---
title: "The house edge"
url: https://180gambler.net/house-edge/
description: "The house edge is the operator's expected share of each unit staked. This article derives it and tabulates it for common wagers."
published: 2026-08-17
updated: 2026-08-17
---

# The house edge

Published 2026-08-17

[180Gambler](https://180gambler.net/)

Reference on games of chance

180Gambler > Mathematics

Field: Mathematics. This page was last modified on 17 August 2026.

The house edge

**Field**: Mathematics of chance

**Also called**: advantage, vigorish, hold

**Definition**: negative expected value per unit staked

**Single-zero wheel**: `2.70%`

**Double-zero wheel**: `5.26%`

**Craps pass line**: `1.41%`

**Set by**: the payout schedule

The house edge is expected value seen from the other side of the table: the share of each unit staked that the operator keeps on average. It is produced by paying winners at slightly shorter odds than the outcome deserves, it is fixed by the rules of the game rather than by luck, and it is the reason the mathematics of these games has only one long-run direction.

House edge on five common wagers, drawn to the same scale. The rightmost bar is a single-roll proposition bet.

## Where the edge comes from

Take a single-zero wheel. Thirty-seven pockets, one winner, so the true odds against a named number are `36 to 1`. The game pays `35 to 1`. Over thirty-seven notional spins staking one unit each, the player stakes thirty-seven units, wins once, and receives thirty-six back. The missing unit divided by the thirty-seven staked is `1/37 = 2.70%`.

The same figure appears on every other bet on the same wheel, because the payout schedule was constructed by the same rule throughout. A bet covering eighteen numbers pays even money against true odds of `19 to 18`; a bet covering twelve pays `2 to 1` against true odds of `25 to 12`. Both reduce to `1/37`. A wheel with a second zero has thirty-eight pockets and the same payout schedule, so the shortfall doubles to `2/38 = 5.26%`.

## Edge, hold and drop

Three quantities are often confused. The house edge is a percentage of the amount staked on one wager. Hold is the percentage of the money a player brings that the operator ends up with, which is higher than the edge because the same money is staked repeatedly. Drop is simply the amount of money brought to the table.

The relationship is multiplicative rather than additive. Money staked ten times against a one per cent edge is exposed to that edge ten times, so roughly a tenth of it is expected to be gone by the end, not a hundredth. Speed of play therefore matters as much as the edge itself: a fast game with a small edge can cost more per hour than a slow game with a large one.

## A comparative table

*House edge derived from the payout schedule of each wager*

| Wager | True odds | Paid | Edge |
|---|---|---|---|
| Craps, pass line | `251 to 244` | `1 to 1` | `1.41%` |
| Craps, place the six | `6 to 5` | `7 to 6` | `1.52%` |
| Roulette, single zero, any bet | `36 to 1` | `35 to 1` | `2.70%` |
| Roulette, double zero, any bet | `37 to 1` | `35 to 1` | `5.26%` |
| Craps, five on one roll | `8 to 1` | `7 to 1` | `11.11%` |
| Craps, seven on one roll | `5 to 1` | `4 to 1` | `16.67%` |

Every figure in the table is arithmetic on the two columns to its left. Nothing in it depends on the venue, the equipment or the day.

## Games where the edge is not fixed

In roulette, dice and lottery draws the edge is a property of the rules alone. In games with decisions, it depends on how well the decisions are made. Blackjack is the standard example: with common rules and correct play the edge is a fraction of a per cent, while poor play can multiply it several times over. The published figure for such a game is always conditional on a strategy, and quoting it without that condition is meaningless.

A further class of games takes a commission instead of a payout shortfall. Pari-mutuel pools, described in the [history of betting](https://180gambler.net/history-of-betting/), deduct a fixed percentage from the pool and distribute the rest, so the operator's share is set explicitly rather than being hidden in a rounded payout.

## Why the edge is not a losing streak

The edge does not act on any individual wager. A player can win a great deal from a game with a large edge, and a game with a small edge takes money steadily. What the edge fixes is the direction and the slope of the long-run average. The [law of large numbers](https://180gambler.net/variance-and-the-long-run/) supplies the rest of the story: the more wagers are made, the more closely the observed result tracks the arithmetic, and the smaller the chance that luck has moved it in the other direction.

## See also

- [Expected value](https://180gambler.net/expected-value/)
- [Variance and the long run](https://180gambler.net/variance-and-the-long-run/)
- [Roulette](https://180gambler.net/roulette/)

Categories

[Mathematics of chance](https://180gambler.net/index/#mathematics-of-chance)