Probabilities of Counting Codes

In many cases counters are used to count special events within an endless sequence of events. This paper discusses a specific calculation, related to the probability of a counter overrun if the special event occurs not in a predictable way but with a certain probability. Different counter codes are compared with each other. A probability formula is developed for special scenarios which are normally analyzed by state diagrams and which can be numerically solved by the related Markov chains. The target is to enable a non-numerical discussion of the topic. It is shown how formulas can be found based on the rules of the probability theory, and their correctness is verified by a comparison with Markov chains.