Cancer Lottery is a Scam: What are the odds of that?

So one of my pet peeves came up again this week.

See, I got a flyer for the "Cash for Cancer Lottery" to help support the Oshawa Hospital Foundation. All things being equal, I figure this is a worthy cause and I'm glad they make money off this.

My problem is the advertising.

The flyer promotes amazing "1 in 7 odds you'll win!" Those odds really are amazing - because they're a complete fabrication.

They sell 87,500 tickets and draw roughly 12,500 tickets. That's about 1 in 7 right? Sounds pretty good.

Oh, but wait; it gets better.

You get multiple chances of winning because - get this - they put the drawn names back into the "barrel" after each draw. Wow! Awesome, right?

Wrong. You just failed math.

If they drew all 12, 500 tickets in one shot, yes, you'd have 1 in 7 (12,490 in 87,500) odds of winning. But they don't. They draw one ticket out of 87,500 each time.

Put it this way: I have 100 tickets. I'm going to draw 50 winners in one shot. What are your odds of winning? 50%, right? What if I draw one winner, put the ticket back in and draw 49 more times, one at a time? Is it still 50%?

Nope.

You following this? Ok, let's make it simpler.

I have 100 tickets. I draw 100 winners in one shot. What are your odds of winning? 100%, right? You are definitely going to win. Way to go.

But if after each name I draw I put the winning ticket back in, what are your odds of winning? 100%? Nope. (The original winner could win again, thus usurping your victory - bastard!)

So if the odds aren't 1 in 7, but actually something not quite as good, what are your odds of winning?

Uh...I don't know. I didn't take Probability and Statistics. Didn't need it to get into Theatre.

But I am smart enough to know that it's something akin to this: I flip a coin. What are the odds it'll come up heads? 1 in 2, right? 50%? Good. Now, does that mean that if I flip the coin twice that I'm guaranteed to get heads at least once? Nope. I could get tails twice. You have to look at the possibilities.

Heads + Heads
Heads + Tails
Tails + Heads
Tails + Tails

So, if I flip a coin twice, my odds of getting heads at least once is 75%...that's not quite the same as 100%, is it?

Now, I ask again: if there are 87,500 tickets and I draw one name at a time 12,500 times, but put the winner back each time, what are my odds of winning?

Worse than 1 in 7, that's for sure.

Here's a better question: why are these lotteries allowed to get away with this blatant false advertising?!

I'm calling them right now...