Is Birthday Draw rates better?

So i want to get myself a 4/5 star Tsugu card and is saving up for when her birthday draw comes around (January 7th). Is the chances on these sort of draws better odds to get a high rarity Tsugu?

Any extra steps i can take to increase my chances?

So i want to get myself a 4/5 star Tsugu card and is saving up for when her birthday draw comes around (January 7th). Is the chances on these sort of draws better odds to get a high rarity Tsugu?

Any extra steps i can take to increase my chances?