When I play tanks, I like to choose champions which have a lot of health and can do tons of damage. And can dive towers. So Shyvana was a good pick. I thought her basic abilities were awesome, but when you hit level 6 and activate that rawr, her abilities become awesomer. Shyvana just snowballs, and you'll have a fun time whilst getting tankier.

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Exhaust:
Once you reach level 6, you should have no worries in chasing down enemies and finishing them off, since Shyvana's dragon decent/ulti is a gap closer. However, during early game, you do not have the skill yet, and so exhaust will allow you to burst all your abilities without letting the enemy escape. Also, you can use exhaust in combination with dragon decent once you pass level 6, either to cover greater ground or to secure the kill/assist allies.

Ghost:
Can be switched out with flash, but Shyvana's ulti does have a similar effect to flash.

Ignite:
Ignite can be chosen not only to compliment the whole fire theme of the half-dragon, but also to finish off enemy champions without running the risk of diving.

For this build, the priorities are:
1) Burnout
2) Flame Breath
3) Twin Bite
(Level up Dragon's Decent at level 6, 11, 16 - as you do for the ulti)

Burnout:
Leveling up Burnout allows you to farm more easily early game. It also creates a semi-barrier between you and enemy champions, since it would deal some 'harass' if they try to get near you. Leveling it up faster also allows you to pick up red buff more easily.

Flame Breath:
Flame Breath is a skill shot, and so would be more viable to learn second rather than first. (This is because if you miss the shot, you miss your chance of dealing any damage at all - whereas Burnout allows you to get off a bit of damage even if you have to walk closer to enemy champions.)

Twin Bite:
I choose to level Twin Bite after level 6/learning Dragon's Decent, due to the fact it seems more effective once the ulti has been activated. Twin Bite also works well with an Ionic Spark (which is bought in mid/late game) and so it can be leveled up later.

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