Opportunity Cost of a Casino Promotion

This past week Harrah's Casino in Chester, PA held a promotion where selected patrons could come to the casino and redeem a gift card of a random amount between 20 and 100 dollars. The casino received many more patrons than expected and began to give out free slot play once demand exceeded the supply of gift cards. In fact, there was a line of over two hours to reach the promotional table.Was the over two hour wait worth the gift card promotion?  The most basic principle of economics- that if a  transaction takes place then both the buyer and seller agree on the price an good- tells us that people thought the gift card promotion was worth the wait. But what exactly was the good and what exactly was the price?Determining the good is not difficult. The specific terms of the promotion are not available to this author, but a simple expected value equation would solve that problem. If the chance of "winning" the gift card game (receiving the $100) is even and uniformly distributed then the expected value of the game is $60.  I am sure that the odds were not even (this was at a casino none-the-less), so lets say that the expected value of the game was $50.  So the "good" was a chance of winning $50, with a guarantee of $20.The price is significantly more difficult to figure out.  There was no explicit monetary risk for the patrons.  Instead, patrons had to give up their time, which in econ 101 you learn is the "opportunity cost."  On a Saturday morning, what was their opportunity cost? After many patrons received a $20 gift card (implying that the expected value was probably on the lower end of the spectrum), there were some grumblings that their time could have been better spent.  But, doing what?  Two extra hours of overtime at work may have resulted in a payoff greater than $20 or even the expected value of $50, but the opportunity to work overtime is diminishing.  Production in the home is probably more valuable than a $20 gift card, but $50... thats a lot of groceries... or a nice dinner.Ultimately, despite the grumblings that the promotion was not worth the wait- implying that the opportunity cost was too high- the ultimate economic principle proves the opposite.  People came to the venue (most likely an hour total commute), waited in line for two hours, and were paid by a lottery guaranteeing $20 with a slightly higher (no more than $50) expectation value.  Thus, the transaction took place so the value of the good was equal to the cost.