[oleganza]

Not exactly. It means, you can check two things after you have played:

1. The random number was generated before you even started. So the house could not change the number depending on the actual bets.

2. Distribution of random numbers over time. E.g. if the rule is "win when uniformly random number 0..1 is greater than 0.5", then you can check the history of all random numbers played (at least with your bets, if you don't trust the house to show real bets for other players) and calculate the properties of actual distribution. If it does not contain a significant offset, then it's fair. (Small deviations can be seen simply as part of the fee.)