Python: Randomly split a data frame in half and assign value in a new column

I have a list of Ids (device Ids) in a DataFrame. I want to assign randomly A or B to each one of these devices (split them into two halfs):

Assume we have a DataFrame named devices with a column "DeviceId" and 9364957 rows.

Option 1:

def coin():
    p = 0.5

    r = np.random.random()
    return 'B' if r > p else 'A'


devices['Experiment'] = pd.DataFrame( [coin() for i in range(devices.shape[0])])

g = devices.groupby(['Experiment']).agg(['count'])
print(g.head(10))

Output :

Experiment
A 4681923

B 4683034

there are 1,111 entries more in A than in B!

Option 2: (i got stuck :()

A = devices.sample(frac=0.5, replace=False)
print('\tselect as A: ', A.shape[0])

select as A: 4682478

in a simple calculation this is much better split because this way B will get 4682479 (the delta between both is exactly 1)

But how can i proceed from here?

My target is to get an updated DataFrame devices with two columns: DeviceId , Experiment (which is either "A" or "B"