Cheddarousse holds at 12, so he'll never bust out but he'll also often have really pathetic hand. Moderate your aggression and he'll usually hit just under you
(Or just max your bet every round against him, since if you lose you just restart at him or rarely Albert)
Been a while so I'm not entirely sure, but I think each hand is compared to the opponent's hands individually and the result is summed. One winning hand and a bust will cancel out (unless you've got a Blackjack bonus)
Also your betting strategy is known as the Martingale, it actually pairs pretty well with the Hero ability since without it it's a bit slow