It is important to understand that, if your website changes shape to meet different screen sizes (responsive design), you are going to be preferred by Google over your competitor's website (that has not been design responsively).
Here is where I need to add a word of caution: responsive design should consist of several different versions of your website, right? Well I have come across some websites that claim to be responsive but actually only consist of two versions: mobile and desktop. This means that the mobile version just stretches and shrinks accordingly until you reach a point where it goes to the desktop design. This is not true responsive design, it is lazy design and actually does not look good on large mobiles or small tablets.
To summarise: not all responsive websites are the same and I suspect Google will differentiate between the two! In short, your website should be responsive and built properly!
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