One ticket vs. pool powerball situation

[Salmon Steak]

Some people asked me if I wanted to join a powerball pool. I started thinking, would it be more advantageous to buy my own ticket and claim the total 310 million prize or join the pool and have the prize split nine ways. I thought the Kelly formula could help solve this problem. When I finished, I was confused by the results because it is opposite to what I thought the results would represent. It seems you would need a lower bankroll in the pool to take a shot. It is also possible I did something wrong because I am no Ganchcrow. guys, have a nice weekend.

1 = 175,223,510. Powerball odds


K = (1/175,223,510MillionChancetoWin)*(310Milli on$Jackpot)-((1-(1/175,223,510MillionChancetoWin)/(310Million$Jackpot)

K = (5.7e-9ChancetoWin)*(310Million$Jackpot)-((1-(5.7e-9ChancetoWin)/(310Million$Jackpot)

K = 1.769168 - .99999999 / (310Million$Jackpot)

K = .76916 / (310Million$Jackpot)

K = 2.481e-9 ($2,481,000,000.00)


310,000,000/9 people = 34,444,444 million per entry

K = (9/175,223,510MillionChancetoWin)*(34,444,4 44Million$Jackpot)-((1-(9/175,223,510MillionChancetoWin)/( 34,444,444Million$Jackpot)

K = (5.136e-8ChancetoWin)*( 34,444,444Million$Jackpot)-((1-(5.136e-8ChancetoWin)/( 34,444,444Million$Jackpot)

K = 1.769 - .99999999/ (34,444,444Million$Jackpot)

K = .76916 / (34,444,444Million$Jackpot)

K = 2.2330e-8 ($223,307,000.00)

[ttwarrior1]

buy your own ticket and join them also if allowed

I assume you all don't buy one ticket and one person buys the 9 tickets with 9 diff numbers

[FourLengthsClear]

Overbetting will kill you! LOL.

I am not entirely sure how Powerball works but I assume there is a possibility of the jackpot being split between multiple winners. If so then obviously the required BR would be even higher.

[MoneyLineDawg]

In situations like these, I'd rather take as many chances as possible to hit a life changing amount.....I would be just as happy with 20 mil then with like 200 mil att his point

[Salmon Steak]

Overbetting will kill you! LOL.

I am not entirely sure how Powerball works but I assume there is a possibility of the jackpot being split between multiple winners. If so then obviously the required BR would be even higher.

It is a 2$ lottery ticket to win large amounts of money at terrible odds. I could buy one ticket to win 310 million or buy one 2$ ticket with nine other people and have nine chances to win 34million or so. 310/9

What you said is what I assumed, however, when I did the math, it seems you would need a smaller bankroll in the second option. That is why I posted... because I was confused.

[LT Profits]

If you applied Kelly correctly, the appropriate bet amount would be 0.

[Salmon Steak]

If you applied Kelly correctly, the appropriate bet amount would be 0.

Obviously you never want to play the lottery. If you notice the two required bankrolls though, the lower bankroll seems to be the one in the pool of nine people. This implies, I believe, that the better option would be in the pool of nine people winning 34 million per person. So if you are going to play, play in a pool and have your prize be divided as the single set of numbers for 310 million would require a bankroll of over 2 billion.

[Jayvegas420]

I don't think I like your odds!
Great equation though.

[135steward]

Not necessarily

If you applied Kelly correctly, the appropriate bet amount would be 0.

Full disclosure: I don't play any lotteries.

Powerball, as well as other lotteries, are progressive jackpots. There are a finite number of combinations to win (x*10^6-x*10^10, but still finite). When the pooled money surpasses the possible number of payout combinations, the wager becomes +EV. I read in Fortune (?) a while back where syndicates will buy 10^5+ tickets when the +EV situation arises.

[Jayvegas420]

Am I to assume those syndicates will be terribly upset when they realize there can be more than one winner per draw, thus splitting the implied prize?

[135steward]

More than one person can draw the same number, that's true. It was Fortune, or one of the other popular financial publications, not an economics journal, so the math wasn't detailed at all. And since I don't play lotteries, I didn't follow up. But the big prize isn't the only one, and how many people are projected to play the lottery in question, are other factors to be considered, I'm sure.