This is absolutely incorrect, as seen here:
1 1
2 3
3 7
4 15
5 31
6 63
7 127
8 255
9 511
10 1023
11 2047
12 4095
13 8191
14 16383
15 32767
16 65535
17 131071
18 262143
19 524287
20 1048575
21 2097151
22 4194303
23 8388607
24 16777215
23 losses = almost 1 BTC.
*****
At some point you're going to hit that cap, and statistically it will be long before you've doubled up your money.
And i have seen worst systems, i saw once a guy doing a 10x martingale, this means, betting first 1 satoshi at 90% if he lose then 10 satoshis, then 100 satoshis etc, of course he lost 0.5 btc in seconds.
I've run it all the way down to playing at 98% odds. It never works because the house always wins.