Megamillions is currently at $220mm. I’ve never played, but I know that at some jackpot size your expectation on a $1 ticket moves over $1. Obviously this will have to be based on assumptions about how many tickets will be purchased, which increases at a faster pace when the jackpot grows big. Has anyone done any math around this?
If you ignore the possibility that two people can get the same winning numbers, its possible to get your EV above 1, but when you consider big pots are frequently split by multiple identical tickets, its very very difficult for ev to get over 1.
Assuming only 1 winner, take the jackpot, figure out what the lump sum payment it, and then subtract the taxes. That leaves you with your actual winnings. Then take the odds of winning (you can look this up online usually, or just calculate it yourself) and then multiple the odds as a fraction (i.e. 1/50000000) and multiply that by the winnings you calculated in the first step. If you get a number more than the cost of your ticket, your EV is positive, if its less than the cost of the ticket, its negative.
Back of the envelope for powerball - odds of hitting it all are 1/200MM. Lump sum is usually 50-60% of headline, and taxes take half of that so the lump sum is 25-30% of headline number. Therefore, headline needs to be 200MM/.3 = ~$667M before you have positive EV on your ticket purchase.
Thanks NakedPuts!
Pos. EV or not, I’m willing to skip my morning coffee tomorrow to buy a ticket for the next drawing. Does it bother anyone else when people refuse to play the lotto on the grounds of neg. EV?
No. Why should it bother you. Its personal preference whether one decides to purchase a lottery ticket. I occasionally purchase a ticket when the jackpot is huge. Other than that, I generally don’t play lotto since my personal feeling is that you are throwing your money away on a gamble (no positive expected value). I derive more enjoyment through other means of gambling - for instance poker. Even if I lose money, I still get enjoyment out of the game. There are no intrinsic benefits from buying a lottery ticket (vs. my example given).
ValueAddict Wrote: ------------------------------------------------------- > No. Why should it bother you. Its personal > preference whether one decides to purchase a > lottery ticket. Touche salesman.
A lottery becomes actuarially fair when the expected value of all possible outcomes exceeds the price of admission. The jackpot is only prize of many prizes. You can read this article, which takes into account split prizes as well. http://www.durangobill.com/MegaMillionsOdds.html
NakedPuts Wrote: ------------------------------------------------------- > Back of the envelope for powerball - odds of > hitting it all are 1/200MM. Lump sum is usually > 50-60% of headline, and taxes take half of that so > the lump sum is 25-30% of headline number. > Therefore, headline needs to be 200MM/.3 = ~$667M > before you have positive EV on your ticket > purchase. Didn’t know that. So 200M 8 60% = 120 mm and 50% taxes on it …take home 60m…sucks
NakedPuts Wrote: ------------------------------------------------------- > Back of the envelope for powerball - odds of > hitting it all are 1/200MM. Lump sum is usually > 50-60% of headline, and taxes take half of that so > the lump sum is 25-30% of headline number. > Therefore, headline needs to be 200MM/.3 = ~$667M > before you have positive EV on your ticket > purchase. its actually $550 million based on your assumptions. you forgot to factor in the EV of all non-jackpot winning outcomes.
Thorough analysis, and because of the increasing probability of multiple winners (and taxes), EV never reaches $1. Still the EV (emotional value) of having a few days of hope that I can leave this cubicle behind forever makes up the difference and then some.
dlpicket Wrote: ------------------------------------------------------- > Thorough analysis, and because of the increasing > probability of multiple winners (and taxes), EV > never reaches $1. > > Still the EV (emotional value) of having a few > days of hope that I can leave this cubicle behind > forever makes up the difference and then some. thats not necessarily true as the the number of tickets must max out at some point. the jackpot is not based on the number of tickets purchased, but the amount left in the jackpot from last time plus new tickets expected. i’m sure they’re highly correlated, but this correlation must wear off at some extreme number. but basically yes, less a black swan event, it won’t happen.
thanks, the durango bill site is great stuff.
LPoulin133 Wrote: ------------------------------------------------------- > Does it bother anyone else when people refuse to > play the lotto on the grounds of neg. EV? Eventhough it is -EV, I usually play it within a group pool. I don’t want to be the sucker who misses out if the group wins.
MattLikesAnalysis Wrote: ------------------------------------------------------- > thats not necessarily true as the the number of > tickets must max out at some point. There really isn’t an upper limit on number of tickets. You wouldn’t see exponential growth in the pot if the growth in ticket sales wasn’t also exponential. Sales growth comes from new buyers and existing buyers increasing their purchase.
dlpicket Wrote: ------------------------------------------------------- > MattLikesAnalysis Wrote: > -------------------------------------------------- > ----- > > thats not necessarily true as the the number of > > tickets must max out at some point. > > There really isn’t an upper limit on number of > tickets. You wouldn’t see exponential growth in > the pot if the growth in ticket sales wasn’t also > exponential. Sales growth comes from new buyers > and existing buyers increasing their purchase. hmmm. its not exponential in canada. maybe the limit is sooner? here it usually goes along the lines of 2.5 > 4 > 9 > 14 > 20 > 25 > 32 > 42 > 45 it definitely dies down after the first couple of exponential moves. it would make sense as my perception between 25 million and 40 million is pretty much identical as we have no taxes and i could do a lot with 60% of 25 million. i wouldn’t be able to do much more with another 15 million. there has to be a ‘max out’ period when people are indifferent between the new and last number OR people max out on their lotto spending (i.e. if the lotto is $100 billion, that doesn’t mean i’m going to put in $10,000 to try and win it)
MattLikesAnalysis Wrote: ------------------------------------------------------- > there has to be a ‘max out’ period when people are > indifferent between the new and last number OR > people max out on their lotto spending (i.e. if > the lotto is $100 billion, that doesn’t mean i’m > going to put in $10,000 to try and win it) And that is the difference in Canadians and Rednecks. I believe you and I are observing vastly different populations.
4Tay Wrote: ------------------------------------------------------- > Eventhough it is -EV, I usually play it within a > group pool. I don’t want to be the sucker who > misses out if the group wins. That would suck BIG time.
XSellSide Wrote: ------------------------------------------------------- > 4Tay Wrote: > -------------------------------------------------- > ----- > > Eventhough it is -EV, I usually play it within > a > > group pool. I don’t want to be the sucker who > > misses out if the group wins. > > That would suck BIG time. I guess that’s one way to move from back office to front office.