Although there are several new designs for phase I cancer clinical trials including the continual reassessment method and accelerated titration design, the traditional algorithm-based designs, like the '3 + 3' design, are still widely used because of their practical simplicity. In this paper, we study some key statistical properties of the traditional algorithm-based designs in a general framework and derive the exact formulae for the corresponding statistical quantities. These quantities are important for the investigator to gain insights regarding the design of the trial, and are (i) the probability of a dose being chosen as the maximum tolerated dose (MTD); (ii) the expected number of patients treated at each dose level; (iii) target toxicity level (i.e. the expected dose-limiting toxicity (DLT) incidences at the MTD); (iv) expected DLT incidences at each dose level and (v) expected overall DLT incidences in the trial. Real examples of clinical trials are given, and a computer program to do the calculation can be found at the authors' website approximately linyo" locator-type="url">http://www2.umdnj.edu/ approximately linyo.