Powerball: What is the value of the Powerball?

If you knew with certainty what the red Powerball was going to be in one upcoming drawing, how much would that information be worth? Unfortunately, you don't know with certainty what the "white" ball numbers would be, just the "red" Powerball. If the value of the jackpot makes a difference, assume it is:
A: $10,000,000
B: $100,000,000
C: $400,000,000

I would think the jackpot size would make all the difference. I'm looking at it from an AP math perspective...

So for example on roulette if you bet $10 on red... your EV is the sum of your odds of winning and losing:

EV = (20/38)*(-10) + (18/38)*(10) = -5.26 + 4.74 = -0.52... and the HE is |EV|/bet = 0.52/10 = .052 = 5.2%

So I'd attack this the same way...

Your odds of winning "anything" were previously based on 5 number picks + 1 powerball pick. The difference now (or value to you) would be that you only now need to pick the 5 numbers. To do all the math for all of the difference scenarios would take longer time than I have and/or want to take, so let's just look at the jackpot.

Your odds of winning the Powerball would normally be 1 in 292,201,338... This is the result of
1) COMBIN(69,5) = 11,238,513
2) COMBIN(26,1) = 26

The odds of getting 5 white picks AND the powerball pick would then be (1)*(2) = 11,238,513 * 26 = 292,291,338.

Since you now KNOW the powerball, you would no longer need to multiply by 26, because there's no chance to that... Thus your new odds of hitting the jackpot would be 1 in 11,238,513

So how much is that little red ball worth? Oh, about 280,962,825 combinations...

Also, the JACKPOT SIZE still comes in to affect. You could effectively win 100% guaranteed (no idea if you'd split the jackpot though) if you purchased all 11+ million white ball combinations with your known powerball. So you'd still have to spend $11,238,513 to win the jackpot, which would have to be OVER that amount to be +EV =).

A) Don't play.
B) Win*
C) Win*

*If I 'always' knew the powerball I'd wait for a much larger jackpot, but if it was only on this "one" then I'd have to at least win a couple million to make it worth my time and lobbying and selling of things and taking out loans, etc, to find a way to get all $12 million in combinations =P.

**EDIT** After reviewing (because I don't play the lottery) apparently just hitting the powerball alone wins you $4 for your $1 investment. So knowing the powerball gives you a guaranteed 400% advantage apparently. Buy as many tickets as you can with that powerball and you'll win 4x whatever you spend, AT A MINIMUM.

Quote: Romes

**EDIT** After reviewing (because I don't play the lottery) apparently just hitting the powerball alone wins you $4 for your $1 investment. So knowing the powerball gives you a guaranteed 400% advantage apparently. Buy as many tickets as you can with that powerball and you'll win 4x whatever you spend, AT A MINIMUM.

Powerball tickets are $2 apiece, for a guaranteed minimum 200% edge, but other than that, yeah, what Romes said. Buy as many as you can. Need a partner? :)

PB is $2 ($3 with Power Play), not $1.

Quote: Ibeatyouraces

PB is $2 ($3 with Power Play), not $1.

Oh, yeah. I forgot about Power Play. You definitely want that with each ticket. Your minimum return would then be 267%. Plus time will be a factor in buying the tickets, but purchasing/printing the tickets takes the same amount of time whether you get the Power Play or not.

I'm not sure if you can choose the PowerBall number and Quick Pick the white ball numbers, but if you can, I think you would just bubble in the PB number, QP the rest on all 5 sections of the slip, and run the same slip through 24/7.

Quote: Joeman

Oh, yeah. I forgot about Power Play. You definitely want that with each ticket. Your minimum return would then be 267%. Plus time will be a factor in buying the tickets, but purchasing/printing the tickets takes the same amount of time whether you get the Power Play or not.

I'm not sure if you can choose the PowerBall number and Quick Pick the white ball numbers, but if you can, I think you would just bubble in the PB number, QP the rest on all 5 sections of the slip, and run the same slip through 24/7.

Yes you can.