Gamemath

A statistical reading room
Australia · en-AU

Contents

03 / Sample ledger

The design is not the receipt.

A theoretical figure is built from possible outcomes. A session figure is calculated from outcomes that happened in a chosen interval. Here the interval is invented.

Hypothetical figures throughout

Two windows · twenty $1 plays

An intentionally small ledger

Suppose an invented, independent $1-stake game pays $9 with probability 10% and otherwise pays $0. Its expected prize is 0.10 × $9 + 0.90 × $0 = $0.90 per stake: a hypothetical 90% theoretical RTP. This is not a real game or an Australian minimum. We write down two possible ten-play windows; the paid plays are numbered explicitly.

Invented record; on narrow screens, scroll the table sideways to read all columns. each play has a $1 stake. All plays not named under “paid plays” return $0.
Window / playsStakesPaid playsPrizesObserved RTP
First / 1–1010 × $1 = $10None$0$0 ÷ $10 = 0%
Second / 11–2010 × $1 = $1012 and 18: $9 each$18$18 ÷ $10 = 180%
Both / 1–20$2012 and 18$18$18 ÷ $20 = 90%

Technical reference — Great Britain. UK Gambling Commission, How to calculate RTP (updated 25 January 2021) defines the observed prizes-to-stakes calculation; the ledger is invented, not GB or Australian game data.

The combined 90% is an artefact of this deliberately constructed example. The second window did not repay the first, and there is no rule requiring another ten or twenty plays to land on 90%. The 180% second-window figure counts all $18 in prizes against $10 in stakes; it does not describe how often that result occurs.

Australian context VGCCC, Understanding poker machines (updated 1 June 2026) distinguishes theoretical RTP from an individual session. Ledger values here are original hypothetical arithmetic, not VGCCC data.

A small grouping of translucent pieces apart from a larger blurred field
Conceptual still life — not a record of plays or a forecast. The invented ledger above defines its own sample and arithmetic.

What changes when the window moves?

  1. 01
    The denominator changes.

    Ten $1 plays put $10 at stake; twenty put $20 at stake. Do not compare prize totals without stakes.

  2. 02
    The numerator changes.

    A paid play enters the chosen interval or drops out of it. The designed probabilities do not change with that bookkeeping.

  3. 03
    No deadline appears.

    “Over many plays” does not specify when a person's recorded result will approach a design figure.