| Play smart...learn how to play casino craps the right way! |
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| Variance by William J. Enslen, Jr. |
Be smart, play smart, and learn how to play craps the right way.
If the casino has such an advantage over the player, why on
Earth does anyone play the game? My guess is that most
people don't have a clue they're playing a losing game. Others
are so arrogant they think they can outplay the casino and turn
a negative expectation into a positive, even over the long term.
Others know they'll lose, but play anyway for fun and
excitement. As a knowledgeable player, why should you even
bother playing a game you know will beat you? As a
knowledgeable player, is there any hope you can walk away a
winner, at least once in a while, even though you're at a
statistical disadvantage?
Craps is a game of numbers and statistics, with the house
having a built-in advantage. Since craps is based on statistics,
let's find a way to use statistics to our advantage. You'll never
beat the casino over the long haul, but you can, indeed, beat it
in the moments of time when the distribution hiccups and things
go your way.
Let's talk about "variance," which is the average squared
deviation of each number from the mean of a data set. Huh?
Don't worry; we don't need a Harvard math degree to
understand this. It's simply a measure of how spread out the
data is. Let's consider the familiar coin-flip example.
Suppose we flip a coin 10,000 times. We expect heads to
appear about 5,000 times and tails to appear about 5,000
times. Suppose we bet $1 on heads for each flip. If these are
even-money bets, we expect to break even--or close to it after
those 10,000 flips. As illustrated in one of my other articles, the
house doesn't give us even money when it loses. In our
coin-flip example, instead of paying us $1 for each loss,
suppose they pay us only $0.96. With this built-in house
advantage, our negative expectation is to lose about $200 after
10,000 flips. Here's the math. If we expect about 5,000 heads
and about 5,000 tails to appear, then we expect to lose 5000 x
$1 = $5000; and win 5000 x $0.96 = $4800. $5000 - $4800 =
$200. This is called "negative expectation."
Now, of those 10,000 flips, suppose we focus on only 30 of
them, and we continue betting on heads. Of those 30 flips, we
might see heads 25 times and tails only 5 times. This data
fluctuation shows that, for a limited number of flips over a short
period of time, we can get lucky and experience Nirvana where
things go our way. I call it a "Nirvana hiccup" in the distribution
that causes a relatively high variance. In this example of only
30 flips, we win $24 for the 25 heads (i.e., 25 x $0.96 = $24),
and lose $5 for the 5 tails (i.e., 5 x $1 = $5), which gives us a
net win of $19. This short term variance temporarily removes
the long-term negative expectation, which means there are,
indeed, times when we can walk away a winner.
Although you'll lose in the long-term, there are times when you'll
win because of variance. Suppose you take a three-day
vacation in Vegas once a year and play four one-hour craps
sessions each day (i.e., a total of 12 hours for the trip). You
could conceivably get extremely lucky and hit that Nirvana
hiccup during each session, and then go home a big winner. In
that case, you go home thinking you're a genius, a craps god,
invincible, a world-class gambling stud. Yeah, sure, okay. I
don't recommend quitting your day job.
Now, suppose you're a Vegas local who plays an hour every
day after work. In this case, it's clear that whatever few Nirvana
hiccups you experience will be properly adjusted over time such
that you'll lose your shirt in the long-term.
Therefore, the infrequent craps player can, indeed, consistently
win if she's lucky enough to hit those Nirvana hiccups.
However, the frequent long term player has no chance of
coming out a winner at the end of his craps life. Part of the
secret to craps is knowing how to be around for those
occasional Nirvana hiccups where the dice fall your way.
If you don't want to lose your shirt, you must learn the secret to
craps. Don't fall for bogus winning systems or ridiculous
dice-setting claims. Distribution variance is the only thing that
makes you a short-term winner. Nothing else. No silly dice
setting technique. No bogus winning system. It's the
distribution variance and nothing else. Got it?
Now you know! Remember, be smart, play smart, and learn
how to play craps the right way.
back to Articles
If the casino has such an advantage over the player, why on
Earth does anyone play the game? My guess is that most
people don't have a clue they're playing a losing game. Others
are so arrogant they think they can outplay the casino and turn
a negative expectation into a positive, even over the long term.
Others know they'll lose, but play anyway for fun and
excitement. As a knowledgeable player, why should you even
bother playing a game you know will beat you? As a
knowledgeable player, is there any hope you can walk away a
winner, at least once in a while, even though you're at a
statistical disadvantage?
Craps is a game of numbers and statistics, with the house
having a built-in advantage. Since craps is based on statistics,
let's find a way to use statistics to our advantage. You'll never
beat the casino over the long haul, but you can, indeed, beat it
in the moments of time when the distribution hiccups and things
go your way.
Let's talk about "variance," which is the average squared
deviation of each number from the mean of a data set. Huh?
Don't worry; we don't need a Harvard math degree to
understand this. It's simply a measure of how spread out the
data is. Let's consider the familiar coin-flip example.
Suppose we flip a coin 10,000 times. We expect heads to
appear about 5,000 times and tails to appear about 5,000
times. Suppose we bet $1 on heads for each flip. If these are
even-money bets, we expect to break even--or close to it after
those 10,000 flips. As illustrated in one of my other articles, the
house doesn't give us even money when it loses. In our
coin-flip example, instead of paying us $1 for each loss,
suppose they pay us only $0.96. With this built-in house
advantage, our negative expectation is to lose about $200 after
10,000 flips. Here's the math. If we expect about 5,000 heads
and about 5,000 tails to appear, then we expect to lose 5000 x
$1 = $5000; and win 5000 x $0.96 = $4800. $5000 - $4800 =
$200. This is called "negative expectation."
Now, of those 10,000 flips, suppose we focus on only 30 of
them, and we continue betting on heads. Of those 30 flips, we
might see heads 25 times and tails only 5 times. This data
fluctuation shows that, for a limited number of flips over a short
period of time, we can get lucky and experience Nirvana where
things go our way. I call it a "Nirvana hiccup" in the distribution
that causes a relatively high variance. In this example of only
30 flips, we win $24 for the 25 heads (i.e., 25 x $0.96 = $24),
and lose $5 for the 5 tails (i.e., 5 x $1 = $5), which gives us a
net win of $19. This short term variance temporarily removes
the long-term negative expectation, which means there are,
indeed, times when we can walk away a winner.
Although you'll lose in the long-term, there are times when you'll
win because of variance. Suppose you take a three-day
vacation in Vegas once a year and play four one-hour craps
sessions each day (i.e., a total of 12 hours for the trip). You
could conceivably get extremely lucky and hit that Nirvana
hiccup during each session, and then go home a big winner. In
that case, you go home thinking you're a genius, a craps god,
invincible, a world-class gambling stud. Yeah, sure, okay. I
don't recommend quitting your day job.
Now, suppose you're a Vegas local who plays an hour every
day after work. In this case, it's clear that whatever few Nirvana
hiccups you experience will be properly adjusted over time such
that you'll lose your shirt in the long-term.
Therefore, the infrequent craps player can, indeed, consistently
win if she's lucky enough to hit those Nirvana hiccups.
However, the frequent long term player has no chance of
coming out a winner at the end of his craps life. Part of the
secret to craps is knowing how to be around for those
occasional Nirvana hiccups where the dice fall your way.
If you don't want to lose your shirt, you must learn the secret to
craps. Don't fall for bogus winning systems or ridiculous
dice-setting claims. Distribution variance is the only thing that
makes you a short-term winner. Nothing else. No silly dice
setting technique. No bogus winning system. It's the
distribution variance and nothing else. Got it?
Now you know! Remember, be smart, play smart, and learn
how to play craps the right way.
back to Articles
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| Remember, learn how to play casino craps the right way! My book teaches you to play in reality, not Fantasyland. |
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