Here is a list of settings which can be adjusted which will effect the battery usage & performance of Sophie's Dice.
Generally, settings which require less battery usage will result in a less quality performance of the app, and vice-versa. The fairness of the dice however, is not effected by any of these settings.

Settings are listed in the order they can have the greatest impact on battery/performance:

• General Tips
• Render Scale
• Quality
• Ambient Occlusion and Motion Blur
• Simulation
• VSync/Frame Rate
• Shaded Dice Fonts

General Tips

The more you ask the app to do, the more battery power it is going to expend - more dice, greater resolution, higher framerates - these will all be a bigger drain on your battery.

The best thing you can do if you want to preserve battery and also have the best experience, is have whichever settings you like the most, and suspend the app when you aren't using it (You don't need to close the app, just turn off the screen or switch to another app).

Render Scale

This graphics setting will change the resolution that 3D elements are rendered and displayed at. It is recommended you reduce it to a point where you are still comfortable reading the dice faces. If your screen has a higher resolution than you can perceive then it is spending time and energy rendering pixels you won't see anyway.

Quality

This changes the overall graphics quality, effecting many things such as texture and shadow detail. Which setting you use is your choice, the app experience is best as Ultra or Very High, but lower quality settings will extend battery life a bit, and may improve framerate.

Ambient Occlusion and Motion Blur

If these options are available to you in the graphics settings, disabling them can greatly imrpove both framerate and battery life, at the expense of less realistic shading and motion.

Simulation

This dice setting determines how detailed the simulation of physics is, "Efficient" will result in better battery usage, but dice may appear to stutter slightly as they roll (even if this happens, the dice remain fair). "Detailed" simulation will usually appear much smoother, but will increase the battery usage of the app.

VSync/Frame Rate

VSync and framerate settings determine how many times per second the 3D scene is rendered - more frames expends more battery power, but will make motion appear smoother. On many mobile devices, "VSync On" will actually result in a framerate much less than the screen can draw - if you want the smoothest possible motion, try disabling VSync and set the Frame Rate to be "Uncapped" or "60fps". These settings are worth increasing if dice motion is a strain on your eyes.

Shaded Dice Fonts

Drawing the dice labels is actually one of the more battery-costly parts of rendering dice, using a simpler shader for them can improve battery usage, readability, and improve frame rate.