Started to do some math for this since I was curious about the difference between playing the Mega Millions lottery all in one huge ticket or spread out over your life. Ended up making a formula to figure it out:
This is sort of fuzzy numbers, but to simplify it a bit, lets assume a 1/300million chance of winning, you play 5 numbers per week for the next 50 years and the game never changes (odds or price wise).
chance of winning = C
number of times played per week = N
number of years played = Y
(((1-C)^N)^52)^Y
so as an equation:
(1-(((1-C)^N)^52)^Y)100 = x
where x = percentage chance that you will win the lottery in Y years
Had to use wolfram alpha to get something close to accurate for this since the fraction was 20 pages long:
So a 1/23077.5 chance which is actually better than I thought. You have a 0.00433323948191015% chance of winning if you play 5 number sets every week for the rest of your life assuming you live 50 years.
If you bought all the tickets in one batch (5 tickets, $2 per ticket, 52 weeks, 50 years): 5252*50=$26000 which is 13,000 tickets
so if you did this all in one huge ticket one week, you'd have a 13000/300000000 chance of winning or 13/300000
to get a percentage, * 100 which gives us 13/3000 which is:
x≈0.00433333333333333
Very close, slightly better odds but very close. I think i'd still rather play over the course of my life though, considering I don't actually think I'll win the lottery but it makes me feel good to play.
Date_Posted: 2018-07-24 14:02:45
Started to do some math for this since I was curious about the difference between playing the Mega Millions lottery all in one huge ticket or spread out over your life. Ended up making a formula to figure it out:
This is sort of fuzzy numbers, but to simplify it a bit, lets assume a 1/300million chance of winning, you play 5 numbers per week for the next 50 years and the game never changes (odds or price wise).
number of years played = Y
(((1-C)^N)^52)^Y
so as an equation:
(1-(((1-C)^N)^52)^Y)100 = x
where x = percentage chance that you will win the lottery in Y years
Had to use wolfram alpha to get something close to accurate for this since the fraction was 20 pages long:
(1-((1-(5/300000000))^52)^50)100 = x solve for x
[Wolfram Alpha Equation](http://www.wolframalpha.com/input/?i=(1-((1-(5%2F300000000))%5E52)%5E50)100+%3D+x+solve+for+x)
so an approximate % answer would be :
x≈0.00433323948191015
So a 1/23077.5 chance which is actually better than I thought. You have a 0.00433323948191015% chance of winning if you play 5 number sets every week for the rest of your life assuming you live 50 years.
If you bought all the tickets in one batch (5 tickets, $2 per ticket, 52 weeks, 50 years): 5252*50=$26000 which is 13,000 tickets
so if you did this all in one huge ticket one week, you'd have a 13000/300000000 chance of winning or 13/300000
to get a percentage, * 100 which gives us 13/3000 which is:
x≈0.00433333333333333
Very close, slightly better odds but very close. I think i'd still rather play over the course of my life though, considering I don't actually think I'll win the lottery but it makes me feel good to play.