A counting-out game

People are standing in a circle.
Counting begins at a person in the circle and proceeds around clockwise. The player who is selected at the conclusion of the rhyme is out.
The count starts with the next person.

Four children stand in a circle in the following order: Alex, Betty, Craig, and Diana.

If the count-out game starts from Alex, who will win the game?

They use the most common English rhyme:

Tinker, Tailor,
Soldier, Sailor,
Rich Man, Poor Man,
Beggar Man, Thief.