Casino Maths: The House Edge Explained
Knowing the house edge of casino games is vital to deciding what games to play, and understanding how it works is central to any statistical strategy.
Definition
If you're new to casino betting, or you've decided to take a more mathematical approach, the chances are you've encountered discussions about the 'house edge' or 'house advantage'. But what exactly does it mean?
The house edge shows the advantage held by the casino (or gaming website) in any given game. It is a statistical calculation, expressed as a percentage, based on the discrepancy between the odds of something happening (you win) and the odds of it not happening (house win). It is therefore a representation of the statistical advantage that any game gives to the house. Another way of viewing the house edge is the average percentage profit the house should statistically make from bets over a prolonged period of time; or the average losses you would make if you played with large sums, over a long period of time with no strategy.
An Example
To see how a house edge is calculated, let's take one of the simplest bets in the game: red/black bets in Roulette. A common misconception is that you have a 50% chance of winning, because there's two outcomes and the casino pays evens. But on a US Roulette table, the two zeroes change the odds by pushing the total possible outcomes to three (red, black or neither), with 38 individual variations (being numbers 1-36, plus 0 and 00). Because only 18 of those 38 numbers result in a win, your chances are calculated as:
18/38 = 47.37%
Because the house also wins on 0 and 00, 20 numbers deliver a win and so the odds are:
20/38 = 52.63%
The house edge is the difference between those figures:
52.63 - 47.63 = 5.26%
And the more permutations a game has, the more complex the calculations become.
How to Use It
House edge calculations are easily found for most popular games, making it simple to identify games that are good for beginners: those which will average out to a small cost for a lot of fun, or where a little luck can leave you up for the night. On a slightly higher level the house edge tells you how much you're risking if you push a lucky streak, and helps promote rational behaviour and fight gambler's fallacy with cold hard stats. But the most important use for the house edge is as a tool to dissect the mechanics of a game. By understanding where the odds are more or less against you, you can start to analyse the outcomes that push the payouts one way or the other, and try to turn the tide more in your favour.
Check Out: New Casinos for Welcome bonus and offers.
Statistical Strategies
Blackjack is a prime example of where the house edge can help develop your strategy. In blackjack, the source of the house edge (generally 0.28%, but rule variations can complicate things) is the player bust - since the dealer automatically wins. So reducing the edge is about calculating when to hit and when to stick, based on the likelihood of going bust vs. losing on value.
Once you've calculated the odds and made your decisions, you can road test your strategy online at 32Red Casino!
Recommended Casino Sites
- Our Top Pick#ad. 18+. Gamble Responsibly. Begambleaware.org. The Welcome Bonus is only available to newly registered players who make a minimum initial deposit of £10. The welcome offer can be activated only once, when making your first deposit. In order to receive the maximum of £ 200 bonus, you will need to wager an amount equal to 35 times the value of your first initial deposit within 60 calendar days from the date on which the Welcome Bonus option has been activated under the 'My Bonuses' section of your account.. Full Terms Apply. Gamble responsibly.www.begambleaware.orgExtensive Library of Slots & Jackpot Slot GamesWeekly 'Rainbow Friday' CashbackEarn Spins on 'The Wheel of Vegas'not requiredBonus CodeThe code required to claim this sign-up bonus (if any)Bonus WageringThe number of times you have to play through your bonus before you are able to withdraw any winnings35xPayout TimeThe usual withdrawal processing timeInstantOur RatingGambling.com's rating of this casino site out of 10099Casino GamesThe total number of all casino games available7000+Live Casino GamesThe total number of Live Dealer casino games available750+Mr Vegas Casino stands out with its vast games inventory, including thousands of slots titles. It also offers a 'Rainbow Treasure' reward program - the more you stake during the week, the more cash-back you get the following Friday (up to £300 per day).
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New depositing players only. Min. deposit: £10. Max. bonus: £200 + 25 Bonus Spins on Book of Dead. Offer valid on the first deposit. No wagering is required on Bonus Spins. Wagering Required on Bonus Cash: 40x. The match-up bonus that requires a deposit must be wagered 40x. In order to withdraw your winnings, you must first use up all of your bonus spins or wait for them to expire (whichever comes first). Bonus Policy and Terms of Service apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. #AD New customers only, min deposit £10, wagering 40x, max bet £5 with bonus funds. Max bonus is 100% up to £100. No max cash out on deposit offers. Welcome bonus excluded for players depositing with Skrill or Neteller. Cashback is cash with no restriction. Full T&C’s apply. +18, Please Gamble responsible. BeGambleAware.org - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New depositors only. UK residents only. Minimum deposit £10. Once the offer is claimed, players will receive 50 Extra Spins (value £0.10 each, selected games, valid 7 days) and will have 30 days to release a bonus equivalent to the initial deposit up to £100 (35x wagering, selected games, valid 30 days) Certain deposit types are excluded. T&Cs apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. Opt in & deposit £10+ within 7 days & wager 35x to get up to £100. Wagering contributions vary. 7 day expiry. Receive 10 - 50 Extra Spins worth 10p on Big Bass Splash. 3 day expiry. Eligible on 2 deposits. T&Cs Apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. Welcome bonus for new players only | Maximum bonus is 100% up to £100 | Min. deposit is £20 | No max cash out | Wagering is 35x bonus | Maximum bet with an active bonus is £5 | Eligibility is restricted for suspected abuse | Cashback is cash with no restrictions | Skrill & Neteller deposits excluded | Cashback applies to deposits where no bonus is included - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. First deposit only. This offer is only available for first time depositors. Min deposit is £10. 80 Extra Spins on Big Bass Bonanza. Spin Value: £0.10. This offer cannot be used in conjunction with any other offer. This offer is only available for specific players that have been selected by PlayOJO. If you have arrived on this page not via the designated offer via PlayOJO you will not be eligible for the offer. OJO’s Rewards and Game Play policy applies.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. First deposit only. Min deposit & spend £20. Max 75 spins on Big Bass Splash at 10p per spin. Spins credited upon spend of £20. Full T&Cs apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New players only. Min deposit: £20. Max bonus: £100. Wagering requirements: 35x. Offer valid 24h since entering the bonus code. Spins are credited in Big Bass Bonanza. Bonus code: GDC2024. The bonus code needs to be entered during the registration. Gambling can be addictive. Please play responsibly. T&C's apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New customers only, min deposit £10, wagering 40x, max bet £5 with bonus funds. Max bonus is 100% up to £100. No max cash out on deposit offers. Welcome bonus excluded for players depositing with Skrill or Neteller. Full T&C’s apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New customers by invite only. Min Deposit £20 (exc paypal). Max Bonus £30, and 100 Extra Spins playable on selected games only. 30x Wagering for £30 Bonus. Max win £2000. Extra Spins in cash. *T&Cs Apply. - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. 1st dep. of £20-£300, max bonus £300 on selected slots; 50x wagering on the sum of deposit & bonus applies. Max convertible 5x bonus amount received. Use code: GDOTCOM when depositing in the cashier. Extra Spins: 3 Batches of 10 FS Daily. Winnings capped at £10 per batch. - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New players only, £10 min fund, £200 max matchup bonus, extra spin wins credited as bonus, 65x wagering requirements, max bonus conversion to real funds equal to lifetime deposits (up to £250), full T&Cs apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. Bonus only available to new Players at PeachyGames. One welcome bonus per Player. Minimum first deposit of £10 required to participate. Maximum promotion amount per Player is £50 Bonus and 20 Bonus Spins. The welcome offer is not available on pre-paid card or e-wallet (Neteller and Skrill) deposits. Further T&C's Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New players only. Min deposit £20. Max bonus 100% up to £66 on 1st deposit. 66 spins on Big Bass Bonanza on 2nd deposit. 35x wagering applies, within 21 days. Max wins from spins £100. Spins expire after 24 hours. Full T&Cs Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New players only. Min deposit: £20. Max offer: 100% Bonus up to £400 & 125 Spins (on game of our choice). Bonus and Spins split over 3 deposits (min £20 dep required for each). 1st deposit 100% up to £100 + 45 Spins, 2nd deposit 50% up to £150 + 40 Spins, 3rd Deposit 50% Up to £150 + 40 Spins. Bonus & Spins winnings must be wagered 35x before withdrawal. Spins expire after 5 days. Withdrawal & full T&Cs apply. Valid until 31.12.2024.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. | 1st deposit only | min deposit £10 | max bonus £100 | X40 wagering | bonusspins valid for selected games only | X40 wagering on bonus spins winnings | expires within 24 hours | user agreement & bonus T&C's apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. Welcome bonus for a new players only | Maximum bonus is 100% up to $/€/£ 123 | Min deposit is $/€/£ 10 | No max cash out | Wagering is 50x bonus | Maximum bet while playing with a bonus is $/€/£ 5 | Eligibility is restricted for a suspected abuse | Skrill and Neteller deposits excluded | - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New Players Only. Min. Deposit: £10. Wagering Requirement: 35x. Spins are given as follows: 15 Spins upon a first deposit of minimum £10. Spins may only be used in specific games. The game allowed: Fire Joker. No wagering is required on the spins. Spins expire after 24 hours. Promotion available for 72 hours. Terms and Conditions apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New members only, must opt in. Min £10 deposit & wager. 30 day expiry from deposit. 18+. Extra Spins: on Secrets of the Phoenix Megaways. Spins value: 20p each. Game availability & restrictions apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. Min 1st dep (Exc PayPal) £20 for 100% match, up to £100 selected slots.40x wagering & Max Wins 5x bonus + Guaranteed live bonus wheel up to £7. Live bonus & winnings are playable on selected live games 20x wagering & MaxWins x5 bonus. T&Cs apply. Full T&Cs apply. - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. Deposit a minimum of £10.Turnover initial deposit x1 on slots to qualify, upon qualification initial deposit will be matched with free slots funds up to £25.Bonus funds to be credited into account next day.The promotion is only valid for players living in the United Kingdom who are 18 years or over.Valid for players who register on or after 12/01/2024.In order to be eligible for this promotion and receive the welcome casino bonus, customers must deposit a minimum of £10 or more.This offer is valid for a player's initial deposit only.BetGoodwin Terms and Conditions apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. 1st dep (Exc PayPal) of £20 with code Magical. Max bonus £300 on selected Match Slots, 40x wagering on the sum of deposit & bonus, 5x MCR. 50 Extra spins on Starburst Slots, spin value 0.20P. Extra spins and Winnings playable on Starburst Slots only, 50x WR. 5x MCR. 18+ only. Full T&Cs apply. - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. Min Deposit £10. Welcome package splits over 3 deposits, 35x wagering requirement applies to match up bonus. Offer valid for 1 week. 100 spins split to 20 spins per day for 5 days. 50x wagering applies to spins.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New Players Min. deposit £20. UK players. Max. bonus 1st deposit 100% up to £50 and 2nd deposit 50% up to £100. 35x wagering applies, within 21 days. 20 spins on 1st deposit and 30 spins on 2nd deposit. Spins expire after 24 hours. Full T&Cs apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New players only. min. dep £20. max. bonus bet £5. 150% match up to £300 + 100 bonus spins on Starburst on your 1st deposit. Winnings from all spins credited as bonus funds and capped at £100. Bonus funds are separate to cash funds & subject to wagering requirement (x deposit plus bonus). Only bonus funds contribute towards wagering requirement. Bonus funds must be used within 30 days, spins within 72hrs. Affordability checks & terms apply. Please gamble responsibly. BeGambleAware.org.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. The Legal Stuff: New players. Deposit £10, stake £10 on Bingo, get £30 bonus (x4 Wagering) & £10 Club voucher, &/or stake £10 on slots, get 200 x 10p Fishin’ Frenzy The Big Catch Jackpot King (x20 wagering) & £5 Club slots voucher. Use winnings in cash balance/further deposit to claim both. £5 minimum withdrawal. 18+.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New players only. Min deposit £20. Max bonus 100% up to £25 on 1st deposit. 50 spins on specific game only on 2nd deposit. 35x wagering applies, within 21 days. Max wins from spins £100. Spins expire after 24 hours. Full T&Cs apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New customers only. Opt In required. £/€10 min stake on Casino slots within 30 days of registration. Max bonus 200 Extra Spins on selected games credited within 48 hours. Extra Spins expire after 7 days. iOS app restrictions may apply. Email/SMS validation may apply. Not available in NI. Full T&Cs apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New players only. min. dep £20. max. bonus bet £5. 150% match up to £300 + 75 bonus spins on Big Bass Bonanza on your 1st deposit. Winnings from all spins credited as bonus funds and capped at £100. Bonus funds are separate to cash funds & subject to wagering requirement (x deposit plus bonus). Only bonus funds contribute towards wagering requirement. Bonus funds must be used within 30 days, spins within 72hrs. Affordability checks & terms apply. Please gamble responsibly. BeGambleAware.org. - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. 18+. Play Safe. 1st time depositor at 888casino only • £20 min deposit • Claim within 48 hrs • Valid for selected games • Bonus wins capped at £500 • 30x wagering – req. vary by game • Bonus expires within 90 days • Payment method & country restrictions apply • Withdrawal terms & T&Cs apply. #ad - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. To activate this promotion, you must deposit and stake a minimum of £10. You must place a minimum of 5 rounds during the qualifying period and 4 of these rounds must be at least half the value of your highest placed wager. T&Cs apply | New UK Customers Only | BeGambleAware.org | Gamble Responsibly
- #ad. 18+. Gamble Responsibly. Begambleaware.org. Opt-in required. 20 Bonus Spins on “Sahara Riches Cash Collect” at 10p per spin and 100% Deposit Bonus up to £25 on first deposit (payment method and play restrictions apply). Min. deposit £10. 30x wagering for Bonus Spins and Deposit Bonus (game weighting applies). Max. £5/spin or £0.50/line. 30 days expiry. - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New members only, must opt in. Min £10 deposit & wager. 30 day expiry from deposit. Extra Spins: on Rainbow Riches. 1p coin size, max lines. Bingo: Advertised ticket value based on £1 tickets. Game availability & restrictions apply. **£10 lifetime deposit for Daily Free Game., must opt in. Min £10 deposit & wager. 30 day expiry from deposit. Extra Spins: on Rainbow Riches. 1p coin size, max lines. Bingo: Advertised ticket value based on £1 tickets. Game availability & restrictions apply. **£10 lifetime deposit for Daily Free Game.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. Wager £/€20 on slots and Get 40 Cash Extra Spins for five consecutive days.* New customers only. £/€20 stake on slots each day within 5 days of 1st deposit to qualify. £0.1 Spins on Book of Dead. £/€250 total max withdrawal. Full T&Cs apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New players only. Min. deposit £20. Max. bonus bet is £5. Bonus spins on selected games only and must be used within 72 hours. Winnings from Bonus spins credited as bonus funds and capped at £100. Bonus funds expire in 30 days, unused bonus funds will be removed. Welcome Offer is 100% match up to £200 plus 50 bonus spins on your 1st deposit, 50% match up to £50 on your 2nd deposit. Bonus funds are separate to Cash funds, and are subject to 35x wagering the total bonus & cash. Only bonus funds count towards wagering contribution. Affordability checks apply. Terms apply. - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New Players Only. Wager from real balance first. 50X wager the bonus. Contribution varies per game. Selected games only. Wager calculated on bonus bets only. Bonus valid 30 Days from receipt/ extra spins valid for 7 days from issue. Max conversion: 3x the bonus amount or from extra spins: £20.Withdrawal requests voids all active pending bonuses. Excluded Skrill and Neteller deposits. Full Terms apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. 18+ New customers only. Opt in, deposit, and wager a min of £10 on selected games within 7 days of registration. Get a 3x £10 bonus for selected games and 30 Extra Spins on Fishin' Frenzy. Offer valid until 23:59 UK time on 31.12.24. Debit Card/Apple Pay Payments only. T&Cs apply, see below. begambleaware.org Please gamble responsibly.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. First 3 deposits only. Min deposit £10. Max total bonus £500 and 150 spins. 30x wagering (dep + bonus). 30x on spins, 4x conversion, bonus and spins valid on selected slots. Full T&Cs apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New players only, £10 min fund, £200 max bonus, max bonus conversion equal to lifetime deposits (up to £250), 65x wagering requirements and full T&Cs apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New Casino players only. Deposit required. Min bet £10 on qualifying games. 40x wager reqs (bonus only) on selected games. £30 Bonus + 30 Extra Spins for a selected game. Accept within 14 days. Valid for 30 days. Spins value £0.20 each. Certain deposit types excluded. Player restrictions & T&Cs Apply. - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New members only, must opt in. Min £10 deposit & wager. 30 day expiry from deposit. Extra Spins: on Double Bubble. 1p coin size, max lines. Bingo: Advertised ticket value based on £1 tickets. Game availability & restrictions apply.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New player only. 7 days to claim offer and deposit a min of £10 with a further 7 days to wager 35x. Cash stakes only and wagering contributions vary. Max reward £150. 50 wager-extra spins 0.10p each on Big Bass Splash awarded after wagering complete, winnings paid as cash. 3 day expiry. - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New members only, must opt in. Min £10 deposit & wager. 30 day expiry from deposit. Extra Spins: on Double Bubble. Spins value: 20p each. Bingo: Advertised ticket value based on £1 tickets. Game availability & restrictions apply. **£10 lifetime deposit required.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New Players only. 1st, 2nd and 3rd ever deposit: spin multiplier wheel and win a Matchup Bonus up to 10X your deposit amount (£2,000 max bonus), £10 min fund for all 3 offers, 65x Bonus wagering requirements, max bonus conversion to real funds equal to lifetime deposits (up to £250) - Full Terms Apply
- #ad. 18+. Gamble Responsibly. Begambleaware.org. 18+. new players only. min. dep £20. max. bonus bet £5. 100% match up to £200 + 200 bonus spins on Book of Dead on your 1st deposit. Winnings from all spins credited as bonus funds and capped at £100. Bonus funds are separate to cash funds & subject to wagering requirement (40x deposit plus bonus). Only bonus funds contribute towards wagering requirement. Bonus funds must be used within 30 days, spins within 72hrs. Affordability checks & terms apply. Please gamble responsibly. BeGambleAware.org.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. Cashback offers are available to all registered players at No Bonus Casino. Cashback is calculated on all deposits of any day, given that all deposited money has been lost. After 24 hours of the initial deposit the accumulated cashback becomes available to activate. The cashback offer is valid for ten (10) days, during which the cashback has to be withdrawn or played with. Cashback refunds are rounded to the nearest Euro.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. 18+ New customers only. Opt in + wager £25 on selected games, within 15 days. Get £25 casino bonus on selected games, 40x wagering, + 25 extra spins on Starburst. Redeem promo upto 4x. 30 day bonus expiry. Max Redeemable £2,500. Card payments only. T&Cs apply. http://GambleAware.org | Please gamble responsibly.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New Players Only 18+ (UK only). Minimum Deposit: £10. Maximum Offer: 100% Bonus up to £50 & 100 Spins on Starburst. Bonus & Spins winnings must be wagered 35x before withdrawal. Spins expire after 5 days. Promo Code: 100SPINS. Withdrawal terms apply. Valid until 31.12.2024.
- #ad. 18+. Gamble Responsibly. Begambleaware.org. New UK and IRE players only. Once per player. Valid 22/01/24 and 17/03/24. 50 (£/€0.10) Extra spins (FS) on selected game credited the day after depositing (£/€10) and staking on a horse bet (£/€10) requirement are made. Min odds (1/1). Cashed out/voided bets will not qualify. 72 hrs to accept and play with FS. Game, Payment & Player restrictions apply. T&Cs apply.
Stay In The Loop With New Casino Sites & Offers!
Free Spins. Exclusive Bonuses. Sent Weekly.