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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 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

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

Mega Millions Just The JackpotReply
I should of mentioned, for the variance question, that an unbiased mean estimator is used. I ask the variance question because the answer makes explicit the ridiculously large sample size needed to get a reasonably low variance of the estimator of the Mega Millions EV. The normal lotto player has a relatively small sample size, so the applicability of this EV analysis is of limited value.
Jul 17, 2023, 2:28 pm - Wavepack - Mathematics Forum

Megaball predictionReply
About a year ago, I did the Chi-square test on Mega Millions and Powerball, both white and non-white balls. I was going from memory that each had too high probability estimates for a non-uniform pdf test. Those test results from a year ago is what motivated me to see if there was any pdf non-uniformity that could be used to improve predictions. It's been a fun side project every since that I work on every now and then. The project drives home probability and statistics fundamentals, along w
May 10, 2023, 5:55 pm - Wavepack - Mathematics Forum

Megaball predictionReply
Wait, I thought you were talking about Megaball (red) non-randomness in the original post. You're saying now the white balls (main pool) is where the apparent non-randomness is. Correct? Your post: I've found a method, using only past draw information, to correctly predict the next Megaball draw at 8.07% (N = Number of tests = 322). The expected prediction match with uniform random guessing is 4%. ... I have found no method that predicts Mega Millions white balls over expected w
May 10, 2023, 4:04 pm - Orange71 - Mathematics Forum

Megaball prediction
Because of the limited draw data set size and high noise, it's very difficult to ascertain whether there is any signal in the past data that can be used to predict future draws. I've found a method, using only past draw information, to correctly predict the next Megaball draw at 8.07% (N = Number of tests = 322). The expected prediction match with uniform random guessing is 4%. No training cheating (other than adjusting two time length/window parameters). I have found no method that
May 4, 2023, 11:49 pm - Wavepack - Mathematics Forum

Chances of 1,2 or three winners in PowerballReply
It's relatively simple. The probabilities follow the Binomial Distribution if you assume the numbers for every ticket are chosen independently and randomly. (That is the case for a Quick Pick .) The probability of an individual random ticket winning Mega Millions is 1 in 302575350, for example. Powerball is slightly higher probability. Let's call that probability (1 in 302575350) p . P (capital letter) is the probability of x winners, where x = 0, 1, 2, 3, ..., N, where N is the number of ti
Jul 18, 2023, 7:38 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

Megaball predictionReply
Indeed, the data is posted here for 577 draws since 2017. The Chi-square Goodness of Fit results analysis are shown below using the usual alpha = 0.05. Nothing appears amiss to me. Null Hypothesis of randomness is not rejected. https://www.lottonumbers.com/mega-millions/number-frequency
May 10, 2023, 2:23 pm - Orange71 - Mathematics Forum