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Recent years have seen growing efforts to develop spoofing countermeasures (CMs) to protect automatic speaker verification (ASV) systems from being deceived by manipulated or artificial inputs. The reliability of spoofing CMs is typically gauged using the equal error rate (EER) metric. The primitive EER fails to reflect application requirements and the impact of spoofing and CMs upon ASV and its use as a primary metric in traditional ASV research has long been abandoned in favour of risk-based approaches to assessment. This paper presents several new extensions to the tandem detection cost function (t-DCF), a recent risk-based approach to assess the reliability of spoofing CMs deployed in tandem with an ASV system. Extensions include a simplified version of the t-DCF with fewer parameters, an analysis of a special case for a fixed ASV system, simulations which give original insights into its interpretation …