You've explained it well, I only disagree with your last sentence. I think the chance of winning is absolutely the same either with martingale or betting with 1.1x multiplier. With this particular multiplier you have 10%+ chances of losing your whole balance right away, with the very first bet, even on a site with the smallest house edge.
You are right. I calculated the chance of winning in both cases.
Let's say I have 1 BTC and I want to convert it to 1.1 BTC.
If I put the whole 1 BTC is a single bet with multiplier of 1.1, my chance of winning would be 86.36%.
If I use martingale method and set the base bet to 0.001 mBTC, the chance of converting the 1 BTC to 1.1 BTC would be:
(1 - 0.525
10)
100 = 0.852 = 85.3%