This piece is the result of an effort to tie the three-dimensional world of gambling to the two-dimensional pages of a text on probability and statistics and then to take care of a few other details before going on to address the practical concern of “bankroll management” in the next chapter. Those who get migraines from math-talk may be tempted to skip this chapter, but they will miss the rationale for how and why Type II bettors behave the way they do, and what the “real” objectives of Type II bettors really are. It may not affect gaming skill to skip over the graphs, but that’s a risk the reader takes. As explained earlier, the central question for a serious gambler (Type II all the way) is how to evaluate the physical expectation and then compare it to the proposition before him or her. This is just another was of stating what is meant by Part I and Part II of a bet.

Recall that “proposition” is used here in a very broad sense. It can mean a “prop” in the sports book, like the point total in the Browns and Bears not exceeding 40. It can also mean the decision whether to bet in the Texas Hold’em example on the third betting round, hop-ing for a flush. It can also mean whether to insert a coin or token and pull a handle or push a button. Likewise, table games implicitly present a proposition every time they offer an opportunity to make a bet. So “proposition” is used here to mean the betting opportunity presented by the house or the game.

This narrative commences with a consideration of what we mean by “odds.” It’s such a familiar term that it’s easy to skip over it without considering how “odd” it really is.