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Winning the lottery is as easy as flipping a coin
By Mr. Stupid | April 7, 2008
True story. My best friend is a bit of a maroon when it comes to money. He lives paycheck to paycheck. He buys stuff he can’t afford (HD TV, new computer). Hell, he leases stuff he can’t afford (2008 Sienna minivan). He is a very bright guy, but can’t seem to get out of his spending ways long enough to improve his situation.
So he called me up the other day to tell me he was depressed. I asked him why, seeing as how he’s my best friend. He said, “I was driving around a neighborhood today and saw a woman playing with her kid on her front lawn. She was pulling him in one of those open wagons.” I quickly responded with “So you’re depressed ’cause she was hot and you knew you could never get her?”
“No, that’s not why,” he said. “It’s because I know I’ll never have a front lawn.” It’s true, he rents a small apartment and has no clue how to save for a down payment on a house. He continued, “And I got to thinking about that, and thinking about how I could ever afford to buy a house. The only thing I came up with is that I could try and win the lottery.”
“Uh huh.”
“So I bought two lottery tickets.”
What followed was the typical conversation about the evils of the lottery system and how it just excacerbates the situations of many lower and lower-middle class families. Eventually we got around to discussing the odds of his winning that night. He had two tickets, both MegaBucks. His chances to win MegaBucks were 1 in 5,245,786.
Probability is definitely a big mystery to me.
I know that if I roll a die, I have a 1 in 6 chance of getting a 6. If I flip a coin, I have a 1 in 2 (or 50%) chance of getting heads. If I need that 5th club for the flush, I have a 4 in 23 chance(*). If I forget to bring home flowers on Mother’s Day… Wow… I don’t even wanna calculate the probability of getting laid that night.
The big numbers
The big numbers are just so… big. And abstract. If I play MegaBucks, I have a 1 in 5,245,786 chance of winning the grand prize. Does that mean if I roll a 5,245,786-sided die… I just can’t picture the odds of that.
So I like to put things into perspective, into concrete terms that I can understand. I like to think of things in black and white, zeros and ones, heads and tails. How many times would a coin have to land on heads — in a row — in order for me to say, “Wow, that happens only one in a 5,245,786 times”?
The basics
Assuming a fair coin, the probability of it landing on all heads in N flips is 1 over 2 to the Nth, or:
For example, the probability of flipping a coin once and getting a head is 1/2^1, or 1/2; the probability of flipping a coin twice and getting two heads is 1/2^2, or 1/4.
Given that, the probability of flipping a coin 10 times and getting all heads is 1/1024. Flipping a coin 20 times and getting all heads has probability close to one in a million, and 30 times is close to one in a billion.
Here are the actual numbers, the first column being the number of flips, and the second column being the probability of that many flips coming up all heads. The third column is an approximate chance of something happening:
1. . . 1 in 2 — having a girl
2. . . 1 in 4 — Petraeus gave the surge 1 in 4 chance of success
3. . . 1 in 8 — having ambiguous genitalia if your parents both do
4. . . 1 in 16 — all basins in a house drain the same direction (out of 4)
5. . . 1 in 32 — hitting a flush when you have suited hole cards
6. . . 1 in 64 — picking the winning March Madness team
7. . . 1 in 128 — approximate odds of a baby having autism
8. . . 1 in 256 — being killed on the road in Britain
9. . . 1 in 512 — asteroid “2000 SG 344″ hits earth in 2030
10. . . 1 in 1,024 — getting a busy signal when you dial a random number
11. . . 1 in 2,048 — tubal ligation failing
12. . . 1 in 4,096 — hair dye causing cancer
13. . . 1 in 8,192 — dying in a car accident in America
14. . . 1 in 16,384 — a child will become a professional athlete
15. . . 1 in 32,768 — encounter or hatch a shiny Pokemon
16. . . 1 in 65,536 — being poisoned accidentally
17. . . 1 in 131,072 — killed riding a bicycle
18. . . 1 in 262,144 — someone falling on you at the Eiffel Tower
19. . . 1 in 524,288 — dying in burning pajamas
20. . . 1 in 1,048,576 — dying from an environmental hazard
21. . . 1 in 2,097,152 — be struck by lightning
22. . . 1 in 4,194,304 — you’re Kennedy autograph is real
23. . . 1 in 8,388,608 — dying in a plane crash
24. . . 1 in 16,777,216 — dying on a plane
25. . . 1 in 33,554,432 — being murdered today
26. . . 1 in 67,108,864 — having two sets of triplets
27. . . 1 in 134,217,728 — win Powerball
28. . . 1 in 268,435,456 — Rodham legitimately profits in cattles futures
29. . . 1 in 536,870,912 — dying from anthrax
30. . . 1 in 1,073,741,824 — having same DNA as someone else
To win the lottery, you gotta flip like Rosencrantz.
Summary
So to win MegaBucks, which has a probability of 1 in a 5,245,786, I just need to flip a coin about 22 times and get all heads. Easy! I doubt the State Lottery wants you to think of it in these terms. They’d rather have you buy a ticket with your coins than flip them and see that you’ll never win. Hell, the word “probability” doesn’t even appear on their website. Anywhere. See for yourself. Nor does the word “chances“. Or the phrase “tax on stupidity“.
The next day I called my friend and asked him to flip a coin. “Tell me what it landed on,” I said.
“Tails.”
* — I based this on a common situation in Texas Hold-em, where you have two clubs in your hand and there are two clubs on the board, with the river card to come. You can see 4 clubs and two other cards that aren’t clubs. That leaves 8 clubs remaining in the deck, out of 46 unseen cards, or 4 in 23.
Topics: misc |
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