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Imagine you are standing in front of a row of slot machines, and wish to gamble. You have a bag full of coins. Your goal is to maximize the return on your investment. The problem is that you don’t know the payout percentages of any of the machines. Each has a, potentially, different expected return.
What is your strategy?
You could select one machine at random, and invest all your coins there, but what happens if you selected a poor payout machine? You could have done better.
You could spread your money out and divide it equally (or randomly) between all the different machines. However, if you did this, you’d spend some time investing in poorer payout machines and ‘wasting’ coins that could have be inserted into better machines. The benefit of this strategy, however, is diversification, and you’d be spreading your risk over many machines; you’re never going to be playing the best machine all the time, but you’re never going to be playing the worst all the time either!
Maybe a hybrid strategy is better? In a hybrid solution you could initially spend some time experimenting to estimate the payouts of the machines then, in an exploitation phase, you could put all your future investment into the best paying machine you’d discovered. The more you research, the more you learn about the machines (getting feedback on their individual payout percentages).
However, what is the optimal hybrid strategy? You could spend a long time researching the machines (increasing your confidence), and the longer you spend, certainly, the more accurate your prediction of the best machine would become. However, if you spend too long on research, you might not have many coins left to properly leverage this knowledge (and you’d have wasted many coins on lots of machines that are poor payers). Conversely, if you spend too short a time on research, your estimate for which is the best machine could be bogus (and if you are unlucky, you could become victim to a streak of ‘good-luck’ from a poor paying machine that tricks you into thinking it’s the best machine).
If you are playing a machine that is “good enough”, is it worth the risk of attempting to see if another machine is “better” (experiments to determine this might not be worth the effort).