There's a comprehensive question on UX about touchscreen button sizes. The recommended size depends highly on your game, but the minimum size is quoted as 9-12mm, about half an inch, and this is based on the size of fingers.
Keep in mind that this is a guideline, and the cost of ignoring it is that your users will tap the wrong thing on occasion.
Depending on your game, you may need to go bigger - sometimes much bigger - than this minimum guideline. Here are some factors that will affect accuracy:
- Do you need to tap quickly? Faster means less accurate
- Will players use their thumbs? Less accurate
- Is your demographic experienced gamers or younger? They may have above-average accuracy
- Will your touch zones be right next to each other or have gaps in between? Gaps make it easier to use
You may also decide to accept a certain amount of input errors, as long as you make it easy for your players to correct themselves. Consider:
- Allowing players to adjust their input after the initial tap
- Add a "confirm" step
- Add an "undo" function
- Add clear feedback during the input to show what the game thinks the input will be
- Reduce the impact of errors