You didn't say you were binary betting! I thought you meant trading.
And yes, in a fixed odds 50-50 (as you might find in a casino) you will not win or lose overall. It is not possible to maintain any win. If you have a trading strategy that has an 'edge' over the market however this obviously works in your favour.
And no there is nothing wrong with a basic moving average. I wouldn't recommend it as a sole strategy but it is better than random guessing. As for it working 100 years ago but not today that is rubbish... look at the huge market crash that has happened, following the MA would have gotten you into that nicely. Also, prior to that, the daily MA was rising steadily along with price. Combine it with proper money management and you'd be surprised what is possible!