that the two methods have no correlation means the two methods are independent. it does not mean one is long the other must be short.
With 2 coins, there are 4 possible outcomes. Of these, 1 outcome has 2 heads. Therefore the probability of this is 1/4 or 25% (rounded) And in this case 60*1/4 or 15% In other word BS strategy
Congratulations you found the holy grail. with 4 systems confirmed with each other, you have 100% losing strategy.
Sorry about that, after I posted I deleted my comment because I didn't want to be nitpicking over a detail, but looks like you've quoted it before that. Just wanted to note it because I forget it and get tripped up sometimes -- the range is from perfect negative correlation, to no correlation, to perfect positive correlation. Anyways, for the thread, you might need to mention if the 2 strategies block each other or not -- is it that there can only be on one trade on at a time, or can both systems place a trade on different instruments at the same time?
Is it me or if I have 3 losing systems with 0.35, 0.40 and 0.45 it gives me a wining rate of 0.72!!! I dont think so. IMO the winning rate is (1/3 * 0.60 + 1/3 * 0.60 +1/3 * 0.60)/3 = 0.60 The sharpe would improve though. The more uncorrelated systems you have the less volatility there will be. The greatest gains being from 1 to 20-30. You can read Ray Dalio of Bridgewater for references. Or this is the reason why Buffet has about 30 stocks in his portfolio.
I guess you misunderstood the problem. The problem is that the trading signal from method A must be confirmed by method B so that the signal is valid.
If you have systems of prob p1 and p2, the combined is 2 * p1 * p2 If you have 3 systems, the combined is 4 * p1 * p2 * p3. I know...you are going to ask why you can get > 1 prob. Well, in that case, the systems are not independent, which is why the solution is nonsense. And if they are all coin flips, then you have a 50% probability.