What Did Bayes Really Say? — Bayes’s “Billiards”

Introduction | Problem and Definitions | Propositions 1 – 7 | Bayes’s Billiards | Endnotes | References

Bayes’s “Billiards”

Original text

POSTULATE. 1. I suppose the square table or plane $ABCD$ to be so made and levelled, that if either of the balls $O$ or $W$ be thrown upon it, there shall be the same probability that it rests upon any one equal part of the plane as another, and that it must necessarily rest somewhere upon it.

I suppose that the ball W shall be first thrown, and through the point where it rests a line os shall be drawn parallel to AD, and meeting CD and AB in s and o; and that afterwards the ball O shall be thrown p + q or n times, and that its resting between AD and os after a single throw be called the happening of the event M in a single trial.

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The pdf of this article includes the rest of this section on Bayes’s Billiards and sections on Propositions 8-10; Rule 1 [Solution to the Problem]; Richard Price’s Appendix of Numerical Examples; My Addendum on Bayes’s Real Rule; Endnotes; and References.