For the love of god, add a priority system.

[ICountFrom0]

That way if you didn't get picked for housing one week, then you get placed in a pool of higher priority for the next week. That way if you KEEP losing the lottery, EVENTUALLY THROUGH ENOUGH SUFFERING, you will EVENTUALLY be guaranteed a house.

So you think you should have a better chance then anybody else? That's not how fair systems work. Either everybody has exactly the same odds, or it isn't fair.