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we have a website and will be trying out showing a user one of three different homepages at random which then stores a cookie on their machine and shows them the same page for 24 hours.
The pages will be quite different from each other, can any one see any issues Google may have with this, and if so are there any solutions?
this probably won't cause any cloaking-related issues since the behavior is not based on user agent.
the googlebot won't store a cookie but it probably won't make multiple homepage url requests within 24 hours either.
not sure what the seo issues would be with multiple pages for a url request and it probably also depends on whether this is an internal rewrite or external redirect.
if it is external you should also consider canonicalization issues.
One idea to avoid changing the content of the page is to present the different content in an IFrame, and once the user likes it store the cookie and present the formatted page. After all, robots don't store cookies (at least till today).
Of course this depends on how large is the different part. If it is too large IFrames won't be a practical solution.