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What is the House Edge?
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Introduction
The house edge can be understood as the proportion of the average loss compared to the initial wager . In various games, the initial stake doesn't necessarily remain unchanged until the end of the game. For instance, in blackjack, let it ride, and Caribbean stud poker, players have the option to increase their bets when the circumstances are favorable. Additional bets made are not included in the calculation of the house edge, which can lead to an elevated perception of risk. Games like Ultimate Texas Hold 'Em and Crazy 4 Poker, which require two initial bets, calculate their house edge based only on one of those wagers. The figures for house edge are typically grounded in optimal or near-optimal strategies utilized by players.
The following table illustrates the house edge associated with the most played casino games and their respective bets.
Casino Game House Edge
| Game | Bet/Rules | House Edge | Standard Deviation |
|---|---|---|---|
| Baccarat | Banker | 1.06% | 0.93 |
| Player | 1.24% | 0.95 | |
| Tie | 14.36% | 2.64 | |
| Big Six | $1 | 11.11% | 0.99 |
| $2 | 16.67% | 1.34 | |
| $5 | 22.22% | 2.02 | |
| $10 | 18.52% | 2.88 | |
| $20 | 22.22% | 3.97 | |
| Joker/Logo | 24.07% | 5.35 | |
| Bonus Six | No insurance | 10.42% | 5.79 |
| With insurance | 23.83% | 6.51 | |
| Blackjack a | Liberal Vegas rules | 0.28% | 1.15 |
| Caribbean Stud Poker | 5.22% | 2.24 | |
| Casino War | Go to war on ties | 2.88% | 1.05 |
| Surrender on ties | 3.70% | 0.94 | |
| Bet on tie | 18.65% | 8.32 | |
| Catch a Wave | 0.50% | d | |
| Craps | Pass/Come | 1.41% | 1.00 |
| Don't pass/don't come | 1.36% | 0.99 | |
| Odds — 4 or 10 | 0.00% | 1.41 | |
| Odds — 5 or 9 | 0.00% | 1.22 | |
| Odds — 6 or 8 | 0.00% | 1.10 | |
| Field (2:1 on 12) | 5.56% | 1.08 | |
| Field (3:1 on 12) | 2.78% | 1.14 | |
| Any craps | 11.11% | 2.51 | |
| Big 6,8 | 9.09% | 1.00 | |
| Hard 4,10 | 11.11% | 2.51 | |
| Hard 6,8 | 9.09% | 2.87 | |
| Place 6,8 | 1.52% | 1.08 | |
| Place 5,9 | 4.00% | 1.18 | |
| Place 4,10 | 6.67% | 1.32 | |
| Place (to lose) 4,10 | 3.03% | 0.69 | |
| 2, 12, & all hard hops | 13.89% | 5.09 | |
| 3, 11, & all easy hops | 11.11% | 3.66 | |
| Any seven | 16.67% | 1.86 | |
| Crazy 4 Poker | Ante | 3.42%* | 3.13* |
| Double Down Stud | 2.67% | 2.97 | |
| Heads Up Hold 'Em | Blind pay table #1 (500-50-10-8-5) | 2.36% | 4.56 |
| Keno | 25%-29% | 1.30-46.04 | |
| Let it Ride | 3.51% | 5.17 | |
| Pai Gow c | 1.50% | 0.75 | |
| Pai Gow Poker c | 1.46% | 0.75 | |
| Pick ’em Poker | 0% - 10% | 3.87 | |
| Red Dog | Six decks | 2.80% | 1.60 |
| Roulette | Single Zero | 2.70% | e |
| Double Zero | 5.26% | e | |
| Sic-Bo | 2.78%-33.33% | e | |
| Slot Machines | 2%-15%f | 8.74g | |
| Spanish 21 | Dealer hits soft 17 | 0.76% | d |
| Dealer stands on soft 17 | 0.40% | d | |
| Super Fun 21 | 0.94% | d | |
| Three Card Poker | Pairplus | 7.28% | 2.85 |
| Ante & play | 3.37% | 1.64 | |
| Ultimate Texas Hold 'Em | Ante | 2.19% | 4.94 |
| Video Poker | Jacks or Better (Full Pay) | 0.46% | 4.42 |
| Wild Hold ’em Fold ’em | 6.86% | d |
Notes
- In Vegas Strip blackjack, the rules are quite accommodating: the dealer stands on a soft 17, players can double down on any pair of cards, and they are also permitted to double after splitting. Additionally, players can resplit aces and take a late surrender option.
- The single deck rules in Las Vegas stipulate that the dealer must hit on a soft 17. Players can double down on any two cards, but they cannot double down after splitting, and only receive one card when they split aces. Surrender is not an option.
- Assuming that the player adopts the house strategy and plays against the dealer in a one-on-one scenario, with half of the bets placed being on the banker.
- Yet to be determined.
- The standard deviation is influenced by the size of the bet placed.
- The variability in slot machine payouts primarily stems from the returns set forth by major manufacturers.
- The calculations for standard deviation in slot machines are often based on a single machine. Although there can be exceptions, the standard deviation for these machines tends to be significantly high.
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Guide to House Edge
The reason we consider the house edge relative to the initial bet rather than the average bet is that it simplifies the player's understanding of expected losses. For instance, if a player knows the house edge for blackjack is 0.6%, they can anticipate losing around 6 cents for every $10 they originally wager. Most players may not accurately gauge their average wager in blackjack compared to the initial stakes, making it challenging to apply statistics based on average betting amounts to practical scenarios.
Understanding the conventional definition aids players in estimating their gaming costs based on known information. Yet, this statistic can be misleading as a true indicator of risk. For example, Caribbean stud poker has a house edge of 5.22%, which is only slightly lower than the 5.26% found in double zero roulette. However, when examining the ratio of average money lost compared to money wagered, Caribbean stud's figure stands at just 2.56%. A player focusing only on the house edge might see no distinction between roulette and Caribbean stud poker when, in reality, a better comparison would derive from the ratio of losses to wagers, indicating Caribbean stud poker could be a far superior choice.
Many sources exclude ties when calculating the house edge, particularly in regards to Don't Pass bets in craps and the banker and player bets in baccarat. The logic follows that unresolved bets shouldn't factor into the calculations. I personally favor including ties, although I acknowledge the differing viewpoint.
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Element of Risk
In discussing risk across different games, I propose an alternative measurement that I term the element of risk . This metric is defined as the average loss divided by the total amount wagered . For bets where the initial wager remains unchanged, there will be no significant difference between this measurement and the conventional house edge. Different types of bets are detailed below.
Element of Risk
| Game | Bet | House Edge | Element of Risk |
|---|---|---|---|
| Blackjack | Atlantic City rules | 0.43% | 0.38% |
| Bonus 6 | No insurance | 10.42% | 5.41% |
| Bonus 6 | With insurance | 23.83% | 6.42% |
| Caribbean Stud Poker | 5.22% | 2.56% | |
| Casino War | Go to war on ties | 2.88% | 2.68% |
| Crazy 4 Poker | Standard rules | 3.42%* | 1.09% |
| Heads Up Hold 'Em | Pay Table #1 (500-50-10-8-5) | 2.36% | 0.64% |
| Double Down Stud | 2.67% | 2.13% | |
| Let it Ride | 3.51% | 2.85% | |
| Spanish 21 | Dealer hits soft 17 | 0.76% | 0.65% |
| Spanish 21 | Dealer stands on soft 17 | 0.40% | 0.30% |
| Three Card Poker | Ante & play | 3.37% | 2.01% |
| Ultimate Texas Hold 'Em | 2.19%* | 0.53% | |
| Wild Hold ’em Fold ’em | 6.86% | 3.23% |
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Standard Deviation
Standard deviation serves as a measure of how much your bankroll might fluctuate while playing a specific game . This is a common statistic used to assess the likelihood that the final outcome of a gaming session, defined by a specific number of bets, will fall within particular limits.
To determine the standard deviation of the results over n bets, multiply the standard deviation for one bet (as seen in the table) by the square root of the total number of bets made during the session, assuming all bets are of identical value. There is a 68.26% probability that the session outcome will lie within one standard deviation, a 95.46% probability for two standard deviations, and a 99.74% probability for three standard deviations. The accompanying table illustrates the likelihood of a session outcome being within different standard deviation ranges.
I recognize that my explanation may be difficult to grasp for those who aren't familiar with basic statistics. In such cases, I would recommend referring to a good introductory statistics book for clarification.
Standard Deviation
| Number | Probability |
|---|---|
| 0.25 | 0.1974 |
| 0.50 | 0.3830 |
| 0.75 | 0.5468 |
| 1.00 | 0.6826 |
| 1.25 | 0.7888 |
| 1.50 | 0.8664 |
| 1.75 | 0.9198 |
| 2.00 | 0.9546 |
| 2.25 | 0.9756 |
| 2.50 | 0.9876 |
| 2.75 | 0.9940 |
| 3.00 | 0.9974 |
| 3.25 | 0.9988 |
| 3.50 | 0.9996 |
| 3.75 | 0.9998 |
Hold
While I don’t explicitly address hold percentages on my site, it’s a concept worth discussing as it frequently arises. The hold percentage is the ratio of chips that the casino retains compared to the total chips that have been sold. It is typically measured over the course of an entire shift. For instance, if a blackjack table takes in $1000 and retains $300 from that total (with players taking the remaining $700), the hold percentage for that game would be 30%. If all players lose all their chips, then the hold can reach 100%. It's even possible for the hold percentage to exceed 100% if players bring chips from another table. A mathematician cannot solely assess the hold since it depends on how long players remain at the table and how the same money circulates among players. There's often confusion surrounding the distinction between house edge and hold, particularly among casino staff.
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The next table presents details about the average number of hands played per hour alongside the house edge used for comp calculations in various games. The house edge listed in this table is higher than the previously mentioned figures because those were calculated under optimal strategy conditions, while these figures consider player errors and typical betting patterns. This information was shared anonymously by an executive from a major Strip casino and serves as a reference for rating players.
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Hands per Hour and Average House Edge
| Games | Hands/Hour | House Edge |
|---|---|---|
| Baccarat | 72 | 1.2% |
| Blackjack | 70 | 0.75% |
| Big Six | 10 | 15.53% |
| Craps | 48 | 1.58% |
| Car. Stud | 50 | 1.46% |
| Let It Ride | 52 | 2.4% |
| Mini-Baccarat | 72 | 1.2% |
| Midi-Baccarat | 72 | 1.2% |
| Pai Gow | 30 | 1.65% |
| Pai Pow Poker | 34 | 1.96% |
| Roulette | 38 | 5.26% |
| Single 0 Roulette | 35 | 2.59% |
| Casino War | 65 | 2.87% |
| Spanish 21 | 75 | 2.2% |
| Sic Bo | 45 | 8% |
| 3 Way Action | 70 | 2.2% |
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Footnotes
Vegas Strip rules are quite player-friendly: the dealer stands on soft 17, and players have the liberty to double down on any two cards, can double after splitting, can resplit aces, and can opt for late surrender.