The Power Ball has reached a $340 million dollar jackpot, and a lot of people are talking about it in the news.
I got to thinking, how big does the jackpot have to get before it becomes statistically profitable to buy a ticket for EVERY SINGLE NUMBER. (positive expected value, or Plus EV, to us stat geeks).
So, here are all the calculations I did. For those of you uninterested in the nitty-gritty, go all the way to the bottom for the findings.
$1 gets you a 1 in 150 million chance of winning.
The jackpot is $340 million.
If you play every number, it would then cost $150 million dollars.
If you play every number, and nobody else wins the jackpot you win $340 million.
340 - 150 = $190 million PROFIT.
If the jackpot is split with one other winner, you’d win $170 million.
170 – 150 = $20 million PROFIT.
If the jackpot is split with two other tickets, you’d win $113 million.
113 – 150 = $37 million LOSS.
The post-gazette stated yesterday that there is about a 55% chance someone will win tomorrow.
So, we can assume that if you play EVERY ticket, there is a 45% chance you’d be the only winner, and a 55% chance that you’d have to split the pot.
If we make some conjecture here, and say that the chance of only 1 other winner is 50%, a 30% chance of 2 other winners, and a 20% chance of 3 other winners, we can come up with an approximate expected value for playing every number.
So, $190 * .45 + $20 * (.55) * (.5) + (-37) * (.55) * (.3) + (-65) * (.55) * (.2) = 85.5 + 5.5 – 6.105 – 7.15
Or $77.745 million profit.
But, of course, you need to pay "the man". If tax is 35%, does that take away your advantage?
The EV equation becomes 74 * .45 + (-36.5) * .275 + (-73.55) * .165 + (-91.75) * .11 = 33.3 – 10 – 12.1 – 10
(To be more fair, I added a +3 to all those numbers, because we really only need to pay for 147 million numbers).
-- RESULTS --
Or about $1.2 million profit for playing every number. Damn, that’s still profitable, but just barely, considering you invested $150 million. You'd have a 45% chance of winning a lot of money, and 55% chance of losing money, which probably plateaus as high as a $100 million loss.
I don't recommend buying every ticket.
If there were no taxes, it would be completely different. In that case you could probably start a mutual fund just to buy lottery tickets and give away the dividends to shareholders, over time it would certainly have a net gain better than the stock market. *grin*
Also, as the jackpot continues to grow, the chance you'd have to split the pot also grows because more people play when the jackpot is high. So I'd speculate that the statistical profitability of the game is never going to make it worth buying every ticket.
Wednesday, October 19, 2005
Sunday, October 02, 2005
Let There Be Lightbulbs - Part II (of 2)
Somebody realized it would be cool if you wired up some fiber-optic cable to a big satellite-dish shaped mirror on a roof that always points at the sun.
Fiber optic cable transmits light very well over short distances, and as such, you can run some cable from the roof into the building and get sunlight – natural sunlight – all through the building, as long as the sun is up. It even works if its partly sunny, because there’s so much more ambient light from the sun, compared to lighting we use. Ever turn on a lamp during the day in a bright sunny room? You can’t really tell the lamp is on. Same deal. You’re pumping all that super-bright sunlight into the building, so you can spread out the sun’s light to a lot of rooms.
What is this ideal for? Well, its not so good for homes, because homes like lighting during the night. No sun, no light. But guess what – Americans use more electricity for lighting during the day than at night. What it is good for is the workplace.
The ideal place is short large-area buildings commonly found in quickly-built office parks, and warehouse type construction where internal lighting is required because large parts of a building have no natural light. Sunnier regions will benefit more. Sorry Pittsburgh and Seattle.
Once you get the cable laid down, the energy cost is virtually zero. It just needs a 9 volt battery to run a GPS monitor and a little motor so that the Mirror on the roof always points at the sun. The cable is about as complicated to install as wiring up normal electric overhead lighting, though more expensive. For taller buildings, they need to use a different kind of fiber optic cable that costs way more, so anything over 4 stories is not cost saving at this point.
Like the compact-fluorescent bulb, the cost savings grow over time.
They also have a tax-benefit for installing systems like this.
There are other psychological benefits that go with using natural light too. Its an intangible, but if they can show that people working in natural light have higher attendance and less sick days, then it could add to the savings of a solar lighting system.
Only a few buildings have currently installed this solar lighting system, but I would really like to see some feedback from both people who work in these places, and the financial numbers from the companies.
I admit, this one is a lot more experimental than the compact-fluorescents, but it sure sounds cool.
Fiber optic cable transmits light very well over short distances, and as such, you can run some cable from the roof into the building and get sunlight – natural sunlight – all through the building, as long as the sun is up. It even works if its partly sunny, because there’s so much more ambient light from the sun, compared to lighting we use. Ever turn on a lamp during the day in a bright sunny room? You can’t really tell the lamp is on. Same deal. You’re pumping all that super-bright sunlight into the building, so you can spread out the sun’s light to a lot of rooms.
What is this ideal for? Well, its not so good for homes, because homes like lighting during the night. No sun, no light. But guess what – Americans use more electricity for lighting during the day than at night. What it is good for is the workplace.
The ideal place is short large-area buildings commonly found in quickly-built office parks, and warehouse type construction where internal lighting is required because large parts of a building have no natural light. Sunnier regions will benefit more. Sorry Pittsburgh and Seattle.
Once you get the cable laid down, the energy cost is virtually zero. It just needs a 9 volt battery to run a GPS monitor and a little motor so that the Mirror on the roof always points at the sun. The cable is about as complicated to install as wiring up normal electric overhead lighting, though more expensive. For taller buildings, they need to use a different kind of fiber optic cable that costs way more, so anything over 4 stories is not cost saving at this point.
Like the compact-fluorescent bulb, the cost savings grow over time.
They also have a tax-benefit for installing systems like this.
There are other psychological benefits that go with using natural light too. Its an intangible, but if they can show that people working in natural light have higher attendance and less sick days, then it could add to the savings of a solar lighting system.
Only a few buildings have currently installed this solar lighting system, but I would really like to see some feedback from both people who work in these places, and the financial numbers from the companies.
I admit, this one is a lot more experimental than the compact-fluorescents, but it sure sounds cool.
Let There Be Lightbulbs - Part I
There are a lot of new technologies in the lighting business.
Part I
Compact – fluorescent bulbs give off very nice light, require one fourth the power, and last from four to sixteen times as long as a standard incandescent light bulb. They cost about $4 per bulb.
A 100 Watt incandescent bulb that you run for three hours a day, costs about a dollar a month in electricity. An equivalent fluorescent bulb costs you about a quarter. That doesn’t sound too impressive. But then – the incandescent will burn out sooner.
So, a fluorescent bulb running for 3 hours a day every day will last about four years. During that time, you’d have to change the incandescent light bulb about four times. So that’s an additional two dollars or so you save, assuming an incandescent costs about fifty cents apiece. (Not including the inconvenience of changing a light bulb).
Since the fluorescent light bulb is going to last four years, it makes sense to see how much less energy the fluorescent is over four years compared to the incandescent. That’s about $.75 * 12 months * 4 years. That comes out to $36. Now, if you consider the extra cost of replacing 4 incandescent over that time, that’s $2, but we have to take away the extra cost of the fluorescent to begin with, so that reduces our savings by $2. Still with me?
The bottom line is, over the course of four years, a fluorescent costs about $34 less compared to a standard.
Well, that’s really something now. Thirty four dollars for a light bulb? Who knew. And that’s just one light bulb. And - the total savings over the life of a bulb is the same regardless of how often you use it, but the more you use a light, the faster you’ll save.
I dunno about you, but I'm done with incandescents.
Part I
Compact – fluorescent bulbs give off very nice light, require one fourth the power, and last from four to sixteen times as long as a standard incandescent light bulb. They cost about $4 per bulb.
A 100 Watt incandescent bulb that you run for three hours a day, costs about a dollar a month in electricity. An equivalent fluorescent bulb costs you about a quarter. That doesn’t sound too impressive. But then – the incandescent will burn out sooner.
So, a fluorescent bulb running for 3 hours a day every day will last about four years. During that time, you’d have to change the incandescent light bulb about four times. So that’s an additional two dollars or so you save, assuming an incandescent costs about fifty cents apiece. (Not including the inconvenience of changing a light bulb).
Since the fluorescent light bulb is going to last four years, it makes sense to see how much less energy the fluorescent is over four years compared to the incandescent. That’s about $.75 * 12 months * 4 years. That comes out to $36. Now, if you consider the extra cost of replacing 4 incandescent over that time, that’s $2, but we have to take away the extra cost of the fluorescent to begin with, so that reduces our savings by $2. Still with me?
The bottom line is, over the course of four years, a fluorescent costs about $34 less compared to a standard.
Well, that’s really something now. Thirty four dollars for a light bulb? Who knew. And that’s just one light bulb. And - the total savings over the life of a bulb is the same regardless of how often you use it, but the more you use a light, the faster you’ll save.
I dunno about you, but I'm done with incandescents.
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