Powerball: Is the Powerplay option worth it? (PA has a special)

AA suited · #1 10-17-2005, 03:58 PM

PowerPlay

PowerPlay multiplies the prize from 2x to 5x.

so if you win $3 and the multiplier drawn is 4x, then you win $12.

if you win $10k, and the multiplier is 5x, you win $50k.

It costs $1 extra per ticket. so $20 worth of tix with powerplay will cost you $40.

PA has a special where if you buy 5 powerball tickets with the powerplay option, you get a 6th powerball ticket (with powerplay) for free.
Powerball special in PA

Is it still worth the extra $1 per ticket?

THX!

SheetWise · #2 10-17-2005, 04:27 PM

I had to go look -- the site I went to says the Powerball JP is at 340MM. Consider what that really means -

- In cash, the payoff is 170MM. That's the real value any way you look at it.

- The tax bite will be at least 40%. Assuming you buy your Powerball tickets with taxed dollars, you have to adjust your payoff in taxed dollars (net). The Jackpot is really at 102 Million.

The probability of hitting the Jackpot is 1:146,107,962

Playing for the JP is -EV when advertised at 340MM. It will never be +EV unless the rate of increased play levels off.

The lower winners are at fixed payoff, and the payoff is the same if the JP is 500MM or 15MM. It's not worth the time to calculate. It may be better than the JP, but it's at least -.5

EnderW27 · #3 10-17-2005, 08:41 PM

First, I think their odds are off slightly. The powerball itself is a 1 in 42 chance but they claim it to be 1 in 69. I'm still trying to figure out that one.

Also I've heard that the actual "cash in hand" take from this is approximately 130 mil, so it's only slightly -ev from a pure odds perspective.

But I have a really difficult time defining anything as -ev when the payout, if you win, is greater than what you have or will put in to the pot.
If the pot is at $10 million it is clearly -ev to play. I get that. And if you played it out at $1 a week for infinity with a pot of $10 mil, you'll lose a boatload of money.

But we don't play to infinity. We, as humans, can only play until we die. So if, during your lifetime, you win the jackpot, you will absolutely win more than you invested making the entire game +ev from your perspective. And it doesn't matter whether the pot is $10 million or $340 million. The odds of winning are exactly the same in both instances and your odds of coming out ahead overall when you win are both 100%.

Now, I wouldn't recommend playing the lottery at $10 mil. I'm just saying I have a difficult time defining it as -ev.

KJL · #4 10-17-2005, 09:07 PM

[ QUOTE ]
The powerball itself is a 1 in 42 chance but they claim it to be 1 in 69. I'm still trying to figure out that one.

[/ QUOTE ]
1/42 is the chance that you hit the powerball. This number includes the times you hit the jackpot, and all the other times when you hit the powerball number. 1/69 is the chance that you hit the powerball and only the powerball.
C(5,0)*C(50,5)*C(1,1)/C(55,5)*C(42,1)= ~1/69

EnderW27 · #5 10-17-2005, 10:05 PM

Gotcha. Thanks.

AA suited · #6 10-17-2005, 10:58 PM

ok.. back to the powerplay option.

is it worth it, even if you get a free ticket when you buy 5?

SheetWise · #7 10-18-2005, 12:23 AM

[ QUOTE ]
ok.. back to the powerplay option.

is it worth it, even if you get a free ticket when you buy 5?

[/ QUOTE ]

No. Not even close. (enough to calulate).

[ QUOTE ]
But we don't play to infinity. We, as humans, can only play until we die. So if, during your lifetime, you win the jackpot, you will absolutely win more than you
invested making the entire game +ev from your perspective. And it doesn't matter whether the pot is $10 million or $340 million. The odds of winning are exactly the same in both instances and your odds of coming out ahead overall when you win are both 100%.

[/ QUOTE ]

When playing cards, always play the hand you hold as if you had to play that hand 1,000,000 times. When playing the lottery ...

I don't have a good finish for that sentence. Playing it a million times, I'd lose half a million bucks. OK, I get it -- you don't hold that hand -- you have to choose to hold that hand. Good luck.

EnderW27 · #8 10-18-2005, 12:33 AM

No. It's not.

On average, the powerplay nets you a 3.5x payout.
But let's assume you always win 5x. And let's even throw in the 6 for the price of 5.
So for the sake of simplicity, let's just bump it all up to a 6x payout for everything below the grand prize. It's not that much but I'm being REALLY lazy with math and this is just to prove the point.

OK, what are the odds of winning and how much will you win at a 6x payout?
Let's look at the odds page here http://www.powerball.com/powerball/pb_prizes.asp

You'll win
$1.2 million 1 in 3,563,608.83
$60,000 1 in 584,431.85
$600 1 in 14,254.44
$600 1 in 11,927.18
$42 1 in 290.91
$42 1 in 745.45
$24 1 in 126.88
$18 1 in 68.96

All negative ev. Every single one of them. Really really negative ev. The only thing pushing the entire thing positive is the grand prize and that doesn't get multiplied by any amount in the power play.
If you're going to spend that extra money on the lottery anyway, don't go for the "free" ticket after 5...just buy five more tickets!

AA suited · #9 10-18-2005, 12:59 AM

"If you're going to spend that extra money on the lottery anyway, don't go for the "free" ticket after 5...just buy five more tickets! "

ah.. forgot to add that 2nd prize ($100k) gets a bonus $13M if someone hits all 6 #'s that same drawing.

$13M Bonus for matching 5 of the 6 #'s

Also, I'm spending $10 to buy 6 tix since one is free.

But yeah, it still sounds like it's not worth it in either case, right? (spend the extra $4 to get 4 more chances on 1st and 2nd?)

pzhon · #10 10-18-2005, 02:15 AM

The Power Play option only increases the size of the lesser payouts, which are normally worth about 19.7 cents. For the extra dollar, these are increase by a factor of 3.5, which is worth 19.7*2.5=49.3 cents. That's not worth it.

[ QUOTE ]
PA has a special where if you buy 5 powerball tickets with the powerplay option, you get a 6th powerball ticket (with powerplay) for free.

[/ QUOTE ]
When you buy the Power Play option on the first 5 tickets, you lose $2.54. For the sixth Power Play ticket to be worth at least $2.54, a regular ticket would have to be worth at least $2.04, and even if that were the case, it would be better to buy 10 regular tickets rather than 6 Power Play tickets.