I do not know if the house edge is the same for all games or not, but I know that how many times you lost in a row has nothing to do with house edge for sure. The idea is that if you are in a situation where you are dealing with gambling, house edge could be 1% or 10% and the result won't change.

I mean the result won't change in the sense that you will not have a win or lose depending on the house edge, of course you will have a different profit or loss, like win 99 but lose 100 type of result is depending on the house edge but when it comes down to win or lose outcome that has nothing to do with the house edge. Which means if you were gambling on 50% to win, that could happen, you could lose 20+ times in a row as well, that happens more than people realize, it is of course rare in the sense that you do not have it per hour, but it is still quite possible if you gamble 10k+ times.