How is keno probability calculated?

Each match level uses the hypergeometric distribution: C(picked, hits) × C(pool−picked, drawn−hits) / C(pool, drawn), where C(n,k) is the binomial coefficient. This gives the exact probability of matching exactly k of your picked numbers when the house draws a fixed count from the pool.

What is expected value in keno?

Expected value (EV) is the average return per dollar wagered. It equals the sum of (probability of each outcome × its payout). An EV of 0.75 means you get back $0.75 on average for every $1 bet. Most keno games have EV between 0.65 and 0.80.

What is the house edge?

House edge = 1 − EV. A game with EV 0.75 has a 25% house edge, meaning the casino keeps 25 cents of every dollar wagered on average over many plays.

Does picking more spots give better odds?

More spots give bigger potential payouts but also lower probability of any win. The expected value usually stays similar or drops slightly as you pick more spots, depending on the paytable.

What are typical keno pool settings?

Most land-based and online keno games use a pool of 80 numbers with 20 drawn. Some variants use 70 or 100. The tool supports any pool size from 20 to 120 and any draw count up to half the pool.

What if I leave the payout table empty?

The tool still shows the full probability table for every match level. The EV and house edge columns require a payout table to calculate. You can enter payouts as a comma-separated list (one value per match level, starting from 0 matches).

Keno Odds Calculator

Name: Keno Odds Calculator
Availability: InStock
Author: Nham Vu

Enter how many spots you picked and the pool size to see exact odds, expected value, and house edge for your keno ticket.

Game Settings

Pool size (total numbers)

Numbers in the draw pool, e.g. 80

Numbers drawn per game

How many numbers the house draws, e.g. 20

Spots you picked

How many spots on your ticket, 1–15

Payout multipliers (optional)

Comma-separated multipliers starting from 0 matches.
Example for 5-spot: 0,0,2,5,25,100

Odds by Match Count

Matches	Probability	1 in N	Payout (× $1)	EV Contribution

Configure your keno settings and click Calculate.

Defaults are set to a standard 80-ball, 20-draw, 5-spot ticket.

Summary

Enter how many spots you picked and the pool size to see exact odds, expected value, and house edge for your keno ticket.

How it works

Enter the total pool size (how many numbers are in the draw pool, e.g. 80).
Enter how many spots are drawn each game (e.g. 20).
Enter how many spots you picked on your ticket (typically 1–10).
Optionally enter a payout table — type the multiplier for each match count separated by commas.
Click Calculate to see the probability and expected value for every match level.
Review the house edge to understand how much the game returns to players on average.

Use cases

Compare keno game variants by house edge before playing.
Verify whether a casino keno paytable is fair.
Learn how picking more spots changes your odds.
Teach combinatorics and probability using a real-world game.
Evaluate online keno bonus promotions against expected value.
Understand why multi-spot keno tickets have lower return rates.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu