There is a well-known puzzle involving finitely iterated prisoner's dilemmas (FIPDs). It is the result of the conflict between a pre-theoretic intuition that players faced with a finite sequence of prisoner's dilemmas might cooperate at least once and the game-theoretic contention that both players will defect in all the rounds, a contention that is backed by a seemingly valid backward induction argument (BIA). The proper approach to solving this puzzle begins by examining sets of assumptions that characterize FIPDs to identify the ones that really do entail mutual defection throughout (MDT). Once this first step is accomplished, the second step is to assess these sets. They can be assessed in various ways. For example, we could see what remains of the puzzle: if the only sets that entail the MDT conclusion are very strong (especially in certain unexpected ways), their strength could undermine the pre-theoretic intuition that a player might cooperate. For another example, we might see whether the sets that do entail MDT have any applicability, determining whether any real-life situations could be modelled by these sets. Though the second stage of this two-step approach is interesting and pivotal, I promise not to do any assessing. The current state of the literature requires that some time be spent exclusively on the first step. I will focus my attention on one important set of FIPD assumptions. It includes an assumption describing the basic game configuration (BGC). BGC says that players 1 and 2 will play a prisoner's dilemma n times (n 2 2), that both players will be rational throughout, and that they will remember what happened in the earlier rounds. The set also includes an assumption describing the players' epistemic states vis-ai-vis BGC. I call this the common belief requirement (CBR). It says that both players presently (i.e., just prior to the first round) believe BGC, that both presently believe that they both presently believe BGC, and so on ad infinitum. Officially, that is all that our central set of assumptions includes, just BGC and CBR. There is, however, a lot built into these assumptions: For the purposes of this paper, I will assume that believing is identical to assigning unit probability. For these same purposes, I will also assume that S is rational only if (i) S has coherent probability assignments just prior to each of the rounds, (ii) S updates probability assignments via conditionaliza-