This paper is on binary randomized consensus in an n-process asynchronous distributed system, where each process is equipped with a binary random coin, and up to t processes may crash. Ficher, Lynch, and Paterson proved that the Consensus problem cannot be solved deterministically in such a context. It has been known since Ben-Or and Rabin in the early eighties that randomization allows solving the problem with probability 1 using round-based algorithms. Moreover, while local random binary coins may entail an exponential number of rounds in the number of processes of the system, a common coin that delivers the same random and unpredictable sequence of random binary values to all processes allows consensus algorithms that terminate within a constant average number of rounds. One may think that a common coin is The Oracle that needs to be provided for time-optimal randomized consensus. This paper studies the round complexity and the optimality of randomized consensus algorithms for different coins and different ratios n/t. For instance for n/3