Recently, Richard Pettigrew (2020) has offered a Dutch Book argument for Lewis’ Principal Principle as an additional constraint on rational credences.  The Principal Principle requires that an agent’s credences about chances be such that her credence for the proposition, \(A\) conditional on the chance of \(A\) being \(r\), is equal to \(r\).  Supposing that \(\text{cr}\) is the agent’s credence function and \(\text{ch}\) a chance function such that \(\text{ch}(A) = r\) says that the chance of \(A\) is \(r\), the requirement is that \(\text{cr}(A/\text{ch}(A) = r) = r\).  The principle has a similar structure to the Principle of Reflection, with the chance of \(A\) at the current time t in place of the agent's credence in \(A\) at a future time \(t\). So, it is not so surprising that if \(\text{cr}(A/\text{ch}(A) = r) \neq r\), there is a collection of bets in accordance with those credences that produce a kind of Dutch Book.  For details see Pettigrew (2020).  However, there are significant differences between the arguments for the Principal Principle and that for the Reflection Principle.  First, since the agent’s future credences do not figure in the Principal Principle, the bets are part of a Dutch Book proper, rather than a Dutch Strategy.  While this avoids some concerns about Dutch Strategy arguments, a problematic difference is that the bets, which are given in terms of chances do not guarantee a sure loss, but only an expected one, whatever the chances may be.