Question Regarding The Odds of The Pennsylvania Millionaire Raffle

Reply #23

LottoMetro — Sun, 17 Jan 2016 22:42:21 GMT

PA didn't have a Halloween raffle in 2014 but you're right in that not all have sold out (I believe up until they offered more than 1 per year they did all sell out). The one this past October only sold 356,904 tickets. The ones offered this year seem to have better padding built into the timeframe that tickets are made available.

As I stated earlier you can determine the probability of there being a winner based on tickets sold by simply using a hypergeometric distribution which unsurprising... [ More ]

Reply #22

JADELottery — Sun, 17 Jan 2016 21:19:47 GMT

Thank you.

If we helped to your satisfaction, we'll consider this closed and no more replies.

Good Luck.

Reply #21

sirbrad — Sun, 17 Jan 2016 19:55:22 GMT

Nope, much like a barrel or hat raffle one number wins one prize that is it. The biggest prizes are all drawn first.

5. Prizes: The prizes that can be won in this game are $100, $1,000, $100,000 and $1,000,000. A player may only win one time on each ticket or chance.

Reply #20

sirbrad — Sun, 17 Jan 2016 19:46:26 GMT

They used to sell out all the time, but now they seem to have stopped. They used to advertise them when they go real low but have not seen that lately. So sometimes I get one for better chances yet. I won $100 last year on one ticket and was close to the $1,000 twice, this year by two numbers. They probably don't sell out as much now though as $20.00 is a lot to keep losing and 1 million is not all that much these days. Not to mention the controversial draw error this time, and no one knowing fo... [ More ]

Reply #19

GiveFive — Sun, 17 Jan 2016 19:42:34 GMT

There's been a lot of excellent discussion here regarding odds/chances/probability of the PA Millionaire raffle, and I thank everyone that has contributed to the discussion.

That said, I would respectfully disagree that all Millionaire Raffles have sold out. During the sales cycle of the most recent one, ~474,000 tickets were sold. (Someone here at The LP posted that info, which they said they obtained from the PA Lottery's website.) I believe too, that the Halloween Millionaire raffle held o... [ More ]

Reply #18

JADELottery — Sun, 17 Jan 2016 18:46:22 GMT

We will redirect to the PA Lottery's own Millionaire Raffle #23 rules - http://www.pabulletin.com/secure/data/vol46/46-2/56.html.

...

10. Number and Description of Prizes and Approximate Odds: The Pennsylvania Millionaire Raffle XXIII lottery game prizes and determination of winners are as follows:

Ticket Matching Exactly the Unique Eight-digit Number Drawn: Win Prize Of: Maximum Odds

Of Winning Are 1 In: Number Of Winners

First-Prize-Tier $1,000,000 125,000 4

Second-Pri... [ More ]

Reply #17

LottoMetro — Sun, 17 Jan 2016 01:19:32 GMT

Not sure a simulation is useful unless you believe the sales follow a specific distribution and/or will be less than the maximum allowed tickets. According to PA lottery records, all past Millionaire Raffle drawings have sold out, which pretty much satisfies the advertised odds. As the simulation approaches infinity it will converge on the theoretical (advertised) probabilities.

Just for kicks I ran a simulation of about 2.5 M trials using a beta distribution* with range of sales from 300k to... [ More ]

Reply #16

JADELottery — Sat, 16 Jan 2016 21:37:01 GMT

well that's odd.

we ran through a billion raffle samples and the lowest odds based on sample simulation we came up with in the top 4 prizes was around 1 : 484026.

Reply #15

LottoMetro — Sat, 16 Jan 2016 19:35:55 GMT

Anytime the lottery uses the terms odds or chances they are illustrating probability based on combinatorics. Their usage is not the same as it is in casino games or horse racing. The difference is purely semantic and though academics frequently point this out when reviewing lottery terminology, nobody really cares.

If you take a hypergeometric distribution with sample success of 1, population success of 4, sample size of 1 and population size of 500k, you will calculate that the probability o... [ More ]

Reply #14

JADELottery — Sat, 16 Jan 2016 19:26:24 GMT

actaully, they don't even use the word 'Odds', they use 'Chance'.

from the PA Lottery website:

Chance is an undefined mathematical philosophical pseudonym of probability.

Real probability has mathematical constructs like: probability of success, probability of failure, odds and their interwoven computational relationships.

Reply #13

GiveFive — Sat, 16 Jan 2016 19:13:59 GMT

Couldn't agree more.

Yes, it's a raffle, so 4 out of 500,000 tickets are guaranteed to win $1,000,000. So that's 4/500,000 or 0.000002%. And if you reduce 4/500,000 to it's least common denominator of 1/125,000 that's also 0.000002%. So technically, the odds can be stated as 1/125,000. And that's why the PA Lottery can advertise odds of 1/125,000.

But as can be seen in JADE's posts above, the odds are really 1 : 499,999, 1 : 499,998 etc. But if they advertised the odds in that particular f... [ More ]

Reply #12

JADELottery — Sat, 16 Jan 2016 18:33:36 GMT

Let's look at the manual aspect of a raffle.

If we assume there are 500,000 raffle tickets sold and each prize winning ticket is drawn one at a time from the mixing drum, then we need to examine what is happening at each moment of selection.

In the 1st Top Prize, one ticket is selected from the drum of 500,000.

The odds of one purchased ticket winning the 1st Top Prize is 1 : 499,999.

Now, the drum is closed and the tickets are mixed again.

How many tickets a left in the drum... [ More ]

Reply #11

JADELottery — Sat, 16 Jan 2016 18:16:52 GMT

The sequential nature of a raffle is verified by the PA Lottery's own Millionaire Raffle #23 rules.

From the PA State Lottery Law,

7. Conduct of Drawing: The results of the Pennsylvania Millionaire Raffle XXII lottery game will be posted to the Lottery's publicly accessible website on January 2, 2016, at or after 10:00 p.m. A computer-generated randomizer will be used to conduct the drawing. Six-thousand (6,000) unique eight-digit numbers will be drawn from the range of numbers repre... [ More ]

Reply #10

JADELottery — Sat, 16 Jan 2016 17:53:52 GMT

Before we get into the logic of why we say the odds are as stated, we need to understand the truest sense of what a raffle is.

Raffles are similar to Lotteries in the fact they are a game of probability.

However, that's where the similarity ends.

Raffles differ from Lotteries because they guarantee a prize will be won by someone at the time of selection, Lotteries do not.

Typical manual raffles use a ticketing system where one buys a dual ticket stamped with identical numbers; seen b... [ More ]

Reply #9

GiveFive — Fri, 15 Jan 2016 23:50:49 GMT

What are Odds ? They're simply a tool used to measure the probability of something either happening or not happening.

In the case of playing the lottery, they're when the probability that the event will not happen is greater than the probability that it will, then the odds are said to be against that event happening.

Players don't buy odds. They buy tickets. See, I have trouble with the PA lottery advertising the odds for the Millionaire raffle being 125,000 to 1 (against the player) Yes,... [ More ]

Reply #8

GiveFive — Fri, 15 Jan 2016 22:54:21 GMT

To me, the above explanation makes the most sense.

The first four unique eight-digit numbers drawn will be the first-prize-tier winning numbers. A player may win only one time on each ticket. So that means after each one is drawn, it is no longer eligible to win any other prize.

Sure, from a mathematical calculations stand point, 4/500,000 yields the same results as 1/125,000. But, assuming all 500,000 tickets are sold, after the first ticket number has been drawn and is removed from the

Reply #7

JADELottery — Wed, 06 Jan 2016 22:58:22 GMT

If the raffle only sold 375,000 tickets and you only purchased 1 ticket, then the odds for winning the top 4 prizes are:

1st Top Prize Odds 1:374,999

2nd Top Prize Odds 1:374,998

3rd Top Prize Odds 1:374,997

4th Top Prize Odds 1:374,996

Reply #6

dr65 — Wed, 06 Jan 2016 21:58:54 GMT

Jade, what are the odds when the tickets sell only to the quarter point and the 4 top winners

are in that first 125,000 but they sell 375,000 tickets out of 500,000?

I think your answer above has made at least 2 posters happy....now the OP still has the task

explaining it.

Reply #5

JADELottery — Wed, 06 Jan 2016 15:34:05 GMT

Assuming all raffle tickets are sold and one raffle tick is purchased, then the Odds for winning the 4 Top Prizes are:

1st Top Prize Odds 1:499,999

2nd Top Prize Odds 1:499,998

3rd Top Prize Odds 1:499,997

4th Top Prize Odds 1:499,996

Reply #4

GiveFive — Wed, 06 Jan 2016 11:54:42 GMT

Here's something else I'm curious about regarding the raffle.

Can a player win a prize twice with the same ticket number?

I would think that once ticket number, 00123456 had won a prize, it would no longer be eligible to win another one, ie that it would be removed from the prize pool of 500,000 possible winners. Anybody know?

And... are the first 4 numbers drawn (and I'm using that term loosely) the top prize winners? I guess there's a lot I don't know about the raffle! G5... [ More ]

Reply #3

dr65 — Wed, 06 Jan 2016 11:30:43 GMT

Overall odds are that there are 4 winners in 500,000 tickets so simple math would calculate to 1/125,000

If the 4 top prize tickets were sold in the first 4 tickets, that would seem to throw the odds out of whack and that's

probably where the disagreement comes in at work.....they/you are thinking in terms of top prize winnings being sold right

off the bat..then what happens to the odds?...it makes some sense thinking like you do and if that scenario happened,

it would seem the odds... [ More ]

Reply #2

GiveFive — Wed, 06 Jan 2016 02:40:19 GMT

Thank you. Your explanation made perfect sense to me.

That said, I'm definitely not going to try to explain to the guys in my pool why it's so. See, we're a bunch of cranky old curmudgeons, and we'll throw down in a heart beat. Matter of fact I though that's exactly what was going to happen today when the argument began!!

I can see the headline in the local newspaper now; Old Fools Brawl at IBM Plant! Lotto argument causes punches to fly

Reply #1

Murgatroyd — Wed, 06 Jan 2016 01:07:59 GMT

There are at most 500,000 tickets, of which exactly four will win the top prize. If all the tickets are sold, the chances of a given ticket winning are exactly 1 in 125,000. If the deadline passes before all the tickets are sold, the chances of winning are better at 4 in however many tickets were actually sold.

You're right that if the top prizes are the first ones drawn, the chances of your ticket being the first, second, third, or fourth are 1/500000, 1/499999, 1/499998, and 1/499997 r... [ More ]

Question Regarding The Odds of The Pennsylvania Millionaire Raffle

GiveFive — Tue, 05 Jan 2016 21:00:12 GMT

Hopefully someone smarter than I can answer a question regarding the odds for the Pennsylvania Millionaire Raffle and help to settle an argument at the same time.

A little background. Yesterday at work, the members of the pool that I run for the PA Millionaire Raffle were discussing the latest raffle. Someone said The odds are 125,000 to 1 to which another person replied No they're not. Not really And that's when the argument got started.

Assuming all 500,000 tickets are sold, why are the... [ More ]