Lottery with free tickets to another lottery. Calculate EV?

[AA Suited]

Scenario 1:

Lottery A:
Chances of winning are 1:550k
Price: $1/ticket
Current prize $400k
Promo- But 5 Lottery A tix, get 1 free lottery B tix

Lottery B:
Chances of winning are 1:150k
Price: $1/ticket
Current prize: $150k


Scenario 2:

Lottery A:
Chances of winning are 1:550k
Price: $1/ticket
Current prize $550k
Promo- But 5 Lottery A tix, get 1 free lottery B tix

Lottery B:
Chances of winning are 1:150k
Price: $1/ticket
Current prize: $300k


In both scenarios, I think Lottery B is more +EV, but i cant do the math to prove it.

Am i right? If so, how do you do the math to figure it out?