This article tests Duverger’s law through an analysis of the 2017 elections of Slovakian regional presidents which were held under the new first-past-the-post (or single-member plurality) system, and comparison with results of the previous election of 2013 which used a two-round system (absolute majority run-off). The main aim of the article is to test the expectations of strategic voting in the context of the so-called second-order elections, under which regional elections can be classified. The results show that strategic voting was not a universal phenomenon under the plurality rule in 2017, as indicated by electoral results and party competition at the level of electoral precincts. In most electoral precincts, the character of electoral competition was not in compliance with theoretical expectations and two-party competition. More importantly, the introduction of FPTP, instead of TRS, should lead to increasing two-party competition and strategic voting, but the opposite was true. Competition at precinct level in 2017 went far away from the Duvergerian equilibrium, as two-party competition increased in only one out of eight regions, Trnava, compared to 2013. Finally, segmented Nagayama diagrams likely proved as the most suitable indicator of competitiveness and strategic behaviour, helping us identify the patterns, but above all, changes to the patterns, of electoral competitiveness between elections. Our research thus confirmed that the effect of electoral institutions (institutional structure) is contingent upon and (at the district, or precinct, level) inhibited by country-specific conditions, with potentially strong influence of the second-order character of the Slovak regional elections.