Calculating Raffle Ticket Odds

I'd have to get my books out, but it's something to do with permutations (nPr), and I'm pretty sure it's an easy calculation...

either that or something like this:

p(exactly 1)

1/3000 + 1/2999 + 1/2998 + 1/2997 . . . 1/2901

p(exactly 2)

da da da

yes a little vague sorry, but this time last year i could have told you easily.

you have got me thinking now! i'd like to know the answer

Just Betting Exactas and Quinellas

wheel the #8 horse the next time you're at the track.

Send me half the money.

This may not be what Your looking for but interesting non the less.

In a similar raffle afriend of mine had 24 of the possible 25 winning tickets, unbelievably the ticket that won was the one He did not have!

oilcan13

Very interesting raffle.

I think that you would find that type of raffle would be illegal in the UK. All raffles sold to the general public must meet with the Lottery, Betting and Gaming Act in which ALL must have an equal chance of winning the first prize.

The raffle, as you describe, is totally unfair inasmuch as the first pre selection of 100 tickets excludes the remainder a fair chance of winning. The second stage is also unfair as the first 99 drawn are also excluded from a fair chance of winning.

My suggestion would be to check on the legality of this type of raffle and secondly, not to work out what chances of winning but what are the chances of losing!

Raffles conducted within a closed function do not need to be registered with the necessary Act. Tickets on sale to the public must also identify the organiser.

Tony

Your posting reminded me of a related situation, which I'd like to post now as another puzzle.

The following may seem a concocted math puzzle, but it actually happened. Some years ago, I had been working at the installation of the electronic equipment for a Bingo House. During the "Grand Opening", a motorcycle was to be awarded to the first person getting bingo. As there were many people engaged to gambling, three of them got bingo at the same time. Then I suggested that the fairest way to break the tie would be letting them choose a different number, and then starting to (randomly) pick balls until one of those numbers were found. But the manager told me that it would be too time consuming, and decided that each of the candidates chose a number, and then just one ball were picked, so that the number being closest to that on the ball would win.

The first person asked chose 82; the second, 13. The third person was a lawyer, who was sitting by my side, and his choice was 10 (For those who are not familiar with bingo gambling, the numbers on the balls range from 1 to 90). Then a ball was randomly picked, and its number happened to be 37, so the second person, having chosen the 13, was favored.

Ten minutes later, the lawyer suddenly turned to me and said:

-- I think I made a stupid choice, didn't I?

-- You surely did,—I answered—but don't forget you're a lawyer.—He didn't take any offense (nor sued me, which is more important).

Had he chosen any number between 14 and 81, he would have had a fat chance (38.33%). Instead, his poor choice gave him a tiny chance of only 13.33% (just the numbers from 1 to 11).

So far, this seems crystal-clear. But, which would have been the best strategies for participants 1 and 2 (supposing that everyone expected the others to do their best)? The more I re-read my draft, the more it sounds to me as a set up, but it actually occurred, and I find that amazing. I didn't think about it since then, but now I realize that it is a challenging problem.

So, I hope learning from your opinions, and will try to get my way and post my own point of view after this question is settled (not by a lawyer, of course).

That's a delightful puzzle, all the more so for being real-life. You might consider presenting it as a challenge question. Now I'll have to start thinking about it!

If you do present this as a challenge question, you will need to state the conditions precisely. If the three persons announce their choices aloud and in order, persons 2 and 3 will have advantages. If all three make their selections silently and write them down, the whole story will be different, and different strategies will apply.

I will hold this in reserve for a few days, but if you don't submit it, then I may.

Tornado:

First, I'd suggest considering three men. This would save a lot of "she/he" and "his/her". The rule is: each one makes his choice and then announces it aloud (in order).

At first I viewed the problem exactly as you did: the first man would have a disadvantage. But later I discovered that this puzzle is counterintuitive enough to be interesting.