To determine that a competitor has lost a match, by a referee's enumeration aloud of the increments of time for which the competitor has been incapacitated
The champ was knocked unconscious and counted out in the third round.
If you count out a sum of money, you count the notes or coins as you put them in a pile one by one. Mr. Rohmbauer counted out the money and put it in an envelope
If you tell someone to count you out, you mean that you do not want to be included in an activity. If this is the standard to which I have to drop to gain membership, then count me out! count in