Even if a trader has a high win rate like 60%, the martingale would still eventually wipe out the account. The reason is that for any finite account equity, there is SOME maximum number of times you can double the trade amount before you bankrupt the account. And that string of losses is not as uncommon as people think.
Suppose you have $1000 and you start with a $1 trade. How many times can you lose, doubling the amount of the next trade each time, before running out of funds? Let's see...
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, uh ohhhh!
10 losses in a row and you're done.
But then you think, "But how likely is it that I'll get 10 losses in a row? I have a 60% win rate after all."
Well, let's see. The probability of 10 losses is 0.40 to the tenth power. That's a pretty small number: 0.0000105. That's about 1 time in every 9,500 trades. Or about 9-1/2 1KT traders.: So for every 10 1KT traders who use martingales, chances are, one has gone broke doing it.
Another way to look at is if you're a scalper and do 100 trades a week, you'll go broke about once every 95 weeks, or about once every couple of years.
This isn't exact of course, but it gives a good idea of the realities involved.
Some problems in your math:
1. In your example, you assume the loss will come at the end of the 9,500 trade string. On average, it will come in the middle though!
2. To be able to withstand 9 losses with double-up-and-reverse-style martingale, the expected return on equity will be marginal and not worth the risk.
While you're doing that, I'll go take a trading lesson. You'd probably laugh if you saw some of common things I still mess up. On the martingale, I actually learned about the math behind it because...you guessed it! I lost a bunch of money years ago trying to use it. I finally got so frustrated when I couldn't understand why it didn't work that I sat down and worked it out for myself.