TCP is one of the main transmission protocols used in the Internet. It has also been recently observed that opening parallel TCP sessions might be of interest for a user in order to increase his overall average throughput. We suggest in this paper to charge users per TCP session, and we investigate the resulting game in a homogeneous context: how many sessions should each user open? Given the discrete (and even finite) space of strategies, we propose to implement a probabilistic adaptation algorithm, analyze its theoretical properties and provide numerical illustrations.