i think martingaling leads to bust eventually. the house edge will eventually kick in
This is true. I've also attempted to "exploit" the system by using rounding errors for a bigger edge. Out of many trials, it still fails (what I mean by rounding errors is, for example, finding a sweet number spot where you will actually get slightly more from a win than you should because, for example, you get 1.5 coins instead of 1, which rounds up to a win of 2). Even so, the house always picks up eventually and dominates it.
Even without a house edge, you do not have an unlimited bankroll and you will eventually bust
Theoretically. The house edge will always make a difference, though, as it means out of 100 rolls, you should only get, say 48 wins, rather than 50. This means you will bust much faster than without one. The theory remains the same, yes, but the house edge decreases the chances of hitting your goal significantly.
There's an interesting question you've missed. The house also doesn't have unlimited bankroll.
Question is: Should the house have at least the same size of bankroll as you, for the chances to bust you to be in the house favor? Assuming 0 house edge, of course.