All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the games that you play with your cousin are free from religious prohibitions, like looking at the ‘Awrah and the like, and it does not distract you from Islamic obligations, like the prayer and the like, and it entertains and amuses you, then it is permissible for you to play it but it is not permissible to compete in it, not because it is gambling, but because of the invalidity of the contract in such a case.
Shaykh Zakariyyah Al-Ansaari (from the Shaafi’i School of jurisprudence) said: “If one of the competitors stipulates the money for the winner, i.e. to give it if he was the loser and keep it if he was the winner, or that another person than them stipulates that, then this is not gambling; rather, it is an invalid competition because it is a competition in other than tools of war. However, it is forbidden as well because it is like conducting invalid contracts.”
As regards his (your cousin’s) statement to you "if you drink a whole bottle of lemonade I will give you 10", then this is also a void fun and a void play and it is spending money on useless matters, therefore, it is forbidden in the Sharee’ah.
Allaah Knows best.