Casino games offered by online casino are designed to provide those house an advantage. Because of this, casinos will win in the long run for any game played. However, players can beat the odds in the short-term and as such win more than they bet.
A simple demonstration of the odds favoring the house can be illustrated by the game of Roulette. One chip placed on a number bet has a payout of 35-1 (i.e. a $1 winning bet returns $36). Note though, that a roulette wheel has 36 numbers plus a zero in European Roulette (and a double zero for American Roulette). As such, the true odds of a the white ball landing in your favor is 36-1 or 37-1. With that in mind, even if a player covered every number on the roulette wheel (which comes to a cost of $38 on a double-zero table recognised as a green "00") they would get back $36, with $2 going to the house.
When looking at card games such as Blackjack, Red Dog, Three-Card Poker or Stud Poker the game odds are determined by the rules of the game in much similar fashion to roulette. However, with certain games such as Blackjack the true odds that a player experiences is dependent on their style of play (i.e. choosing to hit or stick).
Video Poker games odds are set ultimately via the pay table. The true odds of hitting specific winning combinations have been calculated by statisticians. Although it's true that certain Video Poker games have near 100% payback, the paytables, however, do not pay true odds. So even though Video Poker games cannot be fixed in terms of cards that appear, the paytables can be reduced so that the long-term payback is leaned towards the casino's favour.
The one game that can be altered in favor of the host are slots. This is because slot games can be configured so that the difficulty to reach winning combinations can be much higher (e.g. by removing symbols from wheels). Similarly, the paytables can be reduced to again alter the expected payback percentage.
When it comes to common online casino games, all games are really determined by a random number generator that works as a card is turned, a dice is rolled or a slot is spun (which depends on the game being played). However, although this random number generator decides game outcomes, this is only true insofar is cards selected or roulette number selected etc. Games will still play the same as their land-based counterparts. As such, looking for things like full-pay Video Poker games or single-deck blackjack will alter the odds a player experiences for the positive.