How did you manage to convince yourself that such a risk is the correct decision and the right strategy?
By having statistics that prove it is: I don't trade any strategy without statistically significant evidence that it has a positive net expectancy. So my answer to the question boils down to "I let the evidence convince me", I think.
Clearly, every time I enter a trade, I have little idea whether it's going to be a winning or losing trade, but I know with a
very high degree of probability that my next 300 trades,
collectively, are going to have a positive expectancy, and that's good enough for me. Then all I need to do is calculate position-sizing appropriate for things to go as badly as they can (and allow an error factor in case they go even worse than that, because I'm really conservative about position-sizing), and trade the set-ups as and when they arise.
I realise that this makes it sound really easy, and of course it really isn't: statistics and probability are pretty counter-intuitive subjects, and there's quite some learning-curve to working out how to do all that reliably; but once you're very familiar with that, it does then become relatively simple, mundane and even pretty boring, sometimes.