It is actually pretty easy to double your starting bankroll if you use 2x. No matter with what amount you start, the chance to double up will be aroung 50% - the houseedge you are betting with.
On the other hand. If you have unlimited funds, its impossible to double them. because you can't double unlimited founds per definition
On the other hand. If you have unlimited funds, its impossible to double them. because you can't double unlimited founds per definition
Let's say you start with 1 BTC, and you're going at 2x. It will depend on how much you're risking. Let's say you want to risk:
1 BTC at 0.00001 BTC starting (2x on loss) = you can lose 13x in a row. it will take 100000 wins before getting to doubled up (which is around 200000 rolls). Essentially you're dealing with (tl;dr version):
Won amount per win: 0.001%
Chance to lose 13x in a row: 0.00179%
You're statistically going to bust 1.8x for every 1x you double up, giving a 35% or so chance of making it happen.
Let's say you decide to risk 0.001 BTC per roll instead. Now you can lose up to 8x in a row. This puts the stats at:
Won amount per win: 0.1%
Chance to lose 8x in a row: 0.2136%
Now you're statistically over 2x more likely to bust than to double up, leading to a 30% or so chance of success.
If we did just one satoshi, you're at a 1.93:1 odd of busting before doubling up (with a 25x fail streak required).
Edit: someone check this and make sure I'm calculating the odds right? This is how I inferred how you'd figure out the true odds. I may be wrong on that...?