Mega Millions
Poll
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27 members have voted
As long as I took the trouble to analyze the "just the jackpot" option, I created a new page for the Mega Millions in general. There isn't a lot of data on the relationship between sales and jackpot amount since the rule change so I ignored that for now. I'll add that to my analysis once we see a Mega Millions jackpot of a half billion dollars or so. I would expect a similar relationship as in Powerball, since the two games are now so similar.
Anyway, please have a look at my new page on Mega Millions. I welcome all comments, questions, and especially corrections.
The question for the poll is do you play Mega Millions?
Also, should the extra cost of the "Megaplier" be deducted from a jackpot win in the table, since it had no effect on the prize?
Quote: AyecarumbaIf you invoke the "Just the Jackpot" option, isn't the benefit from the "Megaplier" void since the jackpot is the one win that doesn't multiply?
I would imagine that Just The Jackpot and Megaplier are mutually exclusive.
Quote: WizardThe question for the poll is do you play Mega Millions?
Quote: AyecarumbaIf you invoke the "Just the Jackpot" option, isn't the benefit from the "Megaplier" void since the jackpot is the one win that doesn't multiply?
I doubt the player would even be allowed to do both, since the Megaplier would multiply nothing under the Just the Jackpot option. Is there something on my page that makes you think otherwise?
Quote:Also, should the extra cost of the "Megaplier" be deducted from a jackpot win in the table, since it had no effect on the prize?
How the Lottery funds the jackpot is not my concern. I'm looking at this from the player point of view.
Quote: gamerfreakI would imagine that Just The Jackpot and Megaplier are mutually exclusive.
So would I.
Quote: gamerfreakNormal disclaimer that I am often wrong about these things, but I think you are dividing the total return of the Megaplier by 2 instead of 3 in the table on your Megamillions page.
Let's look at the line item for the $1,000,000 base prize with the Megaplier.
The expected return should be = base prize * probability of winning * average megaplier / bet amount = $1,000,000 * (1/12607306) * 4.733333 / 3 = 0.125148.
Where is my math in error?
Quote: WizardI doubt the player would even be allowed to do both, since the Megaplier would multiply nothing under the Just the Jackpot option. Is there something on my page that makes you think otherwise?
It could just be me, but the “Just the Jackpot” write up makes it sound like invoking the multiplier is an option.
Quote: Wizard
How the Lottery funds the jackpot is not my concern. I'm looking at this from the player point of view.
I bring this up as the multiplier table shows the jackpot win as 40 mil, but should it be 39,999,999 since the “Megaplier” was paid for but not refunded? As I type this, I have a growing suspicion that the cost was factored in the “per dollar” calculation.
Quote: AyecarumbaI bring this up as the multiplier table shows the jackpot win as 40 mil, but should it be 39,999,999 since the “Megaplier” was paid for but not refunded? As I type this, I have a growing suspicion that the cost was factored in the “per dollar” calculation.
The win shown is the base win, before the megaplier.
Quote: WizardLet's look at the line item for the $1,000,000 base prize with the Megaplier.
The expected return should be = base prize * probability of winning * average megaplier / bet amount = $1,000,000 * (1/12607306) * 4.733333 / 3 = 0.125148.
Where is my math in error?
Your average Megaplier is too high. The average is 3. ( 5*2X+6*3X+3*4X+1*5X)/15. = 3X
Quote: mipletYour average Megaplier is too high. The average is 3. ( 5*2X+6*3X+3*4X+1*5X)/15. = 3X
Dang. I multiplied by he probabilities by the weights, not the prizes. You're absolutely right. After making that change, I show the strategy is to buy the Megaplier at jackpots below $224,191,728. At a jackpot of exactly $224,191,728, all three options have the same expected value at 0.493963411. Above $224,191,728, the player should take the Jackpot Only option. This, as usual, is before considering taxes, the annuity, and jackpot sharing. If you factor those things in, always do the Megaplier.
I agree.Quote: WizardDang. I multiplied by he probabilities by the weights, not the prizes. You're absolutely right. After making that change, I show the strategy is to buy the Megaplier at jackpots below $224,191,728. At a jackpot of exactly $224,191,728, all three options have the same expected value at 0.493963411. Above $224,191,728, the player should take the Jackpot Only option. This, as usual, is before considering taxes, the annuity, and jackpot sharing. If you factor those things in, always do the Megaplier.
Mega Millions or Mega Money.
It goes high often but that is because its so unlikely to pay very much at lower level.
At highlevels duplicate tickets are possible.
I will be playing zero dollars.
Quote: WizardI'm quite sure Megamillions never goes positive, due to increased demand for tickets when the jackpot gets big and thus more players chopping the jackpot. I've shown this to be true in my Powerball analysis.
I would like to find out the average number of winning tickets there are when the jackpot is won at 500 million or higher. Just going by memory it seems as though more often than not it’s still just one winner , even with the increased number of tickets sold
Quote: michael99000Quote: WizardI'm quite sure Megamillions never goes positive, due to increased demand for tickets when the jackpot gets big and thus more players chopping the jackpot. I've shown this to be true in my Powerball analysis.
I would like to find out the average number of winning tickets there are when the jackpot is won at 500 million or higher. Just going by memory it seems as though more often than not it’s still just one winner , even with the increased number of tickets sold
There isn't much data for jackpots that big since Megamillions changed the rules in October 2017. Nevertheless, I'll try to find some data on ticket sales and make an estimate.
Quote: WizardDang. I multiplied by he probabilities by the weights, not the prizes. You're absolutely right. After making that change, I show the strategy is to buy the Megaplier at jackpots below $224,191,728. At a jackpot of exactly $224,191,728, all three options have the same expected value at 0.493963411. Above $224,191,728, the player should take the Jackpot Only option.
This, as usual, is before considering taxes, the annuity, and jackpot sharing.
If you factor those things in, always do the Megaplier.
whoa.. WHAT?! if fed tax = 30%, state = 5% and you take the lump sum, ALWAYS take the Megaplier?
I guess mathematically, you're right.
but the only reason Im buying the lotto ticket is for the life changing jackpot.
I only play when the top prize is $300M+ and get 'Just the Jackpot.'
but am torn because the $1M second prize is also life changing for me.
so taking my condition into account, is it better to buy a regular ticket, 'Just the jackpot' or a regular ticket with Megaplier?
Quote: 100xOddsso taking my condition into account, is it better to buy a regular ticket, 'Just the jackpot' or a regular ticket with Megaplier?
My advice is based on maximizing expected value. However, if your goal is to maximize the possible prize and minimize the amount bet, then you should invoke the "just the jackpot" option. Please share some of the prize money with Nathan if you win.
well, it's more for entertainment value and talking with friends about what they would do if they won.Quote: WizardMy advice is based on maximizing expected value. However, if your goal is to maximize the possible prize and minimize the amount bet, then you should invoke the "just the jackpot" option. Please share some of the prize money with Nathan if you win.
some in the group would still buy the regular ticket because of the $1M second prize.
I said the 'Just the jackpot' is a better value when the top prize is large.
I think I'm right?
Assuming that, I show that ticket sales are exponential in nature up to a certain point only. At jackpots over $350 million they are better estimated using parabolic regression. For now, here is my equation of estimated ticket sales for large jackpots, where x is the jackpot amount (in millions) and y is the number of tickets sold (in millions):
y = 0.000255x^2 - 0.041892x + 12.045779
Putting the current jackpot of $654 million* into the equation, we get estimated ticket sales of 93.76 million. The probability of winning is 1 in 302,575,350. This means the expected number of winners is 0.31 and the probability of a winner is 26.6%. These numbers are likely to grow, as we still have over a day to sell more tickets.
* As of 2:30 PM PST Oct 22.
Quote: 100xOddsI think I'm right?
Before considering taxes, the annuity, and jackpot sharing, the expected value is greater with the Just the Jackpot option if the jackpot is over $224,191,728.
Quote: WizardBefore considering taxes, the annuity, and jackpot sharing, the expected value is greater with the Just the Jackpot option if the jackpot is over $224,191,728.
yeah, but considering taxes, lump sum, and a chance of jackpot sharing BUT ONLY CARE ABOUT a life changing prize (top prize or $1M second prize), is 'Just the Jackpot' (no $1M 2nd prize) a better buy than a regular $2 ticket ($1M prize possible) when the jackpot is $300M+?
Quote: 100xOddsyeah, but considering taxes, lump sum, and a chance of jackpot sharing BUT ONLY CARE ABOUT a life changing prize (top prize or $1M second prize), is 'Just the Jackpot' (no $1M 2nd prize) a better buy than a regular $2 ticket ($1M prize possible) when the jackpot is $300M+?
Yes. As I think I wrote earlier, if the jackpot is above $224,191,728, then you should take the Jackpot Only option, if your goal is to maximize expected value.
The optimal jackpot size to play is $1.252 billion. When it gets beyond that, it induces too much demand for tickets and you're more likely to have to chop the jackpot with at least one other winner.
Let's say you play at that maximum value of 1.255 billion.
I show that after the chances of sharing the jackpot, you can expect 61% of that.
Then you'll probably accept the lump sum option, leaving you 62.5% of whatever you won.
After taxes, you'll have only 55% of that amount left (this assumes losing 37% to the IRS and 8% to state/local taxes)
After all that, you'll be left with only $263 million.
You should accept the Just the Jackpot option with jackpots that high, which average to $1.50 a ticket.
The probability of winning is 1 in 302,575,350.
So, the expected return is $263 million / 302,575,350 / 1.5 = 57.9%.
There you have it -- the house edge on the Mega Millions is 42.1% at least.
For the current jackpot of $654 million, I show that after the same factors you'll be left with 198.0 million if you win. That will make the expected return 43.6%.
Any questions?
Quote: unJonThanks, Mike! Really interesting breakdown. I think the missing piece would be data on how many people are not doing quick picks and whether the hand picked numbers are distributed more heavily on numbers 1-12 then 1-31 (for birthdays and kid ages, etc). Likely no good public data out there. But obviously at high jackpockts the EV is heavily dependent on the likilihood of splitting.
You're welcome!
Just from standing in line behind people buying lottery tickets, I think most get quick picks.
Quote: NathanI detest Mega Millions. I have never gotten back more than a couple of dollars back playing this game. Crappy game for me.
I think 100xOdds would say it is a feast or famine game. You don't play it to win $200, you play it to win $200 million. It shouldn't come as a big surprise if you don't hit it.
If your goal is a high hit frequency, I agree, stay away from it. I still say you, and everybody on earth, should say away from every lottery game. However, if you must throw your money away, know your goals and play accordingly.
Quote: NathanI detest Mega Millions. I have never gotten back more than a couple of dollars back playing this game. Crappy game for me.
A .20 quick pick pick 6 at Gulfstream has a +ev.... the horseplayers welcome you with open arms Nathan.
Quote: FinsRuleA .20 quick pick pick 6 at Gulfstream has a +ev.... the horseplayers welcome you with open arms Nathan.
I thought the Horse racing Game at Gulfstream was $2 a Minimum. If it is only .20 I just might bite. :)
Quote: WizardI think 100xOdds would say it is a feast or famine game. You don't play it to win $200, you play it to win $200 million. It shouldn't come as a big surprise if you don't hit it.
If your goal is a high hit frequency, I agree, stay away from it. I still say you, and everybody on earth, should say away from every lottery game. However, if you must throw your money away, know your goals and play accordingly.
But to be fair, many slots have a .50 cent Minimum spin and you can play .50 for the Pick 2, Pick 3, Pick 4, and Pick 5 in The Florida Lottery. I played .50 in Wolf Run a while ago and I got a bunch of winning lines and I won roughly $18, 36 times my bet, not too shabby. I won $100 on a .50 cent Pick 4 game a while ago, 200 times my bet, a really good profit in my money.
Quote: NathanBut to be fair, many slots have a .50 cent Minimum spin and you can play .50 for the Pick 2, Pick 3, Pick 4, and Pick 5 in The Florida Lottery. I played .50 in Wolf Run a while ago and I got a bunch of winning lines and I won roughly $18, 36 times my bet, not too shabby. I won $100 on a .50 cent Pick 4 game a while ago, 200 times my bet, a really good profit in my money.
If your point is that slots are a better value than the lottery, then you're absolutely right.
Quote: WizardIf your point is that slots are a better value than the lottery, then you're absolutely right.
I realize the house edge on lottery is much higher, but as a practical matter I disagree.
The amount wagered by an average lottery player in a given period of time is significantly lower than the amount wagered by an average slot player.
Quote: NathanI thought the Horse racing Game at Gulfstream was $2 a Minimum. If it is only .20 I just might bite. :)
The jackpot pick 6 is 20 cents.
The pick 3, 4, 5 are 50 cents. Those aren’t usually +ev, but they are a ton better than lotto odds.
Don't get me wrong, I appreciate the analysis, Wiz. And yes, overall, lottery HE's border on criminal.
Quote: JoemanOk, I'll probably be shot for saying this, but does the RTP even matter for jackpots >$100M?
For me the lottery (which I may play $10 in a given year) is all about winning a life changing amount.
I can't see how I'd live any differently with $100M in the bank vs $300M. I mean, do you really think Richie Rich's lifestyle is three times better than Scrooge McDuck? :)
Don't get me wrong, I appreciate the analysis, Wiz. And yes, overall, lottery HE's border on criminal.
even winning the minimum $40m prize would be a life changing event. (still 8 figures after lump sum payout + taxes)
but I don't do it because I know the odds of winning is astronomical.
I buy lotto tix (only when jackpots are high) for entertainment value.
ie: talking with friends/coworkers what you would do if won
Quote: gamerfreakThe amount wagered by an average lottery player in a given period of time is significantly lower than the amount wagered by an average slot player.
If somebody will get equal entertainment value between betting $20 on the lottery as $200 on slots, then, yes, you'll lose less money on average on the lottery. However, I'm a math guy. I view the house edge as the cost for playing. I will strive for the most action at the least possible cost wherever I can.
Quote: JoemanOk, I'll probably be shot for saying this, but does the RTP even matter for jackpots >$100M?
Every Mega Millions and Powerball player seems to make this argument in one way or another. Let me ask the players of the 9-figure lotteries this question. How much entertainment value do you get from a losing $2 ticket?
Quote: WizardEvery Mega Millions and Powerball player seems to make this argument in one way or another. Let me ask the players of the 9-figure lotteries this question. How much entertainment value do you get from a losing $2 ticket?
I think in all gambling the entertainment value comes prior to the outcome. For many people I believe they spend time thinking about what they would do if they happened to win. If for example they spent two hours thinking about it and talking with friends about it, $2 would be much cheaper than other forms of two hour entertainment (A movie costs about $12 for two hours).
this!Quote: DRichQuote: WizardLet me ask the players of the 9-figure lotteries this question.
How much entertainment value do you get from a losing $2 ticket?
If for example they spent two hours thinking about it and talking with friends about it, $2 would be much cheaper than other forms of two hour entertainment (A movie costs about $12 for two hours).
it'll actually be $3 for me because of 'Just the Jackpot'.
:)
Quote: DRichQuote: WizardEvery Mega Millions and Powerball player seems to make this argument in one way or another. Let me ask the players of the 9-figure lotteries this question. How much entertainment value do you get from a losing $2 ticket?
I think in all gambling the entertainment value comes prior to the outcome. For many people I believe they spend time thinking about what they would do if they happened to win. If for example they spent two hours thinking about it and talking with friends about it, $2 would be much cheaper than other forms of two hour entertainment (A movie costs about $12 for two hours).
If you are trying to quantify the overall entertainment/enjoyment of a losing $2 ticket, you also have to subtract the disappointment afterwards. And if you say there is no disappointment because you never really believed you had a chance to win , then the net entertainment value is zero.
Quote: michael99000If you are trying to quantify the overall entertainment/enjoyment of a losing $2 ticket, you also have to subtract the disappointment afterwards.
And if you say there is no disappointment because you never really believed you had a chance to win , then the net entertainment value is zero.
can you elaborate cause I cant wrap my head around the net being zero?
