Powerball hits $1 Billion
October 6th, 2023 at 6:52:18 AM
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How much do you guys think Powerball pays for the 'News' shows to always be talking about this?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
October 6th, 2023 at 7:05:05 AM
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Quote: Ace2You’re missing something fundamental in your calculation.
link to original post
I might be...the original calculation includes the 1/e "possibility" that you have one of the zero winning tickets. Er...
Then again, if you change it to (the probability of you having a winning ticket) / (the expected number of other winning tickets), then, by my earlier formula, that should be 1, but then the value of the ticket is 1/2.
The problem may be, "the jackpot divided by the expected number of winning tickets" and "the expected value of your share of the jackpot" are two different things, when you take into account that you only get 1/N of the jackpot if there are N winners.
When I calculate this:
P(winning ticket) / (P(nobody else has one) + P(one other ticket) / 2 + P(two other tickets) / 3 + ... + P(N-1 other tickets) / (N-1))
then I get 1 - 1/e.
Any mathoids out there know if there is a simplified exact solution to either of these (the second one is just the first one with every term multiplied by N):
Q^(N-1)
+ 1/2 C(N-1,1) P Q^(N-2)
+ 1/3 C(N-1,2) P^2 Q^(N-3)
+ 1/4 C(N-1,3) P^3 Q^(N-4)
+ ...
+ 1/N P^(N-1)
C(N,1) Q^(N-1)
+ C(N,2) P Q^(N-2)
+ C(N,3) P^2 Q^(N-3)
+ C(N,4) P^3 Q^(N-4)
+ ...
+ C(N,N) P^(N-1)
Last edited by: ThatDonGuy on Oct 6, 2023
October 6th, 2023 at 9:54:36 AM
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I don't have a dog in this discussion, other than casually playing PB and MM when prizes get super high. But 2 comments, if I may:
(1) A PB or Mega Millions play costs $2, $3 if you want the Powerplay or the Megaplier. In Idaho and Montana, Powerball is bundled with Power Play for a minimum purchase price of $3 per play. I keep seeing assumptions based on $1 play, and there is no play for either game that's $1.
(2) How does multiple plays for the same game/draw impact these calculations? For example, last PB I play 3 draws. That was $6. I won $2.
(1) A PB or Mega Millions play costs $2, $3 if you want the Powerplay or the Megaplier. In Idaho and Montana, Powerball is bundled with Power Play for a minimum purchase price of $3 per play. I keep seeing assumptions based on $1 play, and there is no play for either game that's $1.
(2) How does multiple plays for the same game/draw impact these calculations? For example, last PB I play 3 draws. That was $6. I won $2.
October 6th, 2023 at 11:29:12 AM
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In order to end up with over a billion, I’d probably need to hit MM and PB consecutively. If I hit the Florida Lotto, and PB, FL would all essentially disappear into taxes for PB.
There's no secret. Just know what you're talking about before you open your mouth.
October 6th, 2023 at 2:28:20 PM
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ThatDonGuy,
Using the 300 million scenario, look at it this way. You have one ticket and there are 299,999,999 others. That 299.9M is the same as 300 million for all practical/calculation purposes
The drawing is made. Before even considering your one ticket, there is:
e^-1/0! chance of zero other winners giving you a 100% share of the jackpot IF you win. e^-1/0! * 100% is 0.368
e^-1/1! chance of one other winner giving you a 50% share of the jackpot IF you win. e^-1/1!* 50% is 0.184
e^-1/2! chance of two other winners giving you a 33.3% share of the jackpot IF you win. e^-1/2! * 33% is 0.061
Etcetera. Sum those through infinity and you”ll get an expected jackpot share of 63 % and a jackpot only ticket value of 1/e = 63 cents. Edit: Should say 1 - 1/e = 63 cents
I believe you’re a little off on this part of the calculation
Using the 300 million scenario, look at it this way. You have one ticket and there are 299,999,999 others. That 299.9M is the same as 300 million for all practical/calculation purposes
The drawing is made. Before even considering your one ticket, there is:
e^-1/0! chance of zero other winners giving you a 100% share of the jackpot IF you win. e^-1/0! * 100% is 0.368
e^-1/1! chance of one other winner giving you a 50% share of the jackpot IF you win. e^-1/1!* 50% is 0.184
e^-1/2! chance of two other winners giving you a 33.3% share of the jackpot IF you win. e^-1/2! * 33% is 0.061
Etcetera. Sum those through infinity and you”ll get an expected jackpot share of 63 % and a jackpot only ticket value of 1/e = 63 cents. Edit: Should say 1 - 1/e = 63 cents
I believe you’re a little off on this part of the calculation
Last edited by: Ace2 on Oct 6, 2023
It’s all about making that GTA
October 6th, 2023 at 3:24:16 PM
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Quote: GenoDRPhI don't have a dog in this discussion, other than casually playing PB and MM when prizes get super high. But 2 comments, if I may:
(1) A PB or Mega Millions play costs $2, $3 if you want the Powerplay or the Megaplier. In Idaho and Montana, Powerball is bundled with Power Play for a minimum purchase price of $3 per play. I keep seeing assumptions based on $1 play, and there is no play for either game that's $1.
(2) How does multiple plays for the same game/draw impact these calculations? For example, last PB I play 3 draws. That was $6. I won $2.
link to original post
Are you saying that in Idaho and Montana the minimum purchase price for PB and MM is $3? I have never heard that and it would surprise me. I am pretty sure I bought a ticket in Montana and didn't know that.
At my age, a "Life In Prison" sentence is not much of a deterrent.
October 6th, 2023 at 3:34:01 PM
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Quote: Ace2
Etcetera. Sum those through infinity and you”ll get an expected jackpot share of 63 % and a jackpot only ticket value of 1/e = 63 cents
I believe you’re a little off on this part of the calculation
link to original post
I followed you to here. I think you mean the ticket value is:
Jackpot / (chance of winning * e * cost of ticket)
ETA:
This ignores non jackpot prizes which per Google are worth 0.25 for mega millions and 0.32 for power ball (each a $2 ticket).
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
October 6th, 2023 at 4:13:48 PM
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Quote: DRichQuote: GenoDRPhI don't have a dog in this discussion, other than casually playing PB and MM when prizes get super high. But 2 comments, if I may:
(1) A PB or Mega Millions play costs $2, $3 if you want the Powerplay or the Megaplier. In Idaho and Montana, Powerball is bundled with Power Play for a minimum purchase price of $3 per play. I keep seeing assumptions based on $1 play, and there is no play for either game that's $1.
(2) How does multiple plays for the same game/draw impact these calculations? For example, last PB I play 3 draws. That was $6. I won $2.
link to original post
Are you saying that in Idaho and Montana the minimum purchase price for PB and MM is $3? I have never heard that and it would surprise me. I am pretty sure I bought a ticket in Montana and didn't know that.
link to original post
The PB website states this verbatim: "Powerball® costs $2 per play. In Idaho and Montana, Powerball is bundled with Power Play® for a minimum purchase price of $3 per play."
The ID state lottery states this verbatim "How to Play
Each play costs $3. Pick five numbers between 1 and 69. Pick one Powerball number between 1 and 26. If you'd like random numbers, ask for a quick pick. Multi-draw tickets can be produced for up to 15 consecutive draws. Drawings are Monday, Wednesday and Saturday. The PowerPlay option is automatically included in every Powerball purchase. PowerPlay for Powerball is a way to multiply your prize of $50,000 or less by 2, 3, 4, 5, or even 10 times. IMPORTANT: The 10 times multiplier is ONLY in play when the advertised annuity jackpot is $150 million or I less. The Match 5 prize with PowerPlay is always $2,000,000. If you match all the numbers you win the jackpot!"
The MT state lottery states this verbatim: "Cost per Play: $3.00
Drawing Days: Mondays, Wednesdays and Saturdays at 8:59 p.m. Mountain Time. You have until 8:00 p.m. on draw days to purchase your Powerball tickets.
Multiple Draws: You may play the same set of numbers for up to 24 consecutive drawings.
Power Play is included with every Powerball purchase! Power Play doubles the Match 5 prize from $1 million to $2 million and increases other prizes according to the chart below. The Power Play number will be drawn separately, but at the same time as the winning numbers for every draw.
Overall odds of winning a prize in Powerball: 1:24.9
Overall Odds: 1:24.9"
Near as I can tell, MM is still 2 bucks everywhere.
October 6th, 2023 at 4:15:55 PM
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The example we’re using here is 300 million tickets sold for a $300 million jackpot and 300 million possible combinations. So those numbers cancel and we’re left with 1 - 1/e = 63 cents. This recent discussion has always been about a “jackpot only” ticket, before tax. The non-jackpot ev is constant and easy to calculateQuote: unJonQuote: Ace2
Etcetera. Sum those through infinity and you”ll get an expected jackpot share of 63 % and a jackpot only ticket value of 1/e = 63 cents
I believe you’re a little off on this part of the calculation
link to original post
I followed you to here. I think you mean the ticket value is:
Jackpot / (chance of winning * e * cost of ticket)
ETA:
This ignores non jackpot prizes which per Google are worth 0.25 for mega millions and 0.32 for power ball (each a $2 ticket).
link to original post
I posted the formula yesterday:
The pretax cash value of a “jackpot-only” ticket is:
j/k * (1 - e^(-k/c))
Where j is jackpot value, k is tickets sold and c is number of ticket combinations.
It’s all about making that GTA
October 6th, 2023 at 8:13:40 PM
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Discrepancies in prices is likely the habit of the lotteries to change the promotion over the years. They add bonuses, and double plays. First lottery I ever played in Illinois was straight up 7 numbers. And of course, they've increased the numbers to change odds. The Fantasy 5 in Florida just went from one evening play, to one in the morning and one in the evening.
There's no secret. Just know what you're talking about before you open your mouth.
October 7th, 2023 at 1:41:42 AM
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the cost of a megamillions ticket can be $1.50 if you do the just the jackpot option. You get 2 quick pick for $3 but the only thing you can win is the jackpot. 5 numbers correct but incorrect megaball pay zilch.Quote: GenoDRPhQuote: DRichQuote: GenoDRPhI don't have a dog in this discussion, other than casually playing PB and MM when prizes get super high. But 2 comments, if I may:
(1) A PB or Mega Millions play costs $2, $3 if you want the Powerplay or the Megaplier. In Idaho and Montana, Powerball is bundled with Power Play for a minimum purchase price of $3 per play. I keep seeing assumptions based on $1 play, and there is no play for either game that's $1.
(2) How does multiple plays for the same game/draw impact these calculations? For example, last PB I play 3 draws. That was $6. I won $2.
link to original post
Are you saying that in Idaho and Montana the minimum purchase price for PB and MM is $3? I have never heard that and it would surprise me. I am pretty sure I bought a ticket in Montana and didn't know that.
link to original post
The PB website states this verbatim: "Powerball® costs $2 per play. In Idaho and Montana, Powerball is bundled with Power Play® for a minimum purchase price of $3 per play."
The ID state lottery states this verbatim "How to Play
Each play costs $3. Pick five numbers between 1 and 69. Pick one Powerball number between 1 and 26. If you'd like random numbers, ask for a quick pick. Multi-draw tickets can be produced for up to 15 consecutive draws. Drawings are Monday, Wednesday and Saturday. The PowerPlay option is automatically included in every Powerball purchase. PowerPlay for Powerball is a way to multiply your prize of $50,000 or less by 2, 3, 4, 5, or even 10 times. IMPORTANT: The 10 times multiplier is ONLY in play when the advertised annuity jackpot is $150 million or I less. The Match 5 prize with PowerPlay is always $2,000,000. If you match all the numbers you win the jackpot!"
The MT state lottery states this verbatim: "Cost per Play: $3.00
Drawing Days: Mondays, Wednesdays and Saturdays at 8:59 p.m. Mountain Time. You have until 8:00 p.m. on draw days to purchase your Powerball tickets.
Multiple Draws: You may play the same set of numbers for up to 24 consecutive drawings.
Power Play is included with every Powerball purchase! Power Play doubles the Match 5 prize from $1 million to $2 million and increases other prizes according to the chart below. The Power Play number will be drawn separately, but at the same time as the winning numbers for every draw.
Overall odds of winning a prize in Powerball: 1:24.9
Overall Odds: 1:24.9"
Near as I can tell, MM is still 2 bucks everywhere.
link to original post
October 7th, 2023 at 6:29:20 AM
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Quote: Ace2The example we’re using here is 300 million tickets sold for a $300 million jackpot and 300 million possible combinations. So those numbers cancel and we’re left with 1 - 1/e = 63 cents. This recent discussion has always been about a “jackpot only” ticket, before tax. The non-jackpot ev is constant and easy to calculateQuote: unJonQuote: Ace2
Etcetera. Sum those through infinity and you”ll get an expected jackpot share of 63 % and a jackpot only ticket value of 1/e = 63 cents
I believe you’re a little off on this part of the calculation
link to original post
I followed you to here. I think you mean the ticket value is:
Jackpot / (chance of winning * e * cost of ticket)
ETA:
This ignores non jackpot prizes which per Google are worth 0.25 for mega millions and 0.32 for power ball (each a $2 ticket).
link to original post
I posted the formula yesterday:
The pretax cash value of a “jackpot-only” ticket is:
j/k * (1 - e^(-k/c))
Where j is jackpot value, k is tickets sold and c is number of ticket combinations.
link to original post
Your formula needs cost of ticket.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
October 7th, 2023 at 8:37:58 AM
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I tried to talk someone out of buying $20 in tickets today, but I was unsuccessful.
He tried to talk me out of buying chewing tobacco.
Touché.
He tried to talk me out of buying chewing tobacco.
Touché.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
October 7th, 2023 at 8:43:00 AM
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Quote: Mission146I tried to talk someone out of buying $20 in tickets today, but I was unsuccessful.
He tried to talk me out of buying chewing tobacco.
Touché.
link to original post
Love it. A real chuckle. Trying to stay away from the universal LOL.
tuttigym
October 7th, 2023 at 9:26:18 AM
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Quote: avianrandythe cost of a megamillions ticket can be $1.50 if you do the just the jackpot option. You get 2 quick pick for $3 but the only thing you can win is the jackpot. 5 numbers correct but incorrect megaball pay zilch.Quote: GenoDRPhQuote: DRichQuote: GenoDRPhI don't have a dog in this discussion, other than casually playing PB and MM when prizes get super high. But 2 comments, if I may:
(1) A PB or Mega Millions play costs $2, $3 if you want the Powerplay or the Megaplier. In Idaho and Montana, Powerball is bundled with Power Play for a minimum purchase price of $3 per play. I keep seeing assumptions based on $1 play, and there is no play for either game that's $1.
(2) How does multiple plays for the same game/draw impact these calculations? For example, last PB I play 3 draws. That was $6. I won $2.
link to original post
Are you saying that in Idaho and Montana the minimum purchase price for PB and MM is $3? I have never heard that and it would surprise me. I am pretty sure I bought a ticket in Montana and didn't know that.
link to original post
The PB website states this verbatim: "Powerball® costs $2 per play. In Idaho and Montana, Powerball is bundled with Power Play® for a minimum purchase price of $3 per play."
The ID state lottery states this verbatim "How to Play
Each play costs $3. Pick five numbers between 1 and 69. Pick one Powerball number between 1 and 26. If you'd like random numbers, ask for a quick pick. Multi-draw tickets can be produced for up to 15 consecutive draws. Drawings are Monday, Wednesday and Saturday. The PowerPlay option is automatically included in every Powerball purchase. PowerPlay for Powerball is a way to multiply your prize of $50,000 or less by 2, 3, 4, 5, or even 10 times. IMPORTANT: The 10 times multiplier is ONLY in play when the advertised annuity jackpot is $150 million or I less. The Match 5 prize with PowerPlay is always $2,000,000. If you match all the numbers you win the jackpot!"
The MT state lottery states this verbatim: "Cost per Play: $3.00
Drawing Days: Mondays, Wednesdays and Saturdays at 8:59 p.m. Mountain Time. You have until 8:00 p.m. on draw days to purchase your Powerball tickets.
Multiple Draws: You may play the same set of numbers for up to 24 consecutive drawings.
Power Play is included with every Powerball purchase! Power Play doubles the Match 5 prize from $1 million to $2 million and increases other prizes according to the chart below. The Power Play number will be drawn separately, but at the same time as the winning numbers for every draw.
Overall odds of winning a prize in Powerball: 1:24.9
Overall Odds: 1:24.9"
Near as I can tell, MM is still 2 bucks everywhere.
link to original post
link to original post
Your mileage may vary. I know for a fact that MA does not offer the $1.50 jackpot only play.
October 7th, 2023 at 9:36:09 AM
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Quote: Mission146I tried to talk someone out of buying $20 in tickets today, but I was unsuccessful.
He tried to talk me out of buying chewing tobacco.
Touché.
link to original post
I quit chewing 15 years ago, still miss it.
Bought 3 tickets today what can I say it;s the only sucker bet I intentionally make and only
after it reaches 1B.
October 7th, 2023 at 9:44:52 AM
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Quote: unJonYour formula needs cost of ticket.
link to original post
No - the "value" is what the ticket is worth once you own it. I think "return" is the amount of profit (i.e. value minus cost).
Obviously, if the value is less than the cost, then it is not a good play.
October 7th, 2023 at 12:22:23 PM
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Quote: rainman
I quit chewing 15 years ago, still miss it.
Bought 3 tickets today what can I say it;s the only sucker bet I intentionally make and only
after it reaches 1B.
I hate to say it, but I bought a lottery ticket too.
At my age, a "Life In Prison" sentence is not much of a deterrent.
October 7th, 2023 at 12:26:01 PM
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YA GOTTA BE IN IT TO WIN IT
October 7th, 2023 at 12:37:32 PM
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Quote: DRichQuote: rainman
I quit chewing 15 years ago, still miss it.
Bought 3 tickets today what can I say it;s the only sucker bet I intentionally make and only
after it reaches 1B.
I hate to say it, but I bought a lottery ticket too.
link to original post
The sacrilege! The blasphemy!
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
October 7th, 2023 at 1:08:31 PM
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The non-winning tickets may be usable as second chance drawing entries.
Some lottery commissions offer these.
For the cost of a stamp, you may get to play again.
If you can get non-winning tickets for a good price...
Some lottery commissions offer these.
For the cost of a stamp, you may get to play again.
If you can get non-winning tickets for a good price...
May the cards fall in your favor.
October 7th, 2023 at 3:07:15 PM
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It’s actually fine to spend a year’s salary on tickets right now. Because it’s positive EV
It’s all about making that GTA
October 7th, 2023 at 3:24:34 PM
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Quote: Mission146Quote: DRichQuote: rainman
I quit chewing 15 years ago, still miss it.
Bought 3 tickets today what can I say it;s the only sucker bet I intentionally make and only
after it reaches 1B.
I hate to say it, but I bought a lottery ticket too.
link to original post
The sacrilege! The blasphemy!
link to original post
I know, I am embarrassed. At least I don't play negative EV slots.
At my age, a "Life In Prison" sentence is not much of a deterrent.
October 7th, 2023 at 6:52:13 PM
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Assuming a $614 million cash value jackpot, 100 million tickets sold (85 million last drawing) and 292 million ticket combinations, the pre-tax expected value of a jackpot only ticket is $1.78. Plus $0.32 for fixed prizes is $2.10. Take 40% tax off and it’s $1.26 or 63% of the $2 ticket cost.
Rounded numbers using j/k * (1 - e^(-k/c)) to get $1.78
So it could potentially and theoretically be slightly +EV for a foreigner with no tax on winnings. That said, I bet the US federal government would find some justification to withhold tax on a foreigner. We’re talking over $200 million in tax.
Rounded numbers using j/k * (1 - e^(-k/c)) to get $1.78
So it could potentially and theoretically be slightly +EV for a foreigner with no tax on winnings. That said, I bet the US federal government would find some justification to withhold tax on a foreigner. We’re talking over $200 million in tax.
Last edited by: Ace2 on Oct 7, 2023
It’s all about making that GTA
October 7th, 2023 at 6:55:11 PM
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Quote: Ace2Assuming a $614 million jackpot, 100 million tickets sold (85 million last drawing) and 292 million ticket combinations, the pre-tax expected value of a ticket is $1.78. Take 40% tax off and it’s $1.07 or 53% of the $2 ticket cost.
Rounded numbers using j/k * (1 - e^(-k/c)) to get $1.78
link to original post
If you are going to do a real example you should add the $0.32 cents for non jackpot winnings.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
October 7th, 2023 at 7:02:41 PM
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I just did, I was still editingQuote: unJon
If you are going to do a real example you should add the $0.32 cents for non jackpot winnings.
link to original post
It’s all about making that GTA
October 7th, 2023 at 10:11:47 PM
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115 million tickets sold. There was about a 2/3 chance of no winners
e^(-115/292) =~ 67%
That chance is 50% at Ln(2) * 292 million = 202 million tickets sold
e^(-115/292) =~ 67%
That chance is 50% at Ln(2) * 292 million = 202 million tickets sold
It’s all about making that GTA
October 7th, 2023 at 10:42:29 PM
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Quote: DRichQuote: rainman
I quit chewing 15 years ago, still miss it.
Bought 3 tickets today what can I say it;s the only sucker bet I intentionally make and only
after it reaches 1B.
I hate to say it, but I bought a lottery ticket too.
link to original post
No winner it's over 1.5 I'm counting on you to re-up so I won't be the only sucker here.
October 11th, 2023 at 4:42:41 PM
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Quote: Ace2I posted the formula yesterday:
The pretax cash value of a “jackpot-only” ticket is:
j/k * (1 - e^(-k/c))
Where j is jackpot value, k is tickets sold and c is number of ticket combinations.
link to original post
For those of you AHEM those of us that's better interested in where that formula comes from:
Let p = the probability of winning = 1 / c
Assuming you have a winning ticket, the amount you win = j divided by (1 + the number of other winning tickets)
In a Poisson distribution, the probability of exactly n winners under the given conditions (k tickets, winning probability c) is:
P(n winners) = (kp)^n / (e^(kp) n!)
In this case, your share of the money would be j / (n + 1) * (kp)^n / (e^(kp) n!)
= j (kp)^n / (e^(kp) n! (n + 1))
= j (kp)^n / (e^(kp) (n + 1)!)
= j ((kp)^(n + 1) / kp) / (e^(kp) (n + 1)!)
= j / (kp) * ((kp)^(n + 1) / (e^(kp) (n + 1)!)
= j / (kp) * P(n + 1) other winners
The expected return if you have a winning ticket = j * (1 * P(0 other winners) + 1/2 P(1 other winner) + 1/3 P (2 other winners) + ...)
= j / (kp) * (P(1 other winner) + P(2 other winners) + P(3 other winners) + ...)
Since P(0 other winners) + P(1 other winner) + P(2 other winners) + ... = 1, this equals j / (kp) * (1 - P(0 other winners)
= j / (kp) * (1 - 1 / e^(kp))
Substitute p = 1 / c and 1 / e^x = e^(-x):
= j / (k/c) * (1 - e^(-(k/c)))
...but you still have to multiply by p (= 1 / c), which is the probability of you having a winning ticket in the first place:
= j / k * (1 - e^(-(k/c)))
October 11th, 2023 at 6:04:42 PM
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If I hit the big one tonight, I want all of y'all especially Wiz and MDawg to come do a giant game of craps at one of the high limit rooms in Vegas.
October 11th, 2023 at 7:23:44 PM
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The question is:Quote: ThatDonGuyQuote: Ace2I posted the formula yesterday:
The pretax cash value of a “jackpot-only” ticket is:
j/k * (1 - e^(-k/c))
Where j is jackpot value, k is tickets sold and c is number of ticket combinations.
link to original post
For those of you AHEM those of us that's better interested in where that formula comes from:
Let p = the probability of winning = 1 / c
Assuming you have a winning ticket, the amount you win = j divided by (1 + the number of other winning tickets)
In a Poisson distribution, the probability of exactly n winners under the given conditions (k tickets, winning probability c) is:
P(n winners) = (kp)^n / (e^(kp) n!)
In this case, your share of the money would be j / (n + 1) * (kp)^n / (e^(kp) n!)
= j (kp)^n / (e^(kp) n! (n + 1))
= j (kp)^n / (e^(kp) (n + 1)!)
= j ((kp)^(n + 1) / kp) / (e^(kp) (n + 1)!)
= j / (kp) * ((kp)^(n + 1) / (e^(kp) (n + 1)!)
= j / (kp) * P(n + 1) other winners
The expected return if you have a winning ticket = j * (1 * P(0 other winners) + 1/2 P(1 other winner) + 1/3 P (2 other winners) + ...)
= j / (kp) * (P(1 other winner) + P(2 other winners) + P(3 other winners) + ...)
Since P(0 other winners) + P(1 other winner) + P(2 other winners) + ... = 1, this equals j / (kp) * (1 - P(0 other winners)
= j / (kp) * (1 - 1 / e^(kp))
Substitute p = 1 / c and 1 / e^x = e^(-x):
= j / (k/c) * (1 - e^(-(k/c)))
...but you still have to multiply by p (= 1 / c), which is the probability of you having a winning ticket in the first place:
= j / k * (1 - e^(-(k/c)))
link to original post
What part of the formula/calculation did I not explain on Oct 5-6?
I even helped you understand how the multiple-winner discount factor is derived. Perhaps I don’t go into as much detail as you because I assume the audience here has an above average math level. I do not pull such a formula out of thin air and I’m glad to elaborate further if anyone asks
Last edited by: Ace2 on Oct 11, 2023
It’s all about making that GTA
October 12th, 2023 at 8:26:08 AM
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And someone in CA hit the jackpot. No splits.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
October 12th, 2023 at 4:36:23 PM
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Quote: Ace2The question is:Quote: ThatDonGuyQuote: Ace2I posted the formula yesterday:
The pretax cash value of a “jackpot-only” ticket is:
j/k * (1 - e^(-k/c))
Where j is jackpot value, k is tickets sold and c is number of ticket combinations.
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For those of you AHEM those of us that's better interested in where that formula comes from:
Let p = the probability of winning = 1 / c
Assuming you have a winning ticket, the amount you win = j divided by (1 + the number of other winning tickets)
In a Poisson distribution, the probability of exactly n winners under the given conditions (k tickets, winning probability c) is:
P(n winners) = (kp)^n / (e^(kp) n!)
In this case, your share of the money would be j / (n + 1) * (kp)^n / (e^(kp) n!)
= j (kp)^n / (e^(kp) n! (n + 1))
= j (kp)^n / (e^(kp) (n + 1)!)
= j ((kp)^(n + 1) / kp) / (e^(kp) (n + 1)!)
= j / (kp) * ((kp)^(n + 1) / (e^(kp) (n + 1)!)
= j / (kp) * P(n + 1) other winners
The expected return if you have a winning ticket = j * (1 * P(0 other winners) + 1/2 P(1 other winner) + 1/3 P (2 other winners) + ...)
= j / (kp) * (P(1 other winner) + P(2 other winners) + P(3 other winners) + ...)
Since P(0 other winners) + P(1 other winner) + P(2 other winners) + ... = 1, this equals j / (kp) * (1 - P(0 other winners)
= j / (kp) * (1 - 1 / e^(kp))
Substitute p = 1 / c and 1 / e^x = e^(-x):
= j / (k/c) * (1 - e^(-(k/c)))
...but you still have to multiply by p (= 1 / c), which is the probability of you having a winning ticket in the first place:
= j / k * (1 - e^(-(k/c)))
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What part of the formula/calculation did I not explain on Oct 5-6?
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The part where you show that the sum actually adds up to what you say it does.
March 22nd, 2024 at 11:09:29 PM
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Mega millions 1.1 billions for March 26 drawing Powerball 750 million March 23 drawing
March 23rd, 2024 at 6:10:43 AM
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I find it curious that Mega Millions jackpot remains ahead of the PowerBall jackpot. This is in spite of the fact that PB has 3 drawings per week while MM has only 2 drawings per week. You would think that the PB jackpot would overtake the MM at some point, given the extra drawing.
March 27th, 2024 at 6:05:05 AM
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1 ticket hit mega millions last night. Ticket was sold in new Jersey. Darkoz,did you have any tickets on it?
March 27th, 2024 at 7:27:57 AM
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I won $4!
Gonna buy myself a new comb!
Gonna buy myself a new comb!
There's no secret. Just know what you're talking about before you open your mouth.
March 27th, 2024 at 8:01:53 AM
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Powerball is getting close to a billion again. Probably get there this week or next if no one wins in the next couple drawings.
March 27th, 2024 at 8:33:37 AM
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Quote: rxwineI won $4!
Gonna buy myself a new comb!
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If i was fortunate enough to win $4, I would probably opt for a chili dog.
At my age, a "Life In Prison" sentence is not much of a deterrent.
March 29th, 2024 at 2:09:54 PM
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This was all for the MegaMillions over the past few weeks, I bought 7 tickets total, and won 7, 7, 7, none, 7, none, 10. Obviously could never manage to land the other numbers but I figured this was a decently rare streak of 'wins' vs 'losses'. What do y'all think? 5-2 ain't too bad.
Hopefully I win it tonight haha...Quote: TigerWuPowerball is getting close to a billion again. Probably get there this week or next if no one wins in the next couple drawings.
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March 31st, 2024 at 9:18:17 AM
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(I'm aware such analysis/ideas are mathematically wrong...)
$100 winner, four numbers. Missed 13 and the powerball number. Still on a weird 'hitting at least a few numbers' streak, but can't manage to guess the other couple of numbers. Main strategy is the theory that the physical balls aren't changed out but every so often, and aren't calibrated perfectly so that certain balls will float into the tube more often than other numbers due to those imperfections. Picked a random assortment of numbers that have hit within the past 5 weeks or so.
$100 winner, four numbers. Missed 13 and the powerball number. Still on a weird 'hitting at least a few numbers' streak, but can't manage to guess the other couple of numbers. Main strategy is the theory that the physical balls aren't changed out but every so often, and aren't calibrated perfectly so that certain balls will float into the tube more often than other numbers due to those imperfections. Picked a random assortment of numbers that have hit within the past 5 weeks or so.
March 31st, 2024 at 12:04:50 PM
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Quote: ChallengedMilly(I'm aware such analysis/ideas are mathematically wrong...)
$100 winner, four numbers. Missed 13 and the powerball number. Still on a weird 'hitting at least a few numbers' streak, but can't manage to guess the other couple of numbers. Main strategy is the theory that the physical balls aren't changed out but every so often, and aren't calibrated perfectly so that certain balls will float into the tube more often than other numbers due to those imperfections. Picked a random assortment of numbers that have hit within the past 5 weeks or so.
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I don't know about Powerball, but California's lottery has multiple sets of balls, in part because of the possibility that not every ball in a set is identical.
However, there's no need to be mathematically correct in this instance; there is the (in)famous case of the "devil's lottery," where the Daily Number draw in Pennsylvania on 4/24/1980 came up 666, because somebody had weighted all of the balls not numbered 4 or 6, and bet heavily on those 8 possible results (444, 446, 464, and so on).
