Author |
Topic: Powerball Expected Value (Read 3217 times) |
|
marsh8472
Newbie
Posts: 27
|
 |
Powerball Expected Value
« on: Nov 28th, 2012, 12:13am » |
 Quote  Modify
|
What is the expected return of a powerball ticket.
Assumptions made for this problem
1) ticket costs $2
2) J = jackpot value
3) T = total people playing
4) Each person's ticket numbers are chosen at random
5) 5 balls selected without replacement from 59 balls labled 1-59 and a powerball selected from 35 possible balls labeled 1-35
6) Jackpots are divided evenly among the winners
7) powerball prizes are listed here http://en.wikipedia.org/wiki/Powerball or at www.powerball.com
 assume no one's playing powerplay
I think the trickiest part of this is accounting for every possible outcome of jackpot winners. It's theoretically possible that everyone could win and have the jackpot divided evenly among them in this scenario. So what's the expected rate of return in terms of J and T?
|
|
 IP Logged |
|
|
|
rmsgrey
Uberpuzzler
    
Gender: 
Posts: 2873
|
|
Re: Powerball Expected Value
« Reply #1 on: Nov 28th, 2012, 5:41am » |
Quote Modify
|
Here in the UK, the National Lottery puts half of each ticket's price into the prize fund, meaning, in the long run, you lose half the money you spend on tickets.
In the short run, a £1 ticket is worth slightly less than 50p most of the time because sometimes no-one wins the jackpot - the un-won jackpot rolls over to the next week, making roll-over draws worth more.
|
|
IP Logged |
|
|
|
marsh8472
Newbie
Posts: 27
|
|
Re: Powerball Expected Value
« Reply #2 on: Nov 28th, 2012, 9:41am » |
Quote Modify
|
Here's what I come up with:
(COMBIN(5,5) x COMBIN(34,1) x 1,000,000 + COMBIN(5,4) x COMBIN(54,1) x COMBIN(1,1) x 10,000 + COMBIN(5,4) x COMBIN(54,1) x COMBIN(34,1) x 100 + COMBIN(5,3) x COMBIN(54,2) x COMBIN(1,1) x 100 + COMBIN(5,3) x COMBIN(54,2) x COMBIN(34,1) x 7 + COMBIN(5,2) x COMBIN(54,3) x COMBIN(1,1) x 7 + COMBIN(5,1) x COMBIN(54,4) x COMBIN(1,1) x 4 + COMBIN(5,0) x COMBIN(54,5) x COMBIN(1,1) x 4 - 169,721,370 x 2) / ( COMBIN(59,5) x COMBIN(35,1) ) + summation Y = 1 to T of COMBIN(T, Y) x ((1/175,223,510)^Y x ((175,223,510 - 1)/175,223,510))^(T-Y) x J / Y)
|
| « Last Edit: Nov 28th, 2012, 12:50pm by marsh8472 » |
IP Logged |
|
|
|
whizen
Newbie
hidden:
Gender:
Posts: 13
|
|
Re: Powerball Expected Value
« Reply #3 on: May 29th, 2013, 4:54pm » |
Quote Modify
|
By the dogs... what an expression! What language is that? I mean, can I copy paste this to see the result on a computer...?
|
| « Last Edit: May 29th, 2013, 4:55pm by whizen » |
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Powerball Expected Value
« Reply #4 on: May 29th, 2013, 10:36pm » |
Quote Modify
|
combin(a,b) is a way to write a!/b!/(a-b)! It's the number of combinations to pick b somethings from a somethings (without replacement).
For example combin(4,2) = 6 because you have only the following 6 combination with 2 numbers picked from 1..4: (1,2) (1,3) (1,4) (2,3) (2,4) and (3,4)
I don't know whether "combin" is a standard way to put it, I see "choose" or just "C" more often. It might be from a specific mathematical programming language.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print