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Several communication protocols and applications require a node to know how many neighboring nodes exhibiting a certain attribute it has. Conventionally, such neighbor information is obtained by explicit message exchange between nodes, which is reliable but inefficient in densely connected networks in terms of overhead and delay. An alternative approach is to perform an estimation of the neighbor cardinality using probabilistic methods. This paper pursues such an approach by proposing neighbor cardinality estimators that require no coordination among polled nodes but are based on a simple random access scheme with busy tones, where the number of empty slots is exploited to infer about the neighbor cardinality. We compare three estimators with different levels of adaptability and feedback from the query node and discuss their suitability for IEEE 802.11 and low power sensors. Performance is studied in terms of estimation accuracy and delay.