let's say I have 10btc. what are the chance of me losing it all if I do a martingale with 10satoshi?
I believe 23 losses in a row is your risk, and reward is 10 satoshi, 20 losses is your risk if you wish reward to be 100 satoshi.
Assuming 50/50 which its not because its usually something like 49/51 favouring dealer... the chances of losing 20 in a row on a coin flip:
1 in 2,097,152 (so ~ 1 in 2055208.96 million taking into account 2% dealer edge)..
In general, whatever the odds are of you getting bankrupt, are also the number of tries you need to make to double up. Therefore, at any point in time along the curve of getting through to fulfill every attempt you can go bankrupt, but you can ONLY double up if you complete the sequence 100%, therefore the negative expectancy and failing system.
Actually, the number of wins you need is GREATER than the chance of loss. Even if your example, you say it has a ~1/2m chance. 2m*10=20m=0.2 BTC. He'd then need 50x that to get a double up, or 100m wins (100m*10=10 BTC). The chance of busting is therefore MUCH higher than doubling up.