Gamemath

A statistical reading room
Australia · en-AU

Contents

04 / Payout distributions

One average. Two shapes.

A mean can agree even when the individual outcomes do not. These two entirely invented games are a controlled comparison, not real products.

Independent plays · fixed $1 stake

All probabilities hypothetical

Read the full outcomes

For each independent $1 play, Game A pays $1 with probability 90% and $0 with probability 10%. Game B pays $9 with probability 10% and $0 with probability 90%. Both have expected prizes of $0.90 per play.

Complete outcome table for the invented games; on narrow screens, scroll sideways to read all columns; percentages describe each single-play model, not results promised in ten plays.
GamePrize and probabilityOther outcomeExpected prize / $1 stake
A$1 at 90%$0 at 10%(0.90 × $1) + (0.10 × $0) = $0.90
B$9 at 10%$0 at 90%(0.10 × $9) + (0.90 × $0) = $0.90

For either model, $0.90 expected prizes ÷ $1 stake gives a hypothetical 90% theoretical RTP. Game A's $1 prize merely equals its $1 stake: it is not a net gain. Game B's $9 prize is $8 above the stake for that one play. Neither game's payout frequency guarantees any count of prizes in ten plays.

Chance of any prize on one play

A90%
B10%
Bars encode the labelled percentages, not a sequence of actual plays. Text equivalent immediately above: A pays $1 at 90% and $0 at 10%; B pays $9 at 10% and $0 at 90%. Both expect $0.90 in prizes per $1 stake.

In this particular two-outcome model “any prize” occurs 90% of the time for A and 10% for B; “prize greater than stake” occurs 0% for A and 10% for B. Those are different counts even though the expected return matches. These are mathematical examples, not statements about an Australian game's settings.

An irregular field of unnumbered glass shapes casting distinct shadows
Conceptual still life — not a distribution or payout frequency. The table and labelled bars above contain the hypothetical probabilities.

What the shared number omits

An average alone does not tell you the size of possible prizes or how often any prize occurs. It also says nothing about the exact order of a short run. The sample ledger is one constructed sequence consistent with Game B, not a typical sequence or a balancing mechanism.

Reading rule
If a claim gives one return percentage and then promises a particular pattern of wins, ask for the full outcome model and the definition of a “hit”. The percentage alone does not supply either.