100xOdds
100xOdds
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December 12th, 2017 at 1:00:11 PM permalink
http://www.megamillions.com/how-to-play

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.)
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
DJTeddyBear
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December 12th, 2017 at 1:59:07 PM permalink
There are a lot of people that buy the tickets only when there is a big prize, then don't even check the tickets unless they announce that the winning ticket was sold locally.

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.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ————————————————————————————————————— Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
gamerfreak
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December 12th, 2017 at 2:49:51 PM permalink
I think I did this correctly, someone should double check though.

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.
Ibeatyouraces
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December 12th, 2017 at 2:54:15 PM permalink
Already discussed here:

https://wizardofvegas.com/forum/gambling/other-games/29632-new-rules-for-megamillions/
DUHHIIIIIIIII HEARD THAT!
MaxPen
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December 12th, 2017 at 2:57:12 PM permalink
You're already making a bad bet. Do it all the way. Feel for the first person to get all numbers minus the Powerball over 50 cents.
speedycrap
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December 12th, 2017 at 3:00:07 PM permalink
Dont worry about probability/odds/EV. This is lottery. Just throw in $2/$3/$4 and hope for the best. Hit it and you are set. Case closed.
Ibeatyouraces
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December 12th, 2017 at 3:00:35 PM permalink
Here's my guaranteed way to get a 100% return on the lottery:

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!!!!
DUHHIIIIIIIII HEARD THAT!
100xOdds
100xOdds
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December 12th, 2017 at 3:07:05 PM permalink
Quote: Ibeatyouraces

Already discussed here:

https://wizardofvegas.com/forum/gambling/other-games/29632-new-rules-for-megamillions/

cant find answer to my question there
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
miplet
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December 12th, 2017 at 3:41:58 PM permalink
Quote: 100xOdds

cant find answer to my question there

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.
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Wizard
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December 12th, 2017 at 5:39:53 PM permalink
Quote: miplet

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.



I show the break-even point is $241,998,144.

Would you agree the value of the fixed prizes is $0.27606324?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
miplet
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December 12th, 2017 at 7:42:16 PM permalink
whiteredcombinationsprobabilitypaysreturn
5110.00000000330496188800
50240.0000000793190853110000000.07931908531
413250.000001074112614100000.01074112614
407,8000.000025778702735000.01288935136
3120,8000.000068743207272000.01374864145
30499,2000.001649836974100.01649836974
21436,8000.001443607353100.01443607353
2010,483,2000.0346465764600
113,385,2000.0111879569840.04475182793
1081,244,8000.268510967600
018,259,8880.0272986150420.05459723008
00198,237,3120.655166760900
302,575,35010.2469817055
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Wizard
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December 13th, 2017 at 9:22:35 AM permalink
There are 26 possible Power Balls. This I submit your combinations for 5 whites and 0 red should be 25, not 24.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
miplet
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December 13th, 2017 at 9:31:38 AM permalink
Quote: Wizard

There are 26 possible Power Balls. This I submit your combinations for 5 whites and 0 red should be 25, not 24.

But we are talking about Mega Millions not PowerBall
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100xOdds
100xOdds
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December 13th, 2017 at 11:41:01 AM permalink
Quote: miplet

But we are talking about Mega Millions not PowerBall


lol.. reading is fundamental
(please don't ban me)
:)
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
gamerfreak
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December 13th, 2017 at 1:34:14 PM permalink
My 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
Joeman
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December 13th, 2017 at 1:52:40 PM permalink
Just 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.

Quote: Wikipedia

The 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.

"Dealer has 'rock'... Pay 'paper!'"
gamerfreak
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December 13th, 2017 at 1:59:51 PM permalink
Quote: Joeman

Just 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.
Wizard
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December 13th, 2017 at 3:34:48 PM permalink
Quote: miplet

But we are talking about Mega Millions not PowerBall



Dang it. Another senior moment.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
miplet
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December 13th, 2017 at 3:56:06 PM permalink
Quote: gamerfreak

My 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
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Wizard
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December 13th, 2017 at 5:37:22 PM permalink
Now that I know which lottery we're talking about, I get a breakeven point of $224,191,728.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
gamerfreak
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December 13th, 2017 at 5:43:11 PM permalink
Quote: Wizard

Now 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.
Wizard
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December 13th, 2017 at 5:56:40 PM permalink
Quote: gamerfreak

Looks 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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
100xOdds
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December 13th, 2017 at 6:18:00 PM permalink
Quote: Wizard

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?

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)?
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
gamerfreak
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December 13th, 2017 at 7:24:33 PM permalink
Quote: Wizard

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.


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.
miplet
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December 14th, 2017 at 10:31:23 AM permalink
Quote: gamerfreak

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.


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.
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gamerfreak
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December 14th, 2017 at 11:00:09 AM permalink
Quote: miplet

Quote: gamerfreak

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.


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.
miplet
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December 14th, 2017 at 11:42:51 AM permalink
I 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.
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Wizard
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December 14th, 2017 at 1:45:02 PM permalink
Quote: 100xOdds

wait.. 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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
miplet
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December 14th, 2017 at 1:58:53 PM permalink
Quote: Wizard

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.


Ummmmmmm. Wiz, you multiplied weight times probability instead of multiplier times weight for expected multiplier.
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gamerfreak
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December 14th, 2017 at 2:24:27 PM permalink
Quote: miplet

I 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: Wizard

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.


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


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