Notes:

a

Atlantic City rules are 8 decks, dealer stands on soft 17, player may double on any two cards, player may double after splitting, one card to split aces, no surrender.

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.

d

Yet to be determined.

e

Standard deviation depends on bet made.

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.

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 how much they will lose. For example if a player knows the house edge in blackjack is 0.6% he can assume that for every $10 wager original wager he 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 relative to the original wager, thus any statistic based on the average wager 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. However the statistic is very biased as a measure of risk. In Caribbean stud poker, for example, the house edge is 5.22%, which is close to that of double zero roulette at 5.26%. However the ratio of average money lost to average money wagered in Carribean stud is only 2.56%. The player only looking at the house edge may be indifferent between roulette and Caribbean 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 money 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, especially 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 be ignorred. I personally opt to include ties although I respect the other definition.

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 the number of initial bets made in the session. This assumes that all bets made are of equal size. The probability that the session outcome will be within one standard deviation is 68.26%. The probability that the session outcome will be within two standard deviations is 95.46%. The probability that the session outcome will be within three standard deviations is 99.74%. The following table shows the probability that a session outcome will come within various numbers of standard deviations.

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 would recommend enriching yourself with a good introductory statistics book. There is also a good definition of the term and examples here.