Two rewards with the same expected payoff at the start of training can end a reinforcement-learning run in opposite places, with an honest model or one that bluffs. We study rewards that pay $b$ for a verdict that a checker cannot verify ("this program is correct") and $r$ for a certificate that it accepts (an input revealing a bug). To first order, a GRPO step makes the model more honest exactly when $\tilde{p}\,r/b>1+κ$. Here $\tilde{p}$ is the rate at which the checker accepts the model's certificates, weighted toward the items on which the model still gives both verdicts, and $κ$ is the pull of the items on which the unverifiable verdict is right. Both terms move during training. A checker raises $\tilde{p}$, so near the threshold honesty is a race, which a run just below the threshold can win and a run under a lottery (random pay with the same mean) cannot. The term $κ$ starts large and falls as the other items settle, so a run just above the threshold first dips toward bluffing, on code nearly to zero, before climbing back. Paying the honest verdict also pulls the other items toward it, which predicts a ceiling on the payoff ratio, above which the model gives the honest verdi