What is the House Edge and How Does It Affect Casino Games?

Question

What is the 'house edge' in casino games, and how does it impact my expected losses?

Answer 1

The house edge is the mathematical advantage that the casino has over the players. It represents the expected percentage of each bet that the casino expects to keep over the long run. For example, in a game with a 5% house edge, you can expect to lose 5% of the total amount you bet over time. This ensures that the casino will profit as more bets are placed.

Comments

Probabilities are always a fascinating subject to me.. i like the way it can predict what may happen in future just using some numbers and some expressions

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Worked for an online casino software provider for 14 years. Taught the basics of real odds vs offered odds (the difference is known as the house edge) and the only strategy to win at an odds based casino game is to own the game and encourage as much play as possible. This is why casions balk at large, single plays, and encourage the players to increase their number of plays with smaller denomination machines and bets. As game play tends to infinity,  the house edge tends to a guaranteed income.

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Thank you. YouTube is flooded with "systems" to beat these games, but the basic math ALWAYS says "no." Yet, the comments sections are filled with people in huge denial, often citing anecdotes about how they beat the odds and won.

If they did beat the odds, it's due to variance. We don't lose exactly on the trend line. Sometimes we come out ahead. More times we come out behind. And there's no way to predict when that is.

If a casino game could be beaten, they'd change they payouts to make it less profitable so players would still come out behind. This happens with video poker, where the payout table is crucial. (And usually ignored by players, to their detriment.)

The only casino game that can be beaten is blackjack. But to beat it, you have to play perfect strategy, maintain a running count, convert that to the true count, play variances on perfect strategy based on the count, and vary your bets widely when the count is in your favor. And you have to do all of this while not getting detected by the casino staff. Contrary to popular belief, counting cards is not cheating, nor is it illegal. But the casino can "back off" a player it suspects of card counting, refusing to take his/her bets. The math in card counting is easy. Managing the process is incredibly difficult.

So, why don't casinos just get rid of blackjack? Because it's incredibly popular. They also don't like to back off "advantage" or "skill" players because it looks bad. So, they've resorted to other means of drawing in the suckers and discouraging the card counters. Three important changes are (a) game variances, (b) changed payouts, and (c) automatic shuffling machines.

The casinos are offering more "blackjack-like" table games. But these are horrible, with the odds stacked in favor of the house. The house has also implemented rule changes (like eliminating the surrender rule or what you can or cannot double-down on) and payouts. (The worst of these is the switch to 6:5 payouts for blackjacks. This reduces the card counter's edge, sometimes eliminating it and making the game not worthwhile to play.) Finally, some houses have introduced automatic shuffling machines to eliminate card counting. Period.

What about all the other casino games, like craps, roulette, keno, the wheel of fortune, etc.? They're all bad bets with house odds stacked against you. Have fun. Gamble. But you're playing a losing game. Be comfortable with that.

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Great video.  I find the 'Wizard of Odds' an excellent place to learn about gambling and the odds of going broke, which is more often than not when visiting a casino.

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It's always good knowing what percentage odds the specific casino will allow you to take on your pass line bet. And yeah, house blackjack rules can alter odds as well as the number of decks being used.

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A simple coin toss can show house edge. Natural odds for a coin toss are 50%, only allowing for proper outcomes. So, if a casino offers you $1.95 for heads on $1 bet and $0 for tails, using 10 flips as a proxy for infinity (note over 10 flips these will NOT be the results,  but we're using 10 flips to proxy an infinite number of plays):
Over these proxied 10 flips 5 will be H, 5T. Income is $10 (10 bets at $1 each), winnings paid will be 5 x 1.95 = 9.75. Thus the house keeps 25c of every $10 when the flips tend to infinity. This is a house edge of 2.5%. As the number of plays tends to infinity, the house is almost guaranteed to keep 2.5% of the bets taken.

The casino has no control of the outcome of an individual bet, but they do have control over how much they OFFER you for a win, and this offer is always less than the natural odds. Slot machines don't 'get hot' or are about to pay out.

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If you are good at card counting, you can get an edge in your favor of up to about 0.5% (in blackjack)

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The only game you can play in the casino with no house-edge is old-fashioned Poker (not the video/tablegames versions).  And that's entirely because it's the one game where the house isn't actually playing (you only win or lose based on the other players at the table).  The only money the casino makes from Poker is from their fees for hosting the table (rake/time)

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Roulette is the worst game in the house.  For instance, if you place your bet on 14 and  the ball lands on fourteen, you only get 35 times pay.  However, there are 37 numbers showing.  You should get paid 37 times.

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More about house edge and the line bet on craps (from a career dealer, not a math head)...
It is true that in any casino that offers table games, the best possible bets in terms of house edge are the line bets and come bets. However, reducing house edge requires betting the odds behind the line, and if one is serious about reducing house edge to the lowest possible degree, the player needs to bet the maximum odds allowed. The more odds the house allows (some only allow odds of 2x the pass line bet, others go as high as 100x), the lower the player can reduce the edge by betting the maximum odds.

Come bets and line bets are essentially the same - a flat bet with odds for a number to repeat before a 7. The strategy decision the player has to make is how many numbers to cover. Three numbers is pretty standard, but your bankroll and risk tolerance are going to determine how extended you're willing to be on default.

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You can change the house edge to your favor by counting cards in blackjack, which is NOT cheating or illegal.
But you should do your research before you try. You really have to get it perfect for it to work.

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The House has an edge which covers all kinds of expenses and overheads and (normally) even makes a profit.  But we players have an advantage over them because we are (or should be) 100% in control as to when to play, how to play, how much or little we play, when to stop etc etc.  In fact when it comes to systems/strategies they can never GUARANTEE you win, are never INFALLIBLE; but what they do is they make it easier for you to exercise your free will and have preset goals and limits so you don't get emotionally involved and take the wrong decisions.

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Sadly none of this matters, as every game is rigged electronically now, meaning the house edge is more like 75%

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Here's one aspect of roulette wheels. If they are the traditional mechanical type (vs "virtual" wheels) that machine, over time, will exhibit biases which, if discovered, can actually tip things against the casino.

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There is exactly one bet at the casino with no house edge. That is the "odds" bet on the craps table. The "odds" bet will pay you the exact odds on hitting that role making it a neutral EV bet.

The casino takes a small edge on the 1 to 1 payout on the pass line itself (required in order to play the "odds" bet).

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I always assumed when I saw 97% payout   that it meant you lost 3% everytime you bet - you'd lose everything over time

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OUR FAVORITE (Yes our favorite) statement from new players ( and some old players) is : YES But I win with the 7 & the 11 on the pass line and come bet-  Oh Gee whiz.   OK sit down and work out the "real math" of that statement: You have 8 ways to win on the come out roll with the 7 & 11. That is a very low 22.22% ( less than 25% or 1 in 4) VS 28 ways ( 77.77%) Over 75% that you will lose with the 2,3,&12 or roll a point number 4-10 that you now have to roll TWICE to win and only pays even money. That is a good bet??  Those are not very good odds for the pass/come bettor. 22.22% VS 77.77% This is known as "Casino math ( House edge) VS Real math ( ROI). Any questions? Enjoy the show!!! Casino Math VS Real Math. ☯ "All This house edge is Crap with a Capital C in Craps" From the show on Y.B "Casino Math ( House edge) VS Real math ( ROI $$) .