user expectation - Arranging menu or buttons in Mobile apps

if we can figure out by which hand user is using his phone so that we could arrange the menu items or buttons to the convenient side.

I think if a user is using his phone by right hand then the convenient side could be middle and left side and vice versa in case using by left hand.

If the phone screens are receptive enough to understand user finger prints then we can figure out that way. What do you think?

Answer

Addition to @Noah's post:

The way in which users hold their phone is not a static state. Users change the way they’re holding their phone very often—sometimes every few seconds. And changing the content dynamically will be dangerous to your application.

Here are some key statistics from a study performed on this topic:

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The 49% of users who use just one hand typically hold their phone in a variety of position

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Cradling is my term for using two hands to hold a mobile phone, but using only one hand to touch the screen or buttons.

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We traditionally associate two-handed use with typing on the QWERTY thumbboards of devices like the classic Blackberry or on slide-out keyboards.