The mathematics of raffle odds

[TrogL]

Ank and I are screaming at each other again.

Say you have a raffle of 1000 tickets.

Ank is convinced that buying several raffle tickets significantly improves your odds of winning the raffle ie. the 2nd ticket gives you 1 in 500, the third ticket gives you 1 in 333.

I'm saying that the first ticket improves your odds because it's impossible to win without a ticket. Every ticket after that is pretty much wasted money. Each ticket has a 1 in 1000 chance of winning. If you buy three tickets you have 3 chances in 1000. You cannot connect the "chances" of the ticket.

Who's right?

[Lostmessage]

1. Are you the one in charge?

You can rig it you know.

[TrogL]

2. The situation is actually a bit more complicated

There's actually 1500 prizes (some better than others) and 500,000 tickets and if you win a smaller prize, your ticket goes back in.

Ank's mathematics still include division at some point, which I claim "connects" the tickets.

[Lostmessage]

5. Your chances are

3

[TreasonousBastard]

13. There's no "connection" between the tickets....

but there is the overall odds of winning something, which is entirely different.

The odds with one ticket on the first drawing are 15/5000, which is pretty crappy. Considering the possibility of the second drawing, and buying multiple tickets, your odds are a lot better than that, but I don't remember the math offhand.

This busines of "connecting" is a fallacy, though.

Consider the oft argued coin toss. The odds of heads or tails is always 50%. The odds of two heads in a row, though, is only 25%. The odds of a hundred heads in a row is enormous.

Each individual toss can go only two ways, assuming we forget about it landing on its edge, falling into a sewer, or being grabbed by a passing crow. Ultimately, heads and tails should even out, but there are random patterns that show up, and the odds of calling the next two, or ten, tosses will always be less than that 50%.

See the fallacy of assuming the odds of individual events are equivalent to the odds of a series of indivisdual events?

In the simplest drawing, Ank is right. Throw a thousand markers in a hat, and your odds are 1/1000. If you have 3 markers in there, your odds are 3/1000. Three times as good, but you'd never know it because you still probably won't win. One in 333 still ain't so hot.

[BrewerJohn]

3. 3 chances in 1000 = 1 in 333

It's a fraction, so just reduce it to lowest terms.
Carried out to it's logical extreme: if you buy all 1000 tickets you are certain to win.
If you buy 500 you have a 1 in 2 shot, no?

[TrogL]

6. I vaguely remember this coming up in stats class

but my stats textbooks is at the office.

It's similar to flipping coin. People think if you flip the coin and comes up tails it SIGNIFICANTLY improves the chances of its coming up heads the next time. No. Each flip has a 50-50 chance.

[Lostmessage]

7. It's 3 Trogl

There is a saying that goes along with it but I can't remember it.

[BrewerJohn]

8. Coin flips are independent events

The tickets are not, because their "chances" are all resolved at once when a winner is drawn.
A better analogy would be a problem where you have 1000 marbles in a bag; one of them is red
and the rest are blue. How does the probability of your drawing the red marble from the bag on
a single try increase if you are allowed to take only one out at a time, or two at once, or 10
at once, or 100 at once, etc?

[Guaranteed]

14. Right...but here's the rub...

With coin-tossing, if you toss a coin and it comes up heads 20 times in a row, some would say that on the 21st flip, the chances of tossing heads are GREATER than 50% because the chance of flipping heads 20 times in a row on a legitimate coin are so low as to be practically impossible. And if chances are that low, it seems as if you may have a rigged coin....thus, increasing the chances that you'll flip heads on the 21st flip.

However, one could never be entirely convinced that the coin is rigged simply by flipping it over and over, even if heads comes up a thousand or a million times in a row. 100% assurance would have to come from inspecting the coin itself, and analytically coming to the conclusion that it is impossible for tails to come up (as would be the case with a two-headed coin). And, if in inspecting the coin (and the surrounding area- magnets? etc.), one comes to the 100% assured conclusion that nothing is rigged, that the coin is legitimate, on the 1,000,001st flip, it would still be a 50/50 shot. :)

[tkmorris]

4. You two are talking past each other

1 chance in 333 is the same as 3 chances in 1000, oddswise. Now go kiss and make up. Or whatever.

:evilgrin:

[Pobeka]

9. Ank.

Look, your argument is based on the % improvement of odds. So, your arguing that the % improvement from the 0th ticket to the 1st is infinite. But improvement doesn't mean a hill of beans compared to the actual probability. You know, it's like the old joke -- "I got a %20 bonus! But 20% of my base pay which is zero is still zero".

There is no diminishing marginal returns on the number of tickets purchased in relation to your chances of winning. If you want to be certain to win buy 1000 tickets. Better hurray up before they're gone!

[Skittles]

10. I SHOULD KICK BOTH YOUR ASSES

FOR BEING MIND-NUMBINGLY BORING. :o

[DS1]

12. OK Skittles, you got me

That was funny :7

[SheilaT]

11. You've also spent three times as much money

to improve your chances, which are still well under one percent.

All I know is that math teachers NEVER buy lottery tickets. I only do if the money is going to a cause I support, such as a charity I like, or my kid's school. And last year I didn't buy a lottery ticket for the school fundraiser because the prize was some stupid big SUV (I can't even recall what behemoth it was) and I was very angry that they'd have a prize like that, rather than some more sensible and fuel-efficient vehicle.