 Axiom 1: Suppose that \(Q(H) \lt 0\). In this case, the bookie buys the bet that pays $1 if \(H\) is true and 0 otherwise, for the negative price \(Q(H)\), which means that the agent collects \(Q(H)\), and pays out $1 if \(H\) is true, and $0 otherwise. Here the agent is betting against \(H\) and the payoff table for the agent is as follows: