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Chances of 1,2 or three winners in PowerballReply
OK. My local TV news in TX says the cash value of the $1 Billion PowerBall Jackpot after income taxes is $325 million. (You would instantly become an evil 1%-er.) The probability of a single random ticket winning is 1 in 292201338. Nobody knows how many tickets will be bought before the fact, but 350M might be a reasonable (very rough) estimate based on history. If everybody bought a Quick Pick, the Expected Value of the cash after-tax Jackpot (per the Binomial Distribution) would be about $189
Jul 19, 2023, 8:05 pm - Orange71 - Mathematics Forum

Mega Millions Just The JackpotReply
For those answers, did you assume just one jackpot winner? If not, what number of tickets did you assume were sold? I did the 3rd calculation a while back, factoring in taxes. I remember that it didn't make sense, from an expected return viewpoint, to play Mega Millions until the jackpot was roughly $600M, so your results are in the right ballpark, and are most likely correct. The other calculation of relevance, along these lines, is the number of plays needed for the variance of the EV
Jul 16, 2023, 8:52 pm - Wavepack - Mathematics Forum

Mega Millions Just The JackpotReply
To your point about variance, yes, JTJ is obviously going to be higher than a regular ticket. Both are going to be a huge variance, regardless. So, if variance is the concern, don't play the games to begin with. You will get a few bucks back by playing a regular ticket and hitting the minor prizes, but as percentage of $ spent, it's still very low. The return is basically predicated on hitting the jackpot, which the average person more than likely would not hit in a thousand lifetimes. Ther
Jul 17, 2023, 8:17 pm - Orange71 - Mathematics Forum

Mega Millions Just The Jackpot
In my state the lottery commission offers an alternative to the regular $2 Mega Millions ticket. It's called Just The Jackpot . (I'll call it JTJ for short.) You get two tickets for $3, but you can only win the jackpot. Lower tier prizes are eliminated. Two interesting questions arise: (1) At what Expected Value of the Jackpot does the JTJ offer a better expected value of return per unit bet compared to a $2 regular ticket, and (2) At what Expected Values of the Jackpot do a regular $2 ticket an
Jul 16, 2023, 12:06 pm - Orange71 - Mathematics Forum

"Post-Game Review" - $1.58B MM Jackpot This Week
A single winner in Florida hit the $1.58B Mega Millions this week. The cash value (I saw on TV anyway) was about $783M. This begs the question: playing a regular $2 ticket, did a player have a positive return expectation (expected value of return $2 bet)? Answers: 1. Before income tax - yes, roughly $0.11 gain per $ bet (about +11% return) 2. After income tax - no, roughly $0.28 loss per $ bet if you assume a 35% tax rate on winnings. (about -28% return) First, I looked up the nu
Aug 12, 2023, 12:53 pm - Orange71 - Mathematics Forum

Mega Millions Just The JackpotReply
Answered by Google. Bard The expected value of a lottery ticket is the average of the possible prizes, weighted by their probability. For a regular Mega Millions ticket, the expected value is about $0.63. This means that, on average, for every $2 you spend on a ticket, you will expect to win about $0.63. The expected value of a JTJ ticket is about $1.26. This means that, on average, for every $3 you spend on a ticket, you will expect to win about $1.26. So, the JTJ ticket offers a
Aug 3, 2023, 6:59 am - mrtckw - Mathematics Forum