To which extent do public agencies have to be transparent about algorithmic profiling tools used to combat social welfare fraud and to which extent can they reject transparency requests based on the argument that citizens might ‘game the system’ (GTS)? Or, to phrase the same question in constitutional terms: to which extent is algorithmic Leviathan to be constrained by various transparency rights? In this article I propose a model of communicating vessels of transparency rights, where the Rule of Law (RoL) acts as a common denominator – or connecting tube. I discuss transparency rights following from administrative law (right to a reasoned decision and party access), the rights for meaningful information from the GDPR and AI Act, regulatory oversight and freedom of information (FOI) law. First, I juxtapose individually oriented transparency rights (right to a reasoned decision, party access, right to meaningful information) with those directed towards the public at large (oversight and FOI). Second, I discuss what FOI law requires from public agencies in terms of transparency, by discussing a Danish, Swedish and Dutch case where journalists requested FOI access to fraud combatting algorithms. While each of these jurisdictions has a possibility for secrecy based on the need to prevent GTS, the reach of this secrecy differs depending on which approach is followed in terms of assessing harm: pure harm (Denmark), harm with a presumption of publicity or secrecy (Sweden) or a balance of interests (The Netherlands). Different conceptualizations of harm can impact on the functioning of these communicating vessels of transparency. Third, I show how the communicating vessel model can help to strengthen algorithmic transparency, and to avoid that the transparency ambitions of the AI Act get lost in complexity.