Starting from today, everyday your chances of winning $1 billion increase by 0.005%.
That wording 100% says to me that you get a try every day to win the billion. Looking at it like you would in a legal case, it stands as an every day chance since a year timeframe was never mentioned in the original prompt.
Sure, the million would be nice, but In today's economy "cheap" houses that used to be 100-200k near me are going for nearly half a mil.
The billion is the clear answer to me. Short of some extremely bad luck, you're getting that billion in a year or few. You gain 1.825% per year which doesn't seem like much, but you're getting that ~2% chance every single day.
A few years of living like I already am for a statistically guaranteed (but unpredictable) billion dollars is a win to me.