I don't wish to engage in standard HN negativity, but I'd like to suggest that you should probably don't want to use a carousel at all most of the time. From the user's perspective, a carousel is just a random image. You'll get more conversions if you choose the best image instead of a random one. http://www.bayesianwitch.com/blog/2014/carouselsarebadforcon...
The maths looks wrong; the distribution of clicks is only relevant if the total number of clicks stays the same. Essentially a carousel gives you a "second-bite" at your customer, i.e. the second image is a chance to convert those customers who haven't already been converted by the first image. Imagine you have two images one which converts at 40% and one which converts at 20% - but each image converts completely dif…
In an ideal world, what you should do instead is parametric optimization of some sort instead of a carousel - so you can hit that other 20%