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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

Powerball Powerplay - Is it worth wagering it?Reply
Actually, the point of my post is to show that the long-run Expected Value (weighted average return per unit bet) on a PowerPlay ticket is only higher than a regular ticket when the Jackpot is lower than a calculable threshold. (In the real world, however, we pay income taxes on net winnings, at least from a U.S. perspective, and the assumption here is all net returns are taxed at the same rate.) Most of your expected return statistically comes from the Jackpot, generally by far. The non-Jackpot
Aug 4, 2022, 4:59 pm - Orange71 - Mathematics Forum

Win the Lottery - Your Retirement Strategy (or maybe not)!Reply
Yep, good point. You'll get something back for lower-tier wins. Also, you gotta love how the (U.S.) income tax system works on this. You pay top marginal rate on all net wins, but can't deduct any net loss, and your (gambling) losses only offset against wins for losses within the same calendar year. If you win the PB or MM Jackpot in a state like California, you will probably be paying ~55% tax (combined State and Federal). Next thing will be The Bern and Pocahontas going after Social Securit
Jul 21, 2022, 5:28 pm - Orange71 - Mathematics Forum

Powerball Powerplay - Is it worth wagering it?
Powerball Powerplay - Is it worth paying the extra $1 (meaning, does it improve the expected value of the return per $ bet)? Short answer - not really. Long answer: It depends on (a) the Expected Value of the Jackpot, and (b) whether you consider improvement of a negative Expected Value of the return (less negative return per $ bet, or in other words, smaller loss) worth it. You can read about how Powerplay works at the Powerball website. Basically, you pay an extra dollar per bet
Jul 8, 2022, 5:35 pm - Orange71 - 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

Neural Net Lottery PickerReply
That sounds interesting: I have been doing some research.. and of course and former mathmetician I did notice the Vtrac system if you don't mind crunching a zilion numbers.. does work.. and have an unlimited budget.. :) last night .. after coming up with PB numbers using an old system been around forever.. adding previous number to current number and so forth, I realized that the Vtrac system is actually a math problem .. which could be turned into a Calculus problem.. since it assigns number gr
Oct 25, 2022, 2:22 pm - Nurdug - Mathematics Forum

Expected Value of Lottery Jackpot, Given You Are A Winner
When you play a lottery and win a pari-mutuel Jackpot, there's always the possibility that one or more other players will also have won, and you'll be sharing (splitting) the prize money. Can you calculate what the Expected Value is of the Jackpot prize, given you are a winner? Certainly! We need to assume something first: every ticket bought is a Quickpick - so any given set of numbers (a single ticket) can be randomly replicated on any other ticket. Suppose there are N such tickets sold (1
Jul 18, 2022, 5:07 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