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Link Posted: 2018-07-24 11:38:41
LordT

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).

  • 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:

(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.

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