In variants with an ante, instead of each player posting an ante each hand, the player in the Big Blind will post an amount equal to the Big Blind.
For example, with blinds at 500-1,000, the player in the Big Blind will post 1,000 for his/her Big Blind, followed by 1,000 for the Ante. His/Her total contribution to that pot is 2,000. The Ante (1,000) is dead and is immediately brought into the pot. The Big Blind (the other 1,000) is live and is part of the pre-flop betting.
If a player in the tournament does not have the required amount for both the Big Blind and the Ante, the Big Blind will be paid first, followed by the ante.
No matter how many chips a participant starts with he/she can always win the entire ante. For example: the blinds are 4k/8k and the big blind also antes 8k. A participant who is not in the blinds who starts the hand with only 1k gets involved in a three-way pot against the blinds. If that participant wins, he/she wins 11k (his/her own 1k wager, plus 1k from each opponent, plus the 8k ante). In this scenario, 1 chip can win 11 chips.