What R function should we use if we want to decide the sample size for such a test:
10 ads, we want to use a test to decide which ads has the best click through rate. We are able to count the flow and click throughs.
I don’t think the number of variant experiences makes a difference. In each, you compare a metric to the same metric in control, so in each you’ll have its own significant sample size: the smaller the difference with the control, the larger the sample size.
The point of active debate in recent years is something related: how, at run time, to optimize the traffic split between the experiences so that by the time all the variants are called, the most has gone through your winning experience. Google (Experiments) have devised something they call the Multi-Arm Bandid algorithm for that, but as far as I know it hasn't been published in a peer-reviewed journal, and probably for a reason.
Good Luck!