Haste makes waste.
Yang Yi believed that Zhang Yong's reluctance to teach him was not due to some principled issue; it was purely out of laziness. Just think, if he really entered prison just to find some peace and quiet—though the idea seems laughable, it's entirely possible—then, of course, he wouldn't want his tranquil life to be disturbed.
Everyone has a weakness, and once you find it, you can exploit it.
When Yang Yi arrived, Danny hadn't told him that Zhang Yong was a gambler. However, seeing Zhang Yong deal cards to himself and play 21 Blackjack, Yang Yi couldn't believe he merely liked playing cards for their own sake.
Are there people who simply enjoy playing cards without the gambling? Yes, there are plenty. But those who like playing cards definitely wouldn't study the game of 21 Blackjack on their own.
So, when Yang Yi saw Zhang Yong playing 21 Blackjack alone, he wanted to use Zhang Yong's hobby to achieve his own goals.