# Randomization in Experiment Design

I have seen two ways to conduct randomization in an experiment. I am confused about the difference between them and which one is the correct one.

Assume we have an even number of subjects (say 20).

Method 1. let each subject flip a coin, if it is Head, then go to group A, otherwise, go to group B. This procedure stops until one group has 10 people, then the rest subjects who haven't flip the coin, all go to the other group.

This method will guarantee that each group will have exactly the same number of people. Think about the extreme case, when n = 2

Method 2. let all subjects flip a coin, if it is Head, then go to group A, otherwise, go to group B.

This method will very likely result in the case that group A and B do not have same number of subjects.

Which method is the correct randomization in experiment? And why the other method is wrong?

My hunch is that the Method 2 is correct, but I don't know what's wrong with Method 1. Especially, if n=2 (for theoretical purpose), then I would favor Method 1.

My idea is the following: in order to claim causality in the end, we have to make sure that each subject has same probability of being assigned to group A and B. The Method 2 can guarantee this. However, the situation for Method 1 is tricky. Namely, before the first guy has flipped the coin in Method 1, it is indeed that all subjects have same probability of being assigned to Group A and B. However, once the first guy has flipped the coin and is assigned to one group, say Group A, then the last guy's chance of being assigned to Group A is less than the chance of being assigned to Group B.