If you run 10 million bets on 1.01x, your average losing streak will be equal to 1 since it can't be equal to 0 by definition and it still can't be greater than 1 plus some small fraction since the chances of winning are pretty high.
Every thing is possible. I myself lost 3 times in a row while the odds was 1.01x.
Is the frequency of outliers normalized to some common denominator (i.e. variance or deviation from the mean) going to be the same for these two multipliers? That's what interests me so much
The number you roll does not depend on the odds and probablity of winning. In the long term, we have statistical distribution.