6Betting on a Single Outcome
In the abstract testing protocols that we study in this part of the book, Reality chooses her move 
from a set 
, and Skeptic chooses a payoff that depends on 
. The payoff is allowed to take infinite as well as finite values; it is a function from 
to the extended real numbers 
. We call any function from 
to 
an extended variable.
In this chapter, we study axioms for Skeptic's betting opportunities on each round. We consider two equivalent ways of specifying these opportunities:
- Offer Skeptic certain extended variables for free. We call the set of extended variables offered, say
, an offer. If Skeptic chooses , he receives . - Set a price for each extended variable ...
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