are going to prove that you do get a turn in the winners seat.
There is the fact that the games are using random number generator programs to provide game results, the gold standard in the industry for providing fair-odds games served in a completely and absolutely random manner. The way a RNG works is it has a list of all the possible outcomes for that particular game which it scrolls through at thousands of times per second and the instant the player presses the spin button, or deal or roll the dice button, that RNG stops scrolling through that list of possible outcomes and whichever one it lands on is what is returned to the player for a game result.
All the above said, I offer a personal experience as the reason I know the games are fair. I was playing video poker and increasing my credit values as I went along catching more wins and I had just increased the credit values from one dollar to the maximum this casino allowed which was five dollars per credit value. Incredibly the game dealt me a king high straight flush. The payout on it would match the payout on a royal flush at the credit level I started out wagering. The story gets much better than that however.