equipment Guide is a dnd-3e source, and some of its information on mounts is superseded by the Dungeon Master's Guide for dnd-3.5e. That Dungeon Master's Guide on Intelligent Mounts says
Following the rules for the skill Handle Animal, a trainer takes 3 hours each day for an uninterrupted 3 weeks then makes a Handle Animal skill check to train the wyvern for the general purpose combat riding (DC 67). Success means that if the trainer takes another 3 hours each day for another uninterrupted 3 weeks that the wyvern will gain the general purpose combat riding. Failure means that the trainer must start anew if a trained wyvern is still desired.
Let me explain that DC 67. According to the Player's Handbook, Dungeon Master's Guide, and Monster Manual, there's really no way to train a wyvern. The Dungeon Master's Guide would have a dude—a really persuasive dude—convince a wyvern to serve as his mount then, despite the absence of rules for doing so, have that same dude and wyvern train together… never explaining what that means.
So, if a trainer lacks the feat Dragon Trainer (Races of the Dragon 98-9)—which makes this DC 20—, a trainer must resort to the Epic Level Handbook's rules for Handle Animal (41), which set the DC for "[t]rain other creature" to 60 plus the creature's Hit Dice. And, while those rules are included in the System Resource Document, they weren't updated by the 3.5 revision.
(Further, the Epic Level Handbook sets the time required to train the other creature to 2 months, which a DM may fairly rule increases the time it takes to train a wyvern for the purpose combat riding to one year. That is, it normally takes 1 week to teach a creature a trick but 2 months an other creature… so if every week is instead 2 months, 6 weeks for the general purpose combat riding works out to a modified 12 months. In my experience, rarely does an adventurer enjoy this amount of time off.)
What training a wyvern yields
The Dungeon Master's Guide is unclear on why exactly a wyvern mount must be trained. The Rules of the Game Web Column "All about Mounts, Part Five" on Intelligent Mounts says
It's 5 or higher, but we'll let that slide… and, anyway, I tend to agree with Williams here: the cutoff shouldn't be Intelligence 5 or higher as per the DMG but 3 or higher, the cutoff between just instinct and what we consider intelligence. Anyway, so you know, "All about Mounts, Part 2" on "Aggressive Mounts in a Battle" says
On Intelligent Mounts continues, saying
(Emphasis mine. Note that I reference the Rules of the Game articles here—despite controversy—because other information on mounts is largely unavailable in the dnd-3.5e corpus. While dnd-3e tended to treat even intelligent mounts like uncomfortably acquiescent slaves, dnd-3.5e's more nuanced view tends to treat intelligent mounts like the intelligent and independent creatures they are, and this series of articles in the only place I've found that details the mechanics of that relationship.)
So, in short, after spending 6 weeks to a year training the wyvern for combat riding, it seems as if the wyvern still keeps its limited wits about it and still tends to do what it wants unless its rider convinces it otherwise, making training an intelligent mount at all, ultimately, a pointless exercise.
The wyvern's loyalty
The wyvern is an NPC. A rider that wishes to earn its loyalty earns it the same way she would any other NPC's loyalty—a sheep costs 2 gp (PH 112)—, and rearing a baby wyvern from infancy will probably make it more loyal than normal. Exactly how the wyvern reacts to the rider's overtures is up to the DM.
The wyvern's feats
As an NPC, the DM designs the creature, picking its feats and skills and, if it possesses the nonelite or elite arrays, assigning its ability scores. If it gains class levels, the DM picks those, too. A creature that raises a wyvern typically has no say in the wyvern's choices.
1 The Intelligence 10 giant eagle (Monster Manual 93), Intelligence 5 griffon (139-40), Intelligence 6 howler (Int 6) (154-5), Intelligence 10 giant owl (205), and Intelligence 10 pegasus all require training before they'll bear a rider into combat. What happens when a rider tries to ride them into combat anyway is unclear, but I suspect they—through no fault of their own—behave like Aggressive Mounts in a Battle (see above).
You may also be interested in this question about quickly training creatures, this question about training nonanimals that possess Intelligence scores of 1 or 2, and this pathfinder question that discusses for dnd-3.5e the history of the difference between domesticated and nondomesticated animals.