MegaMillions new 'Just the Jackpot" wager
Megamillions is now $2 per ticket, same as PowerBall.
but they have a 'Just the Jackpot' option where At a price of $3, the player will receive two plays for the jackpot only.
so 2 tickets for $3 instead of $4 but it's either hit the jackpot or get nothing.
Mathematically, Is this a better or worse bet than just buying a $2 ticket?
(yeah, I know.. tax on the stupid.. but humor me.)
Math aside, this is a good deal for those types of people.
Is it a good deal overall? I tend to think not.
Note: It doesn't say, but you gotta assume, that the 2 $1.50 tickets are for different numbers.
It depends on the jackpot.
Given a jackpot of $120 million, the value of a regular $2 Megamillions ticket is about $0.60, or $0.30 per dollar wagered.
The value of a $3 "Jackpot Only" ticket is about $0.80, or $0.27 per dollar wagered.
So with $120 million the regular ticket is a better "deal", but not by much. That could change with a higher jackpot, though.
https://wizardofvegas.com/forum/gambling/other-games/29632-new-rules-for-megamillions/
1) take the money out of your wallet/purse to purchase the tickets.
2) take that money and put it in your pocket.
3) leave the store.
4) DON'T BUY LOTTERY TICKETS!!!!
cant find answer to my question thereQuote: IbeatyouracesAlready discussed here:
https://wizardofvegas.com/forum/gambling/other-games/29632-new-rules-for-megamillions/
Ignoring tax, utility of money, possibly of splitting the jackpot etc, it is better to buy the jackpot only when the jackpot is $225 million or higher.Quote: 100xOddscant find answer to my question there
Quote: mipletIgnoring tax, utility of money, possibly of splitting the jackpot etc, it is better to buy the jackpot only when the jackpot is $225 million or higher.
I show the break-even point is $241,998,144.
Would you agree the value of the fixed prizes is $0.27606324?
| white | red | combinations | probability | pays | return |
|---|---|---|---|---|---|
| 5 | 1 | 1 | 0.000000003304961888 | 0 | 0 |
| 5 | 0 | 24 | 0.00000007931908531 | 1000000 | 0.07931908531 |
| 4 | 1 | 325 | 0.000001074112614 | 10000 | 0.01074112614 |
| 4 | 0 | 7,800 | 0.00002577870273 | 500 | 0.01288935136 |
| 3 | 1 | 20,800 | 0.00006874320727 | 200 | 0.01374864145 |
| 3 | 0 | 499,200 | 0.001649836974 | 10 | 0.01649836974 |
| 2 | 1 | 436,800 | 0.001443607353 | 10 | 0.01443607353 |
| 2 | 0 | 10,483,200 | 0.03464657646 | 0 | 0 |
| 1 | 1 | 3,385,200 | 0.01118795698 | 4 | 0.04475182793 |
| 1 | 0 | 81,244,800 | 0.2685109676 | 0 | 0 |
| 0 | 1 | 8,259,888 | 0.02729861504 | 2 | 0.05459723008 |
| 0 | 0 | 198,237,312 | 0.6551667609 | 0 | 0 |
| 302,575,350 | 1 | 0.2469817055 |
But we are talking about Mega Millions not PowerBallQuote: WizardThere are 26 possible Power Balls. This I submit your combinations for 5 whites and 0 red should be 25, not 24.
Quote: mipletBut we are talking about Mega Millions not PowerBall
lol.. reading is fundamental
(please don't ban me)
:)
I made a new spreadsheet that calculates all the combinations, and the numbers agree with Miplet's, and show that Just The Jackpot becomes a better "deal" when the jackpot is $250 million.
You can view and edit my spreadsheet here
Quote: WikipediaThe annuity -- which was 20 annual payments (no cash option was available) when The Big Game began -- changed from 26 equal yearly installments to 30 graduated annual payments (increasing 5 percent yearly) with the format change on October 19, 2013.
Quote: JoemanJust a thought, but shouldn't we consider the value of the jackpot in terms of today's dollars, since it is paid out as an annuity? A "$250 M" jackpot is not worth nearly $250 M today.
They offer a lump sum payout as well.
Quote: mipletBut we are talking about Mega Millions not PowerBall
Dang it. Another senior moment.
Quote: gamerfreakMy first chart was wrong because I did not factor in the possible outcomes that do not award a prize. I was also stupidly using the odds listed on the megamillions site in the incorrectly labeled combinations column, instead of doing the proper combinatorial math.
I made a new spreadsheet that calculates all the combinations, and the numbers agree with Miplet's, and show that Just The Jackpot becomes a better "deal" when the jackpot is $250 million.
You can view and edit my spreadsheet here
I edited yours to show more decimal places. 2 was just not enough. From $224 to $225 million it flips. I’m
Quote: WizardNow that I know which lottery we're talking about, I get a breakeven point of $224,191,728.
Looks correct, my sheet shows $0.4939634111 EV/Dollar for both tickets when the jackpot is $224,191,728.
Quote: gamerfreakLooks correct, my sheet shows $0.4939634111 EV/Dollar for both tickets when the jackpot is $224,191,728.
Thanks. I see they changed the rules on October 27. Given the new rules, I get a break-even point on purchasing the Megaplier of $483,257,725.
wait.. What?Quote: WizardThanks. I see they changed the rules on October 27. Given the new rules, I get a break-even point on purchasing the Megaplier of $483,257,725.
With the new $2 tix, Buying the megaplier for $1 more is a better choice than spending $2 on another ticket if the jackpot is less than $483m (Annuity)?
Quote: WizardThanks. I see they changed the rules on October 27. Given the new rules, I get a break-even point on purchasing the Megaplier of $483,257,725.
How do you calculate the return of the Megaplier? I am getting 0.256 but I don't think I am doing it correctly.
I'm calculating the return for each Megaplier ball as:
(multiplier*fixed prize return) * probability of that ball being chosen
And then the overall return of the wager as:
sum of return of all megaplier balls * probability of winning a fixed prize
I'm sure I am missing something though.
Quote: gamerfreakHow do you calculate the return of the Megaplier? I am getting 0.256 but I don't think I am doing it correctly.
I'm calculating the return for each Megaplier ball as:
(multiplier*fixed prize return) * probability of that ball being chosen
And then the overall return of the wager as:
sum of return of all megaplier balls * probability of winning a fixed prize
I'm sure I am missing something though.
Looks god to me. Not sure about the .256. A $3 Megaplier ticket just increases the fixed pays. I think the average is 3x. So if you normally would get the $2 prize for just getting the Megaball, you would on average get $6 instead.
PS
We need some new blood experienced sleuths in our games of Clue at DT. Any one is welcome to join.
Quote: mipletQuote: gamerfreakHow do you calculate the return of the Megaplier? I am getting 0.256 but I don't think I am doing it correctly.
I'm calculating the return for each Megaplier ball as:
(multiplier*fixed prize return) * probability of that ball being chosen
And then the overall return of the wager as:
sum of return of all megaplier balls * probability of winning a fixed prize
I'm sure I am missing something though.
Looks god to me. Not sure about the .256. A $3 Megaplier ticket just increases the fixed pays. I think the average is 3x. So if you normally would get the $2 prize for just getting the Megaball, you would on average get $6 instead.
PS
We need some new blood experienced sleuths in our games of Clue at DT. Any one is welcome to join.
Here's an updated sheet with my Megaplier Calculation
The reason I thought I was missing something is because I don't get the breakeven that Wiz listed, and I tend to trust his math skills far more than mine.
Quote: 100xOddswait.. What?
With the new $2 tix, Buying the megaplier for $1 more is a better choice than spending $2 on another ticket if the jackpot is less than $483m (Annuity)?
I'm saying you increase the expected return* buying the Megaplier as long as the jackpot is under $483,257,725.
Here is a table showing the average Megaplier value:
| Multiplier | Weight | Probability | Exp. Multiplier |
|---|---|---|---|
| 5 | 1 | 0.066667 | 0.066667 |
| 4 | 3 | 0.200000 | 0.600000 |
| 3 | 6 | 0.400000 | 2.400000 |
| 2 | 5 | 0.333333 | 1.666667 |
| Total | 15 | 1.000000 | 4.733333 |
* Usual disclaimer about ignoring the effects of taxes, annuity, or jackpot sharing.
Quote: WizardI'm saying you increase the expected return* buying the Megaplier as long as the jackpot is under $483,257,725.
Here is a table showing the average Megaplier value:
Multiplier Weight Probability Exp. Multiplier 5 1 0.066667 0.066667 4 3 0.200000 0.600000 3 6 0.400000 2.400000 2 5 0.333333 1.666667 Total 15 1.000000 4.733333
* Usual disclaimer about ignoring the effects of taxes, annuity, or jackpot sharing.
Ummmmmmm. Wiz, you multiplied weight times probability instead of multiplier times weight for expected multiplier.
Quote: mipletI added 2 comments. You did something weird. You already accounted for the probabilities in your Megaplier balls table. You should get 0.7793644933 for the ev/$ for Megaplier.
Thanks, yea, I adjusted for the probability of winning a fixed prize twice.
Quote: WizardI'm saying you increase the expected return* buying the Megaplier as long as the jackpot is under $483,257,725.
Here is a table showing the average Megaplier value:
Multiplier Weight Probability Exp. Multiplier 5 1 0.066667 0.066667 4 3 0.200000 0.600000 3 6 0.400000 2.400000 2 5 0.333333 1.666667 Total 15 1.000000 4.733333
* Usual disclaimer about ignoring the effects of taxes, annuity, or jackpot sharing.
Now that Miplet fixed my mistake, this is what I get for a the megaplier value, and the ticket values for a jackpot $483,257,725
