 The strategies serve as potential counterarguments to the two ways of answering the problem, rather than showing that it is irrational to switch to ⅓ or stick with ½ per se, since the individual strategies depend upon the plan to have a particular probability upon awakening. If Beauty plans to switch to probability ⅓ for heads, the Dutch Strategy is just an application of the general strategy against someone who violates Reflection. Hitchcock argues that this would not establish Beauty’s irrationality, since in this case the bookie must know during the experiment what day it is in order to implement the strategy, which is information that Beauty lacks. On the other hand, if Beauty sticks with ½, a strategy can be carried out without the bookie having to know more than Beauty by having the bookie undergo the experiment with her and offer a bet against heads on Sunday and a bet on heads whenever Beauty and the bookie awake within the experiment. If the coin lands heads, the bookie sells Beauty just one bet on heads, with her gain totaling less than her loss on the first bet against heads. If the coin lands tails, the bookie sells a bet on heads once on Monday and the same bet again on Tuesday, so as to again produce a loss for Beauty. Hitchcock takes this book to tell against the answer ½, and in favor of ⅓.