[QuotedForTruth]

Its not exactly the same but its pretty close when the chances are so low anyways.

Playing 10,000 times in 1 drawing gives you the probability of winning the jackpot:

0.00003422297813=10000/292201338

Playing 10,000 times in 10,000 drawings gives you the probability of winning the jackpot:

0.00003422239258=1-((292201338-1)/292201338)^10000

The difference gets more significant if you play more. For 10 million plays its:

.0342 vs .0336

If you play only 100 times the probability of a jackpot is the same to 7 significant digits.

-edit I put it on $1M and let it run. I hit the 5 numbers, $1M prize, at some point around $150k spent.

[jholman]

It's true that if you play all your tickets in one drawing, you have a higher chance of winning the jackpot at least once, especially as your number of tickets approaches the number of total tickets. However, your expected value does not go up, because you lose the chance of winning the jackpot more than once.

For an extreme example, consider a lottery with only one number, selected from 1 to 2, costing $1 per ticket, with a $2 jackpot.

Buy 2 tickets at once, you lose $2 on tickets, and you get $2 back. Expected net return, $0 (with probability 100%).

Buy 1 ticket per draw for 2 draws, and you have a 1/4 chance of winning nothing (net -$2), a 1/4 chance of winning both jackpots (net +$2), and a 2/4 chance of winning one and losing one (net $0). Same expected value.

Of course, in a real lottery, usually[0] the expected value is negative. So what's happening is like anti-insurance. In both cases your expected value is negative, but you pay the insurance company money to lower your variance, and you pay the lottery money to raise your variance.

[0] Usually? Well, in theory with a cumulative jackpot the jackpot might get high enough to make the expected value positive... except that usually as the jackpot rises, the number of players rises too, such that you have to take into account the possibility of having the split the jackpot, which of course would cut your take in half, or worse.

[s73v3r]

Shouldn't it stop once you've hit the jackpot? At least until it goes up again? I'd imagine once you've one $800 million, you're not going to be interested in the $40 million reset jackpot.

[kinofcain]

Not just nearly identical to each other, they're nearly identical to zero. So your odds of winning are effectively the same whether you play or not.

It approaches 1.0 as you buy more tickets, but even at $800m, the lump sum payout of $491m is still lower than the cost of buying all possible $2 tickets ($584m).

And even if you could buy all tickets you still might have to split the winnings...

[gvb]

+1 for pointing out that it is actually a $491MM payout that you can choose to take as a $800MM annuity over 20(?) years.

You also have to subtract taxes from the payout, which also eats into the payout. I would expect it would be 30% or higher, depending on how much you spend on a tax lawyer (which, of course, cuts into the payout as well).

The only[1] way to win is to not play.

[1] Odds are 292,201,338 to 1 of winning by not playing.

[bradleyjg]

If you play quickdraw you could get the same numbers twice. I think with that caveat the odds should be the same.

[ethbro]

To be fair, wouldn't the odds of QuickDraw picking the same numbers twice (even if there weren't a built in limit against that) be the same odds as winning the jackpot in the first place?

[QuotedForTruth]

Only if you are only picking two sets of numbers. If you are doing 10k sets, the last set has a 9999/292M chance of being the same numbers as one of the other sets.

[bradleyjg]

Right, that's the birthday problem.

[LanceH]

It evens out on expected payout. There is a chance on 10,000 sequential plays that you win the lottery 10,000 times.