We here examine the fixation probability of a mutant strategy in the evolutionary game dynamics in a finite population. We focus on bistable games, e.g. that played between All-D's and tit-for-tat (TFT)'s in Iterated Prisoner's Dilemma game (IPD), where either of pure strategies is an ESS. Finiteness of population adds two new factors in the evolutionary dynamics. First, it introduces a density-dependent bias in the frequency-dependent fitness scheme of infinite population game dynamics. By this effect, evolutionary outcome in a small population can be significantly different from that of the conventional infinite population game dynamics (e.g. we found that a spiteful strategy enjoys significant advantageous in very small populations). Second, random drift due to finite population size may drive the population out of a local ESS. We ask the condition under which the fixation probability, rho, of an initially disadvantageous mutant strategy exceeds that, 1/N, of a neutral mutant in a bistable game, where N is the population size. In other words, we ask when the evolutionary transition in bistable games is effectively `Darwinian'. We found a simple exact condition called a 1/3 law: there exists a range of population size in which the fixation probability of an initially disadvantageous mutant (e.g. either TFT or ALLD in IPD) exceeds that of a neutral one if and only if the critical frequency Xc of a mutant strategy at which the fitness of a mutant and that of a resident coincides is less than 1/3.