How many samples do I need for OCR problems? I am thinking about collecting samples of hand written digits (0 to 9) from people. I'll try to test different algorithms for optimal character recognition- some form of neural network and random forest may be! I have planned to collect 20 entries from each person (the same digit being asked to write twice) so that I can make a training set and a test set. 
Is my idea correct? How should I statistically decide how many samples will suffice?   
 A: Overall suggestion: 
There are many open data sources for digit OCR available, have you checked about MNIST? Also, there are works done for algorithm comparison as you described in the same line I provided. Please check it first.
If you want to do the same thing, why? Is there anything the MNIST doesn't offer? If there are some, I am sure you can find other open data online. Such as this one. 
Collecting data by yourself is very costly and it is better to have a good reason to do it.

To your question:
It is hard to say how many data are needed. It depends on your model and the complexity of the "task". Finally the quality of the data.


*

*For example, if you want to use a complex model (neural network), it is better to have hundreds of thousands data points. On the other hand, it is a simpler model (say, logistic regression), less data is required.

*For example, if you want to build a classifier to classify 0 vs 1, then it is a relative simple task (comparing to classify 0 and 6), and less data will be needed. 

*In addition, if the quality of data is low, say all the digits are blur or have low resolution, then, more data are needed.
