What you say is correct, Gene. You made two separate bets, each that you would get a royal in one spin.

However, if you had been able to place a bet with the casino before the first win that you would get two in sequence, you should have been offered much higher odds... like 1.3 billion to one!

That's the difference between a priori and a posteriori probabilities. One has the benefit of hindsight... the other does not. Haven't you run into the concept of compound probablilities somewhere in your long gaming career?