Unless it is some risk free arb, but most trading edges cant be mathematically proven like a roulette wheel. You can find an edge by backtesting a strategy. However there is no certainty the edge will hold up going forward. We just hope it will hold up. You have try to lots of strategies, many will look promising, but most will fail when forward tested. If you are lucky you might find an edge that continues to work in forward trading for many years. And bet big while the sun shines.
1. Don't need. As long as you are profitable, it probably means you have an edge 2. Go learn very hard from trading coaches, books.... Then decontaminate / cleanse your mind, and develop your own holy grail. Go do demo trading and practice very very hard.
1. Math is not the only area where you can have an edge. Edge in trade comes from all areas, superior choice of instruments, better assessment of the direction of trend and strength of the trend, the timing of the trade, just to name a few. 2. Studying the chart, studying the price action, researching about the security and the industry, learning about the market, demo trading and backtesting and etc.
Agree with those who have mentioned that it is an edge to have developed a method with positive expectancy in backtesting. I repeatedly backtest new TA-based ideas in ways that sound something like the following: “If the current candlestick has this particular structure, and my chart indicators are showing these specific levels or slopes or patterns, and I place a buy stop order X ticks above the high of the current candle, and at the same time enter a stop-loss price that is Y times the current average true range (ATR) below that entry price, and I also enter a target price that is Z ticks or points above the entry price based on rules designed for that, and trail my stop-loss using a particular method as the trade moves in my favor, and I test every occurrence of this signal on daily charts for the past 5 years, what was the net profit, win%, profit factor, maximum drawdown, net profit-to-max drawdown ratio, max consecutive losses, etc.?” If the numbers are weak, analyze potential improvements and adjust the rules and do the test again. If the numbers are good, then do the test with daily charts again using a different time span to test consistency, and then test other markets that I trade to see if it works in them too. A good system is defined as one that consistently has a win rate of approx. 50% or higher and profit factor near or above 2.0. Other performance metrics are usually acceptable if these two conditions are met. The edge here is that strategies are being traded that were strongly profitable in multiple backtests. Of course there are no guarantees they will continue to work well on future data, though…
Well take ten minutes and do that and see how it works out. Might have to add a few filters to icrease your odds.