The problem is that if she knows what the reward is, she may anchor on already having the reward...The use of a gambling mechanism may be key for this.

Brilliant formulation of the problem & solution.

(Very successful) animal trainers using reinforcement techniques make a distinction between bribe and reinforcement, which was not ever completely clear to me, but appears to be addressing the same problem. But one thing they do, "shaping" the expected behavior, always changing it a little bit to get loser to the "target", might be serving the same purpose as the gambling mechanism: preventing anchoring on obtaining a reward in specific manner.