Pretty rare for this happen,
and yes i realize you can't play enough times at this rate to make your money back.

But straight math, The Jackpot now sits $650 Million, (second largest ever)

the chances of hitting a Jackpot are 1 in 292 Million

the ticket costs two dollars. meaning that if you win one in 594 million times you make your money back...

(yes im not consdiering taxes and a bunch crap that goes with lottos) But its better than you usually get with these.

Whatever happened to mario?

No, because of massive taxes

Aren't splits possible?

Roulette is +EV now! (Yes I'm not considering the green #'s and all the math crap)

All scams must end.

Splits tho.

and multiple winners. Ticket sales go through the roof with jackpots this high, and the EV actually tanks because there's so many tickets that when that jackpot does go out, it'll be split 2-3 ways at minimum.

This is not +EV, don't go wasting bankrolls on it.

I can afford $2 , but yeah chances are slim

anyone else have the feeling we are headed for our first $1B jackpot?

Rainmaker it would be the second. in jan 2016 the jackpot hits $1.6 B it was split three ways

EV is solely based on the entrant's tax situation, the amount of dead money, and the amount of tickets played. "Multiple winners" is a dependent variable based on the number of tickets played. (assuming numbers are chosen randomly)

1 winner in Watertown Mass

The moment I saw all of the numbers were under 32 I figured there would be at least 1 winner.

Expected Value is only meaningful for betting when you have a reasonable expectation of being able to repeat the wager at least N times where the probability of a win is 1/N.

On average, it takes N attempts for the first success to occur. Not just "a" success, but the very FIRST success.

So for very long shot wagers where one can never approach that many attempts in their lifetime, the EV value is totally useless as a decision tool. Bottom line, the lottery was just as bad a bet last month and the month before as it is this time (with the possible exception of a syndicate that can actually wager something approaching N times on the event).

The bolded is incorrect, though it doesn't take away from your point.

I think it's correct.

BruceZ posted a proof of this a few years back, maybe my recollection is wrong.

Edit: here's another proof I found with a short search:
https://www.cut-the-knot.org/Probabi...tSuccess.shtml

It also makes logical sense if you just think about it. The tail of the distribution can extend to (nearly) infinite trials. But it can only go down to 1.

N is an arbitrary choice without mathematical support as far as I can tell, and I don't think this is true regardless of the number of times you expect to be able to repeat the wager. If someone offered me $1000 to my $100 to try to roll a 6 on a 6-sided die, but I could try only once, you're saying I should not accept, but if I could make 10 bets I should accept? This makes little sense.

I would not play the lottery regardless of EV, because the utility will always be less than the value of a ticket & time investment for me.

You are correct. But probably the more important metric would be the probability for >=1 occurrence in N trials. It would not be even money, but 1 - ((N-1)/N)^N. A simple example would be probability of rolling at least 1 seven from 2 dice in 6 trials, = 0.665. So you are very likely to see AT LEAST 1 occurrence in N trials. (assuming independence, of course)

Another way to look at this is to calculate the kelly fraction. The bankroll required to purchase one $2 ticket with an EV of $0 02 is about $8 billion.

N is defined by the probability of success.

I didn't exactly say you should accept/reject based on whether it was a repeatable wager, but was trying to say that for a one-time wager on a very long shot, basing the decision solely on a slightly positive EV is irrational. Basing it on utility as you mentioned, is more valid, but that is true for the lottery every week, not just when it becomes slightly +EV. Everyone can afford a dollar (zilch utility) and everyone would change their life with the win (enormous utility) in any week. This isn't an argument to play the lottery either, but it's a much better and more rational reason than the slightly positive EV.

Bottom line is that for all practical purposes, betting on last week's power ball was not a better or worse wager than any other week. The slight change in EV is so insignificant for making a small number of wagers that it should not be a rational decision factor. Almost everyone will still lose that bet playing it every day for the rest of their life.

For an individual playing a few tickets, yes.

For a large group of individuals who pool their money into playing tens of thousands of tickets or more (yes, these groups exist) then +EV becomes a factor.

Yes, I said that in my original post #15.

# of tickets does not need to approach N, but does need to be significantly more than 1 or 2.

Do you have any math on this? How many tickets does your syndicate need?

I didn't say N wasn't defined, I said your choice of requiring N trials is arbitrary. You could just as easily have said N/2 or 2*N and no choice has better justification than another.

Also most betting decision we make in our lifetime can be evaluated independently of each other. The fact that we will or will not get more opportunities to bet does not matter most of the time.

The reason buying a very large number of tickets could be a valid strategy doesn't have anything to do with being able to make more bets. It is because you are able to play with different numbers on each ticket and lower your overall variance compared to playing the same number of tickets in independent lotteries. Also someone that can afford to do this has the bankroll to actually realize his EV without unreasonable risk.

My utility argument against playing the lottery was supposed to mean that while $10 has fairly insignificant utility for most people, the opportunity to play a $10 lottery ticket is even more insignificant. You'd be better off keeping the $10.