I've done 10 games against the very first mouse in the game, and it seems almost impossible to beat. It always have 15+ total, so you have to get 15+, but doing so has a great chance of busting. In all the game I made, I hit to get over 15 if I don't already have, and I bust. If I would have not hit, I would have lost anyway. If I have 15+, the mouse somehow always have over the amount I had. Am I missing something?

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!