How hard is it to win the
lottery?
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Here are other things that have about a
1 in 50 million chance of happening.
Odds of dealing out 13 cards to each
of four players using a 52-card deck and
all four players having a straight from
two to Ace: 1 in 61 million
(WizardOfOdds.com)
I have a stack of 64 Bibles. I pick
a single word from one of them. Odds of
you picking the exact same word (same
instance) from the same Bible: 1 in 50
million
Flipping a coin 25 times and getting
25 heads or 25 tails: 1 in 34
million
Odds of being dealt a sequential
royal flush (forwards or backwards): 1
in 40 million
(WizardOfOdds.com)
Odds of #7 hitting in roulette, five
times in a row: 1 in 79 million
Chance that radioactive monkeys will
kidnap Britney Spears and convert her to
Buddhism: 1 in 46 million
(estimate)
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All
of us dream about winning the big jackpot. But
how likely is it? Let's find out. The answers may
surprise you.
Multi-Million
Dollar Jackpots
There are exactly two games that offer
multimillion-dollar jackpots: progressive slot
machines and the state lottery. Which is the better
bet? Well, that depends on what your goals are. If
you want the best chance of winning the jackpot,
the lottery is your best bet. But if you want the
best chance of breaking even or winning
anything, you'll want to go with the slot
machine. Let's take a look at the odds in more
detail.
For our slot machine I'll use the Megabucks
slot machine in Nevada since it's the most famous
multimillion-dollar slot, and for the lottery I'll
use the Texas
Lotto since it's the game I'm most familiar
with. (You can look up the odds for your own state
lottery on your state lottery website.)
As I write this, the Megabucks slot machine
jackpot in Nevada is around $16 million, and the
Texas State Lotto is also around $16 million.
The odds of winning Megabucks are 1 in 49,836,032
according to the Las
Vegas Sun, and the odds of winning the Texas
Lotto are 1 in 47,784,352. The prizes and the odds
are almost the same. So what's the difference?
Well, there are two differences. The first is
that the odds of hitting a smaller jackpot with a
slot machine are much, much better. Slot machines
are far more generous in giving small and medium
sized wins. You're less likely to win anything with
the Lotto, and if you do you'll probably win only
$5.
A progressive slot machine generally returns
around 90% of all the money ever played, while the
lotto returns only around 52%. The lotto has the
worst paytable of any game on the planet.
Figuring the odds for multiple
plays
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If your odds of winning a game with one
play are 1 in 2,000,000, you might figure
that if you play two times then your odds
are twice as good -- 1 in 1,000,000. This
shortcut works for estimating the odds
when the odds are very large and when
we're talking about only a small number of
plays. But if the odds are small, or if
you're playing many, many, times, then
that shortcut no longer works.
For example, if the odds were 1 in
2,000,000 and you played a million times,
you might think your odds have increased
to 1 in 2, or 50%. But in fact your odds
of winning are only 39%. Here's another
example: Let's say you're trying to roll a
#5 on a die, and you get three chances to
roll the die. Your odds aren't 50%, of
getting the 5, they're only 42%. How can
this be?
Think of it this way: If three rolls
meant your odds were 3/6, then six rolls
would mean your odds are 6/6, or 100%. But
you obviously you don't get a 100%
guarantee of rolling a #5 just because you
roll the die six times. So we know that
you can't just divide by the number of
trials.
So how do we calculate our odds?
The answer is that we take the opposite of
the odds of losing, which must be the odds
of winning. In the case of trying to get a
5 with three rolls of a die, your odds of
losing on the first roll are 5/6, and on
the second roll are 5/6, and the third
roll are 5/6. That's 5/6 x 5/6 x 5/6, or
125/216, or 58%. If we have a 58% chance
of losing, then we have a 42% chance of
winning.
Here's the general formula for finding
the odds of winning when you repeat the
bet with certain odds (d) a certain number
of times (n), which you can type directly
into Excel:
=1-((1-d)n)
For example, if the odds of hitting a
jackpot are 1 in two million (or
1/2000000, or 0.0000005) and you play one
million times, the odds are:
1/(1-((1-0.0000005)1000000))
= 39%
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On the other hand, even though we're less likely
to win anything with the lotto than with a
slot machine, the lotto actually gives you better
odds of winning the jackpot for the amount of
money you spend. A shot at Megubucks requires
$3 while a Lotto ticket is only a dollar. For for
the price of a shot at Megabucks you could buy
three Lotto tickets. And buying three lottery
tickets increases your chances of winning to 1 in
15,928,118.
So which is the better bet for $3? It's a
tradeoff: If your goal is to have the best shot at
winning the jackpot, then your chances of winning
with three $1 Lotto tickets are almost three times
better than winning with one $3 spin on Megabucks.
But if you're hoping to win anything and
have at least a small win, then a spin at Megabucks
is the better bet.
Million-Dollar
Jackpots
As you might suspect, the bigger the prize, the
harder it is to win. To improve your chances of
winning, you can simply go for a smaller prize.
Winning just a million dollars is easier than
winning several million dollars.
The Texas Lottery has a scratch-off game called
$1,000,000 Classic. There are eight winning tickets
out of the 8,095,350 printed, so the odds are 1 in
1,011,919 of winning by buying a single ticket. But
the catch is that a single ticket costs $20. If
instead we bought twenty $1 Lotto tickets then our
odds of winning the Lotto would be 1 in 2,389,218.
So that's quite a tradeoff: We doubled our chances
of winning by going with the scratch-off instead of
the Lotto, but now we'd only win a million dollars
rather than several million.
(I'm not going to cover every lottery game that
exists, but the one with the best odds of winning a
million dollars that I could find is the Georgia
Lottery's Millionare Raffle,with odds of 1 in
125,000 to win a million bucks with a $20
ticket.)
The Texas Lottery also has a $20 scratch-off
game with a $2,000,000 top prize, with odds of 1 in
2,680,000 of getting it. But that's worse than the
odds of buying twenty $1 Lotto tickets (2,389,218).
With this particular game you get worse odds to win
a smaller amount of money, so it's definitely a bad
bet.
So while going for a lesser jackpot with the
lottery might not improve your odds as much as you
like, going for a lesser amount on a slot machine
probably does. We don't know the exact odds of
hitting a jackpot on a machine whose average top
prize is about half a million dollars, but we can
make an educated guess. Since the average
Megabucks jackpot is $14.4M and the odds of
winning are about 1 in 50M, that puts the odds at
right about 1 in 3.5x the amount of the jackpot.
With a slot with an average jackpot around $0.5M,
that would put the odds of hitting it at 1 in 1.75M
(3 x 0.5M). Again, we don't know these odds for
sure, but it's a very educated guess.
Turning all
this into a strategy
The 1 in 1.75M chance for hitting the jackpot on
a moderately-sized progressive slot are the best
odds we've seen for anything we've examined so far.
So how can you turn this into a playing strategy?
First, let's assume that you can afford to lose a
couple of dollars each week on average while trying
for the big prize. Let's also say that you want to
play fairly frequently, because you want frequent
opportunities to win, which keeps things
interesting.
One way is to play one spin a day. That
shoots your odds of hitting the jackpot up to 1 in
4,795 over that year. And how much will it cost you
to play every day? If the machine you play pays
back about 90% (typical for progressive slots),
that'll come to an expected loss 365 x $3 x 10% =
$109.50 for the year. Of course your actual results
could be anywhere on the map for only 365 spins,
but this gives us a frame of reference. And if
$109.50 is more than you care to lose in a year,
you can always play once a week or a couple of
times a week rather than every day -- though
naturally that makes you less likely to hit the
jackpot.
Another way to get a million
dollars
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Could you live without your car? No?
What if someone offered you $2.3 million
to give it up?
That's how much you'd have if you
invested the $7,754 in average car costs
every year from the ages of 25 to 67 with
an 8% annual return. Staggering, isn't it?
(read
full article...)
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Of course, it's a hassle to go to a casino every
day just to make one spin. We can accomplish the
same thing by going to a casino once a week and
making seven spins at that time. We could take it
even further and play 365 spins once a year, but
that wouldn't be in keeping with our goal of
playing frequently so we have frequent
opportunities to win.
But what if going to a casino even once a week
is inconvenient, or there's no casino where you
live? That's why we save the best for last: Our
preferred solution is to play the Major Millions
progressive slot at Captain
Cooks online casino. The Major
Millions jackpot starts at $250,000 and has gone as
high as $1.6 million. (In fact, Captain Cooks
awarded the very first $1 million+ jackpot ever won
online to a lucky Major Millions player in May
2002.) Using our educated guess from earlier, we
estimate the odds of hitting this jackpot to be the
same 1 in 4,795 for 365 spins. And since you can
play from your home or office, you can easily play
one spin once a day or seven spins once a week.
Major Millions gives the best odds of winning
a big prize with the most convenience.
In fact, if you know of a
game that offers better odds for winning $1
million+ with a $3 bet, I'd like to hear about
it.
You can try
Major Millions yourself at Captain
Cooks.
Odds for winning various large jackpots based on
the amount wagered
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Game
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Number of
Plays
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Jackpot
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Odds of
winning are 1 in....
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$1 bet
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Texas Lotto
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1 ticket
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$4 - $47 million
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47,784,352
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$3 bet
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Major Millions online slot at Captain
Cooks
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1 spin
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$250k - $1.6 million
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1,750,000a
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Texas Lotto
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3 tickets
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$4 - $47 million
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15,928,118
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Megabucks Slot
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1 spin
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$6 - $39 million
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49,836,032
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$10 bet
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Baccarat
Series Bet
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1 series
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$1 million
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205,179b
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Major Millions online slot at Captain
Cooks
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3 spinsc
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$250k - $1.6 million
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583,334a
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Texas Lotto
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10 tickets
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$4 - $47 million
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4,778,436
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Megabucks**
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3 spinsc
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$6 - $39 million
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16,612,011
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$20 bet
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Baccarat Series Bet
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1 series
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$1 million
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103,996b
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Major Millions online slot at
Captain
Cooks
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7
spinsc
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$250k - $1.6
million
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250,000a
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$1M TX Scratch-Off
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1 scratch-off
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$1 million
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1,011,919
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Texas Lotto
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20 tickets
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$4 - $47 million
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2,389,218
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$2M TX Scratch-off
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1 scratch-off
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$2 million
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2,680,000
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Megabucks Slot**
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7 spinsc
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$6 - $39 million
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7,119,434
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NOTES: a. Odds are an educated
guess. b. Odds are theoretical,
because likely no casino would let you
take a series bet high enough to win a
million dollars. (more)
c. Megabucks bet amounts are
actually $9 and $21 instead of $10 and
$20, because Megabucks requires
$3/spin.
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References for this article:
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