Most don't claim to be any more than slot parlors; they emphasize the random number generator, but don't go into detail about how their card games are set up.
From their casino's webpages:

IGS
aka
Aquaonline


"Better than Vegas odds "

Boss Media

Camelot Casino's casino games are based on genuine random numbers. Various computer programs are able to generate pseudo-random numbers. However, Camelot Casino games are played with true random numbers, generated by a radiation monitor. The Geiger-Müller Tube Detector utilizes the unpredictability of background radiation to generate genuinely random numbers.

Camelot Casino adheres to the rules of the Nevada Gaming Commission.

(Mary adds: except those prohibiting taking wagers over the Internet!)

Chartwell

Q: How Do I Know The Game Is Not Fixed?

A: All of our software has been third party audited to confirm that the game is fair and true. All hands are dealt by a certified random number generator using the Lagged Fibonacci method, which has been independently audited. Coral Casino welcomes any of its players to have our software audited for fairness by any reputable third party if they desire.

If you require any further information, please e-mail customer.services@Coral.co.uk

Cryptologic

Casino Australia Blackjack is played and programmed according to Atlantic City Blackjack rules.

Authority: New Jersey Casino Control Commission.

Rule Exceptions: The cards are shuffled after each hand, pairs may not be re-split, and players may not draw additional cards on split Aces.

Diamond

The casino will make its system algorithms and practices available for inspection and review by any legitimate gaming commission or independent testing authority in accordance with generally accepted methods for protecting proprietary information. The random number generator (RNG) generates standard Las Vegas odds and the system maintains an accurate electronic record of all game sessions.

How are the odds created for the casino games?

All payout and odds for our Casino conform to the Nevada Gaming Rules. The odds for the games are created by an advanced Random Number Generator (RNG) module. For all card-based games, the deck or decks of cards are shuffled prior to each hand being dealt.

Dot Com

Fairness

Casino Vega game algorithms have been thoroughly tested. The random number generator used in our software has been tested and found to conform with the results of similar games found in Land based Casinos in Las Vegas with respect to randomness and pay-out frequency. The software developer conducts tests using the random number generator involving a sequence of millions of numbers. Furthermore, the random number generator is tested on an ongoing basis to ensure its continued fairness.


Grand Virtual

Game Fairness and Odds
Q What are your odds?
A All gaming systems are tested continually to ensure that the odds in our casino are the ones typically used in Las Vegas casinos and that all games are totally random.

IGW

Couldn't find any statements about odds, fairness, game results generation.

Microgaming

Aztec Riches Casino is licensed by the Kahnawake Gaming Commission in the Mohawk Territory of Kahnawake, Canada. We use State of the Art gaming software provided by Microgaming Systems, the leading online gaming software provider in the world.
Aztec Riches is dedicated to offering all of our players a fair and enjoyable gaming experience. All of our payout percentages are reviewed by one of the 5 biggest accounting firms in the world, PricewaterhouseCoopers.

Net Entertainment

Randomness

The outcome of the games is generated by a computerised random generator.
Accountability

Our systems, gaming algorithms and practices are available for inspection and review by any legitimate gaming commission, governmental authority or independent testing authority in accordance with generally accepted methods for protecting proprietary information. Ernst & Young is the day-to-day accountant in Mil Treinta y Dos S.a. and also in Net Entertainment.

Certification

CasinoDomain is certified and controlled by the Interactive Gaming Council, the E-gaming Commission and the Internet Gaming Commission.

(Mary sez: all of which don't do anything.)

Fraud

Falsely denying payment on a CasinoDomain account or credit card may result in action against an individual for the amount disputed. In addition, they may also be responsible for the cost of paying the collection agency and/or lawyers processed by an international collection agency with independent representatives in America, Europe and Asia, as well as the costs for round trip airfare, hotel, food, and labor costs for the designated agent to appear in court. Credit card fraud is a serious offence and will be prosecuted to the fullest extent possible. This no tolerance policy of fighting back each and every case of credit card fraud by a designated agent will ultimately cost much more money than the original amount received.

Odds On

It is our mission to provide players with the most enjoyable and rewarding gambling experience online and the best odds in the business. The payouts of all the games are designed to be equivalent to or better than what you would find in the finest of Vegas casinos, ensuring that the payout percentages conform to what would be expected by the Nevada Gaming rules.

Additionally, all information received/transmitted through the Casino software and your Casino server connection is encrypted/decrypted to ensure your security and privacy.

EHNVI operates in full compliance with the Interactive Gaming Council's (
IGC
) Code of Conduct. The
IGC
is the online gaming branch of the Interactive Services Association (ISA).

Playtech

As one of the Web's most respectable and luxurious Online Casinos, We at the Swiss Casino understand the importance of explaining the fairness procedures we have adopted and are practicing on a day to day basis.

The Swiss Casino holds a gaming license from the government of Antigua and Barbuda. It is regulated and monitored by the Antiguan gaming commission but more than that, its operators truly believe that fair gaming is not just a statement. We at the Swiss Casino are truly committed to a professional, friendly and secure gaming experience.

The ‘Dealer’ at the Swiss Casino is actually a computer. To ensure that the performance of this computer is truly random, a sophisticated RNG (Random Number Generator) is utilized. The Random number generator and the Swiss Casino software had been tested by leading international accounting and auditing firms, by running millions of game rounds and analyzing their outcomes. More over, a third party accounting firm is periodically testing the system to ensure its ongoing accuracy. In addition to that, the Swiss Casino average payout percentage, which is the percentage of total winnings to total wagered amounts, is reviewed on a monthly basis to ensure our system on going randomness and fairness.


Real Time Gaming

It is our aim to provide you, our valued customer with the most exclusive entertainment and the best odds in the business. The payouts of all our games are designed to be comparable, and in most times in excess of, the top Casinos in Las Vegas, conforming with the strictest Nevada Gaming rules. Feel free to "PLAY FOR FUN" or with REAL money. All games are independently tested by Safebet™ for accuracy and fairness.


Unified Gaming

(The only software to date that was tested extensively using a robot player. At that time, the positive expectation blackjack was fair!)

WagerWorks

(Actually understates their game fairness...Isle of Man regs are based on Nevada regs.)

Game Audit
PricewaterhouseCoopers Game Payout Reviews
PricewaterhouseCoopers, the world's largest professional services firm, have been engaged to review game payout rates on the HardRockCasino.com site.

The payout rates and the independent report for the previous month's payouts will be posted on the HardRockCasino.com website, accessible by clicking the PricewaterhouseCoopers logo on the homepage.

World Gaming

How are the odds created for the casino games?

The odds for both real money and playing for fun modes are created by a random number generator, which comes from our server. These odds are audited by a third party to ensure they are being created in a fair and random manner.