Well, if you don't have $1m then the house needs to be leveraged too. Interactive Brokers[0] has margin rates lower than my mortgage. I don't think they'd give you the 10x leverage that you can get on a house though.
I did not do the math, but it seems like you’d need to simulate a stochastic process to come out with the likelihood of winning in this scenario, similar to the various FIRE calculators out there [0].