Randomization is very important in clinical trials which can prevent selection bias and valid statistical inference. Block randomization is often considered to prevent treatment imbalance in comparative clinical trials, especially when the sample size is small, or subjects’ characteristics change overtime. In practice, however, treatment imbalance may still occur, especially in multi-center clinical trials. Breaching blindness in clinical trials is another serious problem leading to subjective judgement and observational bias. In this article, we consider two fixed block randomization design with block size of 4 and 2 when comparing a placebo or an active control and a test treatment under investigation. The probabilities of observing various degrees of imbalance and the probabilities of correctly guessing the treatment under three types of prior knowledge are investigated. The results show that smaller block size design is more likely to maintain treatment balance than larger block size; however, the difference of imbalance between the two designs decreases when the sample size gets larger. The number of subjects per site in multi-center trials also has impact on the degree of imbalance. Additionally, both block size and prior knowledge have impact on the probability of guessing the treatment right. Large sample size in conjunction with varying block size are suggested for keeping treatment balance and avoiding the chance of guessers to guess the treatment right.