Cheddarousse's stats are that he only hits to 12 (which is pretty much any two cards) which means he can never go bust, in exchange you only have to beat his initial draw
Pick a somewhat low bet (the slider before hitting the deal button) and focus on not going bust yourself, I'd say hold on anything 15+ unless he has a 10/A card face up. Remember that the most abundant cards in the deck are '10' cards so a good chunk of his hands will just be his face-up card + 8/9/10/A. There's still plenty of other cards though so you just have to wait for good opportunities
Failing that you can always try to brute force the fight with large bets or keep restarting to get Albert (dhampir guy) as your first fight, but I believe you can do it!