How the figures here are derived
Two conventions
Everything on this site follows two rules, and they exist because most of the confusion in this subject comes from ignoring them.
- Every figure is derived on the page that states it. Assumptions are written out, the arithmetic is printed, and the result follows from the printed arithmetic. No figure here rests on an assertion, a survey, an outside authority or an unsourced claim about how often something happens.
- Every percentage is printed with the base it is measured against. A percentage without a base is not a quantity. The small outlined tags throughout this index - per unit staked, per spin, per draw, per market - name that base, and two figures carrying different tags are not comparable.
Why the second rule needs its own page
The same game, unchanged in any respect, produces different percentages under different bases. The figures below all describe one arrangement: an even-money bet on a wheel of thirty-seven pockets, one unit staked per trial, fifty trials in an hour, four hours of play, and a hundred units brought at the start.
The single derived quantity:
expected loss per unit staked = 1/37 = 0.027027
Base 1 - per unit staked
0.027027 = 2.70 % per unit staked
Base 2 - per hour
50 trials x 1 unit x 0.027027 = 1.3514
= 1.35 units per hour
Base 3 - per amount brought
4 hours x 50 trials x 1 unit = 200 units staked
200 x 0.027027 = 5.4054 units expected loss
5.4054 / 100 brought = 5.41 % per amount brought
Three numbers - 2.70, 1.35 and 5.41 - describe one game over one session. None is wrong and none can be substituted for another. The third is roughly twice the first, and the reason is that each unit brought was staked twice on average over the session; had the session run eight hours rather than four, the third figure would have doubled again while the first stayed exactly where it is.
What this site does not contain
This index carries no figure it has not derived. There are no survey results, no claimed proportions of people doing anything, no market sizes and no operator data, because none of those can be worked out from first principles and printed for a reader to check. Where a historical development is described, it is described at the level of mechanism and period rather than by naming an institution, a business or a person.
The index is a reference on how these calculations work and where the rules producing them came from. It describes no service of any kind, recommends nothing, and does not tell anyone what to do.