The problem with your calculation it assumes that people who are likely to get converted by the first image wait around for the second image and get "unconverted".
A good intuitive way to think about it is this: if you're only showing the second carousel image to people who the first image failed to convert then there's zero down-side.
In practice there are some users who would convert if shown the first image for longer who you'll lose by rotating to another image, but that's what you need to measure to decide if it's worth having a carousel.
Re:Slick – Carousel
by yummyfajitas on Tuesday April 01, 2014 @01:22PM
(#7509962)
30% is avg of 20% and 40%. Its the conversion rate of a random person who doesn't stick around long enough to see the second image.
I don't think we really disagree - you should test the carousel, and cases where it wins will be edge cases usually.
It is totally possible that there are edge cases where we are wrong. While we’ve personally performed split tests between carousels and their elements and always came up with an individual slide (rather than the whole carousel) as the highest revenue generating source, it is possible that there will be some cases where a carousel is better for conversions.
To go with your example, assuming each group has 50%, it's still tough. The actual conversion rate of the carousel in your example will be T x 60% + (1-T) x 30%, where T is the fraction of users who actually wait for the second image. Some simple algebra suggests that for this to exceed 40%, you'll need T > 1/3.