It all depends on the relative stakes. Suppose you bet $10 that you wouldn't let a human AI-impersonator out of a box. A clever captive could just transfer $10 of bitcoins to one address, $100 to a second, $1000 to a third, and so on. During the breakout attempt the captive would reveal the private keys of increasingly valuable addresses to indicate both the capability to provide bribes of ever greater value and the inclination to continue cooperating even if you didn't release them after a few bribes. The captive's freedom is almost always worth more to them than your bet is to you.