When there are ways to settle things in a match besides for risking his precious skin, Ace is usually all for it. Even though wounds inflicted here are never permanent, they still hurt and he's been a mercenary for a bit too long to go charging headlong into a painful situation.
Having shared a few drinks with Kazan in the past and heard all about his success in season 36 by getting his opponents to take him on in drinking contests, Ace decided to give that a shot himself and broached the idea to the Red Wizard.
RW, being a generic fantasy hero type, of course loved to drink and happily accepted the challenge.
However, Ace made one small error in judgment when he set this match up. Red Wizard, being generic, has no real personality to speak of. When someone literally has no personality, they aren't effected normally by external mood effectors such as, say, alcohol. So, it came to pass that after they had imbibed enough booze to get a horse tipsy, Ace was nearly passing out and the Red Wizard was still mechanically reaching for another cup while he chatted about how much he liked swords and the number of guards in the castle.
Of course, Ace isn't the type to leave anything empty handed. He had set it up so the winner picked up the tab, insuring that no matter which way it landed, he at least got something that he wanted. He'd have preferred the win, but he certainly isn't objecting to getting completely hammered on the generic's gil.