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House Edge Index Last Update: June 30, 2005 The following tables shows the house edge of most casino games. See below the table for a d efinition of the house edge. b Las Vegas single deck rules are dealer hits on soft 17, player may double on any two cards, player may not double after splitting, one card to split aces, no surrender. c Assuming player plays the house way, playing one on one against dealer, and half of bets made are as banker. f Slot machine range is based on available returns from a major manufacturer g Slot machine standard deviation based on just one machine. While this can vary, the standard deviation on slot machines are very high. House Edge The house edge is defined as the ratio of the average loss to the initial bet. The house edge is not the ratio of money lost to total money wager ed. In some games the beginning wager is not necessarily the ending wage r For example in blackjack, let it ride, and Caribbean stud poker, the player may increase their bet when the odds favor doing so. In these cas es the additional money wagered is not figured into the denominator for the purpose of determining the house edge, thus increasing the measure o f risk. The reason that the house edge is relative to the original wager, not the average wager, is that it makes it easier for the player to estimate ho w much they will lose. For example if a player knows the house edge in b lackjack is 06% he can assume that for every $10 wager original wager h e makes he will lose 6 cents on the average. Most players are not going to know how much their average wager will be in games like blackjack rel ative to the original wager, thus any statistic based on the average wag er would be difficult to apply to real life questions. The conventional definition can be helpful for players determine how much it will cost them to play, given the information they already know. How ever the statistic is very biased as a measure of risk. In Caribbean stu d poker, for example, the house edge is 522%, which is close to that of double zero roulette at 526%. However the ratio of average money lost to average money wagered in Carribean stud is only 256%. The player onl y looking at the house edge may be indifferent between roulette and Cari bbean stud poker, based only the house edge. If one wants to compare one game against another I believe it is better to look at the ratio of mon ey lost to money wagered, which would show Caribbean stud poker to be a much better gamble than roulette. Many other sources do not count ties in the house edge calculation, espec ially for the don't pass bet in craps and the banker and player bets in baccarat. The rationale is that if a bet isn't resolved then it should b e ignorred. I personally opt to include ties although I respect the othe r definition. Element of Risk For purposes of comparing one game to another I would like to propose a d ifferent measurement of risk, which I call the "element of risk." This m easurement is defined as the average loss divided by total money bet. Fo r bets in which the initial bet is always the final bet there would be n o difference between this statistic and the house edge. This statistic is commonly used to calculate the probability that the end result of a session of a defined number of bets will be within certain bounds. The standard deviation of the final result over n bets is the product of the standard deviation for one bet (see table) and the square root of th e number of initial bets made in the session. The following table shows the probability that a session outc ome will come within various numbers of standard deviations. Number Probability 025 01974 050 03830 075 05468 100 06826 125 07888 150 08664 175 09198 200 09546 225 09756 250 09876 275 09940 300 09974 325 09988 350 09996 375 09998 I realize that this explanation may not make much sense to someone who is not well versed in the basics of statistics. If this is the case I woul d recommend enriching yourself with a good introductory statistics book.
Hold Although I do not mention hold percentages on my site the term is worth d efining because it comes up a lot. The hold percentage is the ratio of c hips the casino keeps to the total chips sold. For example if blackjack table x takes in $1000 in the drop box and of the $1000 in chips sold the table keeps $300 of t hem (players walked away with the other $700) then the game's hold is 30 %. If every player loses their entire purchase of chips then the hold wi ll be 100%. It is possible for the hold to exceed 100% if players carry to the table chips purchased at another table. A mathematician alone can not determine the hold because it depends on how long the player will s it at the table and the same money circulates back and forth. There is a lot of confusion between the house edge and hold, especially among casi no personnel.
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