Split Testing and Optimization Techniques

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For example we have 5 landing pages, running under the same URL, being served randomly based on their weightage.

What I want is to check which page is converting more and increase it's weightage automatically so that it get served more.

This is the simple explanation of my problem. Is there any standard algorithms and techniques available to achieve this. What I don't want is to reinvent the wheel.

Thanks.

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I would do something very simple such as keeping a running count of how many times a landing page was converted. After that you have a variety of choices:

a) Sort them by hit count and serve the top one(s)
b) Serve the pages in a fashion weighted by the number of hits. For example, you could serve the pages based on a probability distribution derived from the hit count (e.g. if you have two landing pages and page A is hit twice more than page B, you serve page A twice as often as page B). Tweaking the function will allow to control the relative rates at which different pages are served.

However, this begs a question: if a user returns twice to your site, will they get a different page? If so, wouldn't that be confusing?