I think in Mu Deuk's mind, Jang Uk would feel motivated to win the duel if she was the prize.
There is a scene previewed (ep12) that appears to be a conversation between Mu Doek and the prince. The prince seems to have seen through her game and challenges her to bet herself.
I'm the only one who missed some scene from the preview in this episode? I mean, it was no surprise to me, that Mu Deok is the price because of that one scene in the preview from ep 12.