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.