This is an extremely flawed initial assumption. There is no requirement for chance to be centered around zero. Consider rolling a dice: sometimes you'll get more than the mean, sometimes less, but you'll never roll a negative number. You can certainly win on chance in the long run, that's the foundation of casinos and insurance companies. It's hard to imagine a scenario where trial and error can possibly lead to knowledge regressing.
Consider randomly digging holes in the ground: after enough holes you will eventually strike gold, and you will never lose physical gold in the process. However, you may lose significant time, wealth, and effort that could have been better converted to gold. The optimal way to strike gold is not to dig more, shallower holes, but to learn enough geology to understand where gold is likely to be found and concentrate your prospecting there.
No experiment could ever possibly hurt scientific knowledge. People tinkering will certainly make occasional discoveries. In a brand new field with a lot of low hanging fruit, these discoveries will be numerous and the cost will be low. But in a developed field where people have a good idea where the remaining discoveries are likely to be found and the effort to conduct such experiments is substantial, targeted approaches become optimal. Reducing the unit cost of experiments is always nice, but is not generally feasible. This strategy of "convexity" is a very poor substitute in the real world for understanding.