Odds of winning a mature Queen of Hearts game?

If you are not familiar with the game: A new deck of cards including the jokers is shuffled. Each card is placed in a sealed envelope and those are shuffled. Then a set of 1 to 54 numbered balls or something is used to assign numbers to each envelope. They are arranged in a grid that is locked up until each week’s drawing.

Tickets are a dollar each and are sold in several area bars. Each week (or every other week) all the tickets sold that period are dumped in a hopper and one is drawn. The numbered envelope written on the ticket is opened. If it is the Queen of Hearts you win the pot. There are some small weekly awards and 10% of the pot is used to start the next game but that doesn’t effect the odds. A sheet showing all the remaining numbers is posted in each location where tickets are sold.

So now this game is “mature”. It has been going on for 88 weeks. This week there were ten envelopes remaining. The pot is over 2 million dollars. 100,000 tickets were sold for the drawing. Pretty good payout for the odds. I bought ten tickets and wrote one of the ten remaining numbers on each. So what were my odds of winning? (I didn’t).

The way I figure it is this: I had ten tickets and 100,000 were sold so the odds of one of my tickets being drawn was 100,000/10 = 10,000 to 1. But that ticket only has a one in ten chance of being the correct number on it, so 10 x 10,000 = 100,000 to 1 for me. Is that all there is to it?

Yeah. The two are independent events, so all you have to do is multiply one with the other.

Or to put it another way. Of the 100,000 tickets, there is one winning ticket with your name on it. If they draw that ticket you win. If they draw any other ticket, either a ticket without your name, or one of the nine tickets that have your name but have the wrong number, you lose.

So 1/100,000.