I got an interesting question this week from a PM this week, asking if we could run an experiment with a traffic allocation of 10% to control and 90% to the variation, rather than a traditional 50–50 split. TL;DR: Probably best to keep it 50–50, since your typical A/B test design involves enough factors to consider already.
Here is a somewhat unconventional recommendation for the design of online experiments:
Set your default parameters for alpha (α) and beta (β) to the same value.
This implies that you incur equal cost from a false positive as from a false negative. I am not suggesting you necessarily use these parameters for every experiment you run, only that you set them as the default. As humans, we are inescapably influenced by default choices1, so it is worthwhile to pick a set of default risk parameters that most closely match the structure of our decision-making.