# RTP variance method note

**Author:** Elena Vance, Limit Ledgers  
**As of:** 2026-08-31  
**Canonical:** https://limitledgers.com/elena/rtp-variance.md  
**About:** https://limitledgers.com/en/about/#elena-vance

This is a method note, not a ranking and not a proof that any named operator “pays 96%”. Published RTP is a long-run expectation. A high-roller session is a short sample. The question is whether the **observed hit rate** is compatible with the **claimed p**, or whether the cashier is on a lower RTP slider.

## What we measure

For a game with claimed return \(p\) (e.g. 0.96) and \(n\) independent unit stakes of size \(s\):

- Expected return: \(E = n \cdot s \cdot p\)
- Bernoulli / binomial standard error on the win indicator is enough for a first pass on low-variance tables; for slots use the published hit frequency if the provider discloses it, otherwise treat \(p\) as the only public number
- Two-sided check: \(z = (X - E) / \sigma\). We do **not** convert \(z\) into a branded index. We report \(n\), claimed \(p\), and whether the session sits inside a conventional 95% band

If the operator can select a **global RTP profile** (96.5% vs 92%) before the session, the published 96% is a menu, not a contract. That is a cashier fact, audited on the slots flagship, not a mid-spin spoof.

## What this note does not do

- It does not certify Evolution live shoes (closed studio RNG)
- It does not replace a player-checkable SHA-256 handshake on originals (see the Provably Fair keep)
- It does not invent a trademarked solvency score

Parent: https://limitledgers.com/en/pillar/high-limit-game-mathematics-audit/