http://www.scientificamerican.com/article.cfm?id=fact-or-fiction-living-outnumber-dead&ref=sciam
The human population has swelled so much that people alive today outnumber all those who have ever lived, says a factoid whose roots stretch back to the 1970s.
Tuesday, December 1, 2009
Thursday, November 19, 2009
Math Day
I took some kids from my school down to CSU-Pueblo for a math competition today and our upperclassmen did very well. We lost to only one team and came home with a big trophy for the math bowl competition. In the individual written contest, we got a 2nd place, 5th place, and two honorable mentions - so all our upperclassmen placed. We did the best out of all the schools in our district that went down on the bus together to the competition.
The pictures in this post were taken at the CSU-Pueblo Physics/Math building - they had some neat art reminiscent of Islamic tilings.
Wednesday, July 8, 2009
Math Humor
One evening Rene Descartes went to relax at a local tavern. The tender approached and said, "Ah, good evening Monsieur Descartes! Shall I serve you the usual drink?". Descartes replied, "I think not.", and promptly vanished.
---
"The problems for the exam will be similar to the ones discussed in the class. Of course, the numbers will be different. But not all of them. Pi will still be 3.14159... "
---
Salary Theorem
The less you know, the more you make.
Proof:
Postulate 1: Knowledge is Power.
Postulate 2: Time is Money.
As every engineer knows: Power = Work / Time
And since Knowledge = Power and Time = Money
It is therefore true that Knowledge = Work / Money .
Solving for Money, we get:
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.
---
Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed?
---
Abbott and Costello made arithmetic shenanigans the basis
of a number of their comic dialogs.
Here is a dialog from their movie titled Buck Privates:
Abbott: You're 40 years old, and you're in love with a little girl,
say 10 years old. You're four times as old as that girl.
You couldn't marry that girl, could you?
Costello: No. ?
Abbott: So you wait 5 years. Now the little girl is 15, and you're 45.
You're only three times as old as that girl.
So you wait 15 years more.
Now the little girl is 30, and you're 60.
You're only twice as old as that little girl. ?
Costello: She's catching up. ?
Abbott: Here's the question. How long do you have to wait before you
and that little girl are the same age?
Costello: What kind of question is that? That's ridiculous.
If I keep waiting for that girl, she'll pass me up.
She'll wind up older than I am.
Then she'll have to wait for me!
Here's another encounter from Buck Privates, one echoed in
several later movies.
Abbott: Do me a favor. Loan me $50.
Costello: I can't lend you $50. All I've got is $40.
Abbott: That's okay. Give me the $40, and you'll owe me $10.
Costello: How come I owe you $10?
Abbott: What did I ask you for?
Costello: $50.
Abbott: What did you give me?
Costello; $40.
Abbott: So you owe me $10.
Costello: That's right. But you owe me $40. Give me my $40 back.
Abbott: There's your $40. Now give me the $10 you owe me.
That's the last time I'll ever ask you for the loan of $50.
Costello: How can I loan you $50 now? All I have is $30.
Abbott: Give me the $30, and you’ll owe me $20.
Costello: This is getting worse all the time.
First I owe you $10, and now I owe you $20!
Abbott: So you owe me $20. Twenty and 30 is 50.
Costello; Nope! Twenty-five and 25 is 50.
Abbott: Here's your $30. Give me back my $20.
Costello: All I've got now is $10!
Abbott then entices Costello into a silly, double-or-nothing
number game.
Abbott: Take a number, any number at all from 1 to 10, and don't tell me.
Costello: I got it.
Abbott: Is the number odd or even?
Costello: Even.
Abbott: Is the number between 1 and 3?
Costello: No.
Abbott: Between 3 and 5?
Costello: No. I think I got him.
Abbott: Between 5 and 7?
Costello: Yes.
Abbott: Number six?
Costello: Right. . . . How did he do that?
Toward the end of the movie, during a boxing match, Costello is
knocked to the canvas, and the biased referee gives a quick
count: 2, 4, 6, 8, 10.
Costello: What's this? 2, 4, 6, 8, 10? What happened
to 1, 3, 5, 7, and 9?
Ref: I don't like them numbers. They're odd.
X equals just about everything I learned of math in school
By DAVE BARRY
--------------------------------------------------------------------------------
President Bush says our schools need to do a better job of teaching mathematics, and I agree with him 150 percent. Many high-school students today can't even calculate a square root! Granted, I can't calculate a square root, either, but I USED to be able to, for a period of approximately 15 minutes back in 1962. At least I think that was a square root. It might have been a ``logarithm.''
But whatever it was, if I had to learn how to do it, these kids today should have to learn it, too. As President Bush so eloquently put it in his address to Congress: ``Mathematics are one of the fundamentaries of educationalizing our youths.''
I could not have said it better with a 10-foot pole. We all need mathematics in order to solve problems that come up constantly in the ``real world.'' For example, suppose four co-workers go to a restaurant, and at the end of the meal, the waiter brings a bill totaling $34.57. How much, including tip, does each person owe? If the co-workers do not know mathematics, they will just guess at the answer and put in random amounts of money ranging from $9 to $11, unless one of them is a guy I used to work with named Art, in which case he will make a big show of studying the bill, then put in exactly $4.25.
But if the co-workers know their mathematics, they can easily come up with EXACTLY the correct answer. They can do this using ``algebra,'' which was invented by the ancient Persians. (They also invented the SATs, although they got very low scores because in those days there were no pencils.) The way algebra works is, if you don't know exactly what a number is, you just call it ``X.''
The Persians found that this was a BIG mathematical help in solving problems:
PERSIAN WIFE (suspiciously): How much have you had to drink?
PERSIAN HUSBAND: I had ``X'' beers.
PERSIAN WIFE: Well, how much is THAT?
PERSIAN HUSBAND: It's a (burp) variable.
PERSIAN WIFE (not wanting to look stupid): Well, OK then.
Historical Footnote: Several years later, when the ancient Romans invented Roman numerals, and it turned out that ``X'' was actually equal to 10, there was BIG TROUBLE in Persia.
But getting back to the four co-workers at the restaurant: To figure out how much each person owes, they would simply use the algebraic equation AEPO=1/4$34.57+T(((-SA?)@
(+NSOB!)(-SITE)(H), where ``AEPO'' is the amount each person owes, ``T'' is the tip, ``SA'' is whether the waiter has a snotty attitude, ``NSOB'' is whether the waiter has a nice set of buns, ``SITE'' is a variable used if you think somebody in the kitchen is spitting in the entrees, and H is hydrogen. Using this equation, our four co-workers can easily calculate that each one owes exactly, let's see... carry the 7... OK, it would probably be somewhere between $9 and $11.
So we see that algebra is a vital tool for our young people to learn. The traditional method for teaching it, of course, is to require students to solve problems developed in 1928 by the American Association of Mathematics Teachers Obsessed With Fruit. For example:
``If Billy has twice as many apples as Bobby, and Sally has seven more apples than Chester, who has one apple in each hand plus one concealed in his knickers, then how many apples does Ned have, assuming that his train leaves Chicago at noon?''
The problem is that these traditional algebra problems are out of date. Today's young people are dealing with issues such as violence, drugs, sex, eating disorders, stress, low self-esteem, acne, global warming and the demise of Napster. They don't have time to figure out how many apples Ned has. If they need to know, they will simply ASK Ned, and if he doesn't want to tell them, they will hold him upside down over the toilet until he does. And then Ned will sue them, plus the school, plus his parents for naming him ``Ned'' in the first place. Ultimately the ACLU will get the Supreme Court to declare that the number of apples a student has is protected by his constitutional right to privacy.
So what is the solution? How do we balance our children's need to learn math against the many other demands placed on them by modern life? I believe there IS a solution, one that is both simple and practical. I call it: ``X.''
---
"The problems for the exam will be similar to the ones discussed in the class. Of course, the numbers will be different. But not all of them. Pi will still be 3.14159... "
---
Salary Theorem
The less you know, the more you make.
Proof:
Postulate 1: Knowledge is Power.
Postulate 2: Time is Money.
As every engineer knows: Power = Work / Time
And since Knowledge = Power and Time = Money
It is therefore true that Knowledge = Work / Money .
Solving for Money, we get:
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.
---
Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed?
---
Abbott and Costello made arithmetic shenanigans the basis
of a number of their comic dialogs.
Here is a dialog from their movie titled Buck Privates:
Abbott: You're 40 years old, and you're in love with a little girl,
say 10 years old. You're four times as old as that girl.
You couldn't marry that girl, could you?
Costello: No. ?
Abbott: So you wait 5 years. Now the little girl is 15, and you're 45.
You're only three times as old as that girl.
So you wait 15 years more.
Now the little girl is 30, and you're 60.
You're only twice as old as that little girl. ?
Costello: She's catching up. ?
Abbott: Here's the question. How long do you have to wait before you
and that little girl are the same age?
Costello: What kind of question is that? That's ridiculous.
If I keep waiting for that girl, she'll pass me up.
She'll wind up older than I am.
Then she'll have to wait for me!
Here's another encounter from Buck Privates, one echoed in
several later movies.
Abbott: Do me a favor. Loan me $50.
Costello: I can't lend you $50. All I've got is $40.
Abbott: That's okay. Give me the $40, and you'll owe me $10.
Costello: How come I owe you $10?
Abbott: What did I ask you for?
Costello: $50.
Abbott: What did you give me?
Costello; $40.
Abbott: So you owe me $10.
Costello: That's right. But you owe me $40. Give me my $40 back.
Abbott: There's your $40. Now give me the $10 you owe me.
That's the last time I'll ever ask you for the loan of $50.
Costello: How can I loan you $50 now? All I have is $30.
Abbott: Give me the $30, and you’ll owe me $20.
Costello: This is getting worse all the time.
First I owe you $10, and now I owe you $20!
Abbott: So you owe me $20. Twenty and 30 is 50.
Costello; Nope! Twenty-five and 25 is 50.
Abbott: Here's your $30. Give me back my $20.
Costello: All I've got now is $10!
Abbott then entices Costello into a silly, double-or-nothing
number game.
Abbott: Take a number, any number at all from 1 to 10, and don't tell me.
Costello: I got it.
Abbott: Is the number odd or even?
Costello: Even.
Abbott: Is the number between 1 and 3?
Costello: No.
Abbott: Between 3 and 5?
Costello: No. I think I got him.
Abbott: Between 5 and 7?
Costello: Yes.
Abbott: Number six?
Costello: Right. . . . How did he do that?
Toward the end of the movie, during a boxing match, Costello is
knocked to the canvas, and the biased referee gives a quick
count: 2, 4, 6, 8, 10.
Costello: What's this? 2, 4, 6, 8, 10? What happened
to 1, 3, 5, 7, and 9?
Ref: I don't like them numbers. They're odd.
X equals just about everything I learned of math in school
By DAVE BARRY
--------------------------------------------------------------------------------
President Bush says our schools need to do a better job of teaching mathematics, and I agree with him 150 percent. Many high-school students today can't even calculate a square root! Granted, I can't calculate a square root, either, but I USED to be able to, for a period of approximately 15 minutes back in 1962. At least I think that was a square root. It might have been a ``logarithm.''
But whatever it was, if I had to learn how to do it, these kids today should have to learn it, too. As President Bush so eloquently put it in his address to Congress: ``Mathematics are one of the fundamentaries of educationalizing our youths.''
I could not have said it better with a 10-foot pole. We all need mathematics in order to solve problems that come up constantly in the ``real world.'' For example, suppose four co-workers go to a restaurant, and at the end of the meal, the waiter brings a bill totaling $34.57. How much, including tip, does each person owe? If the co-workers do not know mathematics, they will just guess at the answer and put in random amounts of money ranging from $9 to $11, unless one of them is a guy I used to work with named Art, in which case he will make a big show of studying the bill, then put in exactly $4.25.
But if the co-workers know their mathematics, they can easily come up with EXACTLY the correct answer. They can do this using ``algebra,'' which was invented by the ancient Persians. (They also invented the SATs, although they got very low scores because in those days there were no pencils.) The way algebra works is, if you don't know exactly what a number is, you just call it ``X.''
The Persians found that this was a BIG mathematical help in solving problems:
PERSIAN WIFE (suspiciously): How much have you had to drink?
PERSIAN HUSBAND: I had ``X'' beers.
PERSIAN WIFE: Well, how much is THAT?
PERSIAN HUSBAND: It's a (burp) variable.
PERSIAN WIFE (not wanting to look stupid): Well, OK then.
Historical Footnote: Several years later, when the ancient Romans invented Roman numerals, and it turned out that ``X'' was actually equal to 10, there was BIG TROUBLE in Persia.
But getting back to the four co-workers at the restaurant: To figure out how much each person owes, they would simply use the algebraic equation AEPO=1/4$34.57+T(((-SA?)@
(+NSOB!)(-SITE)(H), where ``AEPO'' is the amount each person owes, ``T'' is the tip, ``SA'' is whether the waiter has a snotty attitude, ``NSOB'' is whether the waiter has a nice set of buns, ``SITE'' is a variable used if you think somebody in the kitchen is spitting in the entrees, and H is hydrogen. Using this equation, our four co-workers can easily calculate that each one owes exactly, let's see... carry the 7... OK, it would probably be somewhere between $9 and $11.
So we see that algebra is a vital tool for our young people to learn. The traditional method for teaching it, of course, is to require students to solve problems developed in 1928 by the American Association of Mathematics Teachers Obsessed With Fruit. For example:
``If Billy has twice as many apples as Bobby, and Sally has seven more apples than Chester, who has one apple in each hand plus one concealed in his knickers, then how many apples does Ned have, assuming that his train leaves Chicago at noon?''
The problem is that these traditional algebra problems are out of date. Today's young people are dealing with issues such as violence, drugs, sex, eating disorders, stress, low self-esteem, acne, global warming and the demise of Napster. They don't have time to figure out how many apples Ned has. If they need to know, they will simply ASK Ned, and if he doesn't want to tell them, they will hold him upside down over the toilet until he does. And then Ned will sue them, plus the school, plus his parents for naming him ``Ned'' in the first place. Ultimately the ACLU will get the Supreme Court to declare that the number of apples a student has is protected by his constitutional right to privacy.
So what is the solution? How do we balance our children's need to learn math against the many other demands placed on them by modern life? I believe there IS a solution, one that is both simple and practical. I call it: ``X.''
Tuesday, April 14, 2009
I love Logic Puzzles
I love Logic Puzzles, but they can be hard/frustrating at times!
Here is a simple (as in not complex, but as for easy or hard, I'll leave that up to you to decide)one to play - can you figure out how to always win this game?
Three Bags
How about this one?
Coin Weighing
Here is a simple (as in not complex, but as for easy or hard, I'll leave that up to you to decide)one to play - can you figure out how to always win this game?
Three Bags
How about this one?
Coin Weighing
Friday, February 13, 2009
A Nerdy Valentine's Gift for Those of You with TI Graphing Calculators
In Y =
Y1 = abs(x) + √(1 - x^2)
Y2 = abs(x) - √(1 – x^2)
In WINDOW
Xmin = -1
Xmax = 1
Ymin = -1
Ymax = 1.5
In FORMAT
AxesOff
In MODE
Simul
Y1 = abs(x) + √(1 - x^2)
Y2 = abs(x) - √(1 – x^2)
In WINDOW
Xmin = -1
Xmax = 1
Ymin = -1
Ymax = 1.5
In FORMAT
AxesOff
In MODE
Simul
Wednesday, June 11, 2008
Statistics in Religious Archaeology
http://www.scientificamerican.com/article.cfm?id=jesus-talpiot-tomb-or-statistical-error&ref=sciam
Tomorrow night on the Discovery Channel there is scheduled to be aired a special about an ossuary in Jerusalem that some are claiming could belong to the family of Jesus (as). Some, of course, would then go so far to suggest that Jesus's (as) bones are there as well - although that is a much more wild claim. An interesting aspect of the names in that ossuary is that they may include the name of Mary Magdalene.
The article above is about a hypothesis test calculated around the probability of the names mentioned in the ossuary existing in that particular combination. Based on certain assumptions and research about naming in Jerusalem at the time, a statistician calculated 600 to 1 odds that that particular set of names belonged to the family of Jesus (as) and not another family with similar names.
This is actually the kind of stuff we're studying in my AP Statistics class right now. The kids are learning to conduct hypothesis tests, so maybe we will discuss this article next week and see if the students can determine what his assumptions were, what his null hypothesis was, etc.
Tomorrow night on the Discovery Channel there is scheduled to be aired a special about an ossuary in Jerusalem that some are claiming could belong to the family of Jesus (as). Some, of course, would then go so far to suggest that Jesus's (as) bones are there as well - although that is a much more wild claim. An interesting aspect of the names in that ossuary is that they may include the name of Mary Magdalene.
The article above is about a hypothesis test calculated around the probability of the names mentioned in the ossuary existing in that particular combination. Based on certain assumptions and research about naming in Jerusalem at the time, a statistician calculated 600 to 1 odds that that particular set of names belonged to the family of Jesus (as) and not another family with similar names.
This is actually the kind of stuff we're studying in my AP Statistics class right now. The kids are learning to conduct hypothesis tests, so maybe we will discuss this article next week and see if the students can determine what his assumptions were, what his null hypothesis was, etc.
Wednesday, March 12, 2008
Dice
Some things I've been learning this week in my training. No, I'm not training to work at a casino or anything - it's statistics and math.
Crooked Dice
With so much money riding on the roll of a die it's no surprise that crooks try to influence the outcome. Here you can learn all about the methods the cheats use to win your money...
Crooked dice are not a recent development. The Indian Hindu Sanskrit, Mahabbarata, the first documented reference to dice, mentions crooked dice and examples have been found in ancient sites in the Orient, South America and the Middle East.
Dice that are fair are known as straight or square dice, perfects or levels. Terms for crooked dice are numerous and there are a number of methods for gaffing dice. Crooked dice do not behave in the same manner on every throw but they do change the odds and so are known as percentage or P.C. dice.
A dice mechanic will substitute crooked or gaffed dice for the real ones and can quickly switch them back once they have gained their advantage. Slight of hand may be used or the switch will take place when the dice are out of sight. Crooked gambling houses used to employ stickmen for Craps who would switch the dice when signalled. Today the major casinos are honest and have no reason too cheat. An expert switcher will almost be impossible to spot. If you suspect a switch has taken place then you could examine the dice yourself. Remember the dice you are playing with may not be the dice that started the game and cheats will switch the dice back and forth as it suits them. A cheat may even let another player take his crooked dice away, just writing his loss off as part of his scam. This means there could be crooked dice in circulation that no one is aware of.
Craps is where the money is so crooks and cheats target this game the most. Passers are crooked dice that favour passes and not the 7, or craps on the come out throw. Missouts are crooked dice that favour the 7 and not the points.
Loaded dice or weight will be heavier on one side. The extra weight may be lead, gold or platinum so it only takes a small amount to change the odds. The weight is often placed nearer one corner or edge rather than at the centre of one face. Transparent dice do not prevent loading because the actual spots can contain the weight. Check if the spots are deeper on some sides than others, although this is no guarantee because a well made gaffed dice will look straight and even. To test for loaded dice simply repeatedly drop the die in a glass of water. It should sink and if a particular number always faces up the die is loaded. The pivot test is one where you hold the die between your thumb and finger by diagonally opposite corners. If the die is loaded it will tend to turn downward as you lightly hold it.
Floats or floaters don't have extra weight added but weight taken away so they become lighter. They are hollow inside and the gap is placed off centre to bias the dice. They are known as floaters because they will often float, with the hollow side up, when placed in water.
Tapping dice or tappers are dice with a hollow dumb-bell shaped chamber inside. The hollow chamber is filled with mercury. When the mercury is in the end of the chamber near the centre of the die it is fair. But when the cheat wants the die to be biased he will tap the die so the mercury runs to the other end and weight one corner. Some tappers use the same principal but with a weight that slides up and down the chamber on a fine wire. These may have a ratchet mechanism to hold it in place until the die is tapped and may have a rubber bumper to prevent any noise. Obviously these dice must be opaque. Tappers are not used often because of their unreliability. To test for these, tap the die on all it's corners and use the loaded die tests.
Shapes are dice that are not true cubes. Shapes may be convex or concave on some sides or edges or a side may have been shaved down.
Bevels are shapes with one or more convex sides. These dice will be more likely to roll off the convex sides and on to a flat one.
Suction dice have a concave side which can create a slight vacuum when rolled on a hard flat surface. On a rough surface the dice tend to stop on the concave side when a flat side would keep on rolling. These dice favour the opposite side of the concave one.
Trip dice have edge work and flat sides. Dice are manufactured with different types of edge. There are different ways to machine the edge of a die and if all the edges are machined the same way the die is fair. Trip dice will have differing edges. They tend to wear after use and need to be replaced by the cheat quite often.
Cut-edge dice are trip dice that have an edge shaved at an angle of 45 degrees while the others may be at 60 degrees which effects the roll.
Raised-edge dice are trip dice with a lip on some sides. These sides have more surface area and also grip when rolled on cloth.
Dice with razor-edge work have different edges. Dice can be razor edged on some sides and turned or rounded on others so the die will roll off the rounded edges and grip on flat ones.
Split-edge or Saw-tooth edge work is serrating some edges of the dice with tiny cuts. The idea is these edges will grip. The bias is hard to ascertain and these dice are said to be worthless to a cheat.
Bricks or flats are shapes that have one side shaved down so the four adjoining sides are made smaller and have less surface area. The shaved side and its opposite face will be the more likely outcome. Six-ace flats will favour the 1 and 6 sides and work against the shooter in a game of Craps. Flat passers are a pair of dice cut down to favour 3-4 and 6-1 so totals of 4, 5, 9 and 10 occur more often (point numbers in Craps). Barred dice is another term used for these.
Bevels can be held together or pressed on to a flat surface. If they rock back and forth you know the die's face is convex. Try running your finger over the sides of the die feeling for lips or edges. Remember to check all sides of a die to determine if it is a shape. There are devices used by casinos called micrometers that measure the sides of dice extremely accurately. Sometimes shapes and loaded dice are combined, with both defects so minute that spotting them is difficult. Different methods of shaping and gaffing dice can also be combined to produce such things as razor edge convexes, bevelled suction shapes, etc. An obviously mis-shaped or loaded die is said to have very strong work that won't pass in fast company.
Raised spots are supposed to cause the dice to roll off that side. The spots aren't finished properly and these are used by amateur cheats. They can be easily felt and are not as effective as other crooked dice.
Capped dice are shaved down on some sides and then have the material replaced by a layer of material that matches in look but differs in elasticity. The dice tend to bounce off these sides and settle on one not doctored. The join should be invisible all though wear and heat may show it up after time. Use your finger nail or something sharp to feel the resiliency of all sides. Liquid capping is the painting of dice with a solution that dries to get the same effect. This isn't worth doing because the substance becomes sticky in players hands and picks up dirt.
You will often see dice players blowing on the dice for good luck. Another way to cheat is to paint sides of the dice with a clear sticky substance which can be activated by the moisture in the cheats breath causing the dice to have a tendency to stick to the throwing surface.
Slick dice are polished on some sides while the other sides are roughened. This is supposed to make the dice slide to a stop on the smooth side and roll off a rough one. This bias is negligible but is hard to spot because even straight dice can become rough after a lot of use.
Bristles are dice gaffed with a pin. The pin is inserted into the centre spot of the 5 side, only slightly protruding, and will hold if rolled on a cloth or baize surface. They are known as bristles because pig or horse bristles were used. It is an extremely old method of gaffing dice. Outmoded and not used by professional cheats because of the likely hood of being discovered.
Mis-spotted dice with duplicate numbers on opposing faces are called tops and bottoms. Other terms for these dice are tops, mis-spots, horses or tees (T's). A gamblers term for these is busters. These can easily be identified simply by examining all the faces of the die. Remember all opposing sides must add up to 7. These dice are not as instantly recognisable as you may think because only three sides of a die are visible at any one time.
Double number dice have two sides of the same number, double deuces will have two 2 spots and no 5. A pair of dice with duplicate sides of 1, 5, 6 and 3, 4, 5 will never produce a total of 2, 3, 7 or 12, the only numbers that can lose in Craps. High-low splitters are marked twice with 1, 2, 3 on one die and 4, 5, 6 on the other. These produce a lot of 7's and a crooked house would switch them in when some one has made a heavy bet on the field in a Craps game. Door pops are a pair of dice that only ever come up 7 or 11. One die is spotted with 6's and 2's the other is all 5's on every side and only a complete idiot would fall for these. Games that require high numbers to win, like Backgammon or High Dice, can be played with high number dice that have two 4's, 5's and 6's. Low number dice have two 1s, 2s and 3s.
Electric dice are metallic on one side or have metal slugs in the spots on one side. These are used with an electromagnet under the playing surface. Greedy Chuck-A-Luck operators sometimes use them under the counter or chuck cage and special Craps tables were manufactured to incorporate the magnet. Electric dice are not as commonly used as they once were due to the fact that many dice players carried a magnet to test for them. If a die sticks to a magnet then without doubt it is crooked. Gambling venues that use electromagnets are known as juice joints or wire joints. These are not strictly speaking percentage dice because when the magnet is on the outcome is certain.
Crooked dice may be unconventionally spotted so a cheat can differentiate between them and a set of straight dice when switching them back and forth from a game.
If playing dice for money you should play with transparent dice to reduce the chances of using crooked ones. Casinos always use these dice and today's major casinos are respectable, professional operations and have no need to cheat. Don't play with strangers but rather stick to a friendly game with people you know well and trust. Should you ever find that you are in a crooked dice game the best advice is to cut your losses and take no further part. Even if you are positive the game is rigged the situation could rapidly turn ugly if you were to accuse some one.
Casinos don't take any chances when it comes to profit so they don't use just any dice when thousands of dollars are riding on a roll.
Casino dice are called perfect or precision dice because of the way they are made. They are as close to being perfect true cubes as possible, measured to within a fraction of a millimetre, manufactured so each die has an absolutely equal chance of landing on any one of its six faces.
Casino dice are specially hand made to within a tolerance of 0.0005 of an inch. The spots are drilled and filled with material that is equal in weight to the material removed. Usually sides are flush and edges sharp. They are predominantly transparent red but can come in other colours like green, purple or blue. Spots are usually solid but a number of different designs can be found.
It is believed all casino dice should have the same conventional arrangement of faces and spots. They're right handed so that if the 1-spot is face up and the 2-spot is turned to face the left then the 3-spot is to the right of it with all opposing sides adding up to 7. If the 1 spot is face up then the 3-spot runs diagonally up from the left and the 2-spot runs diagonally down from the left. A different orientation of the spots is sometimes used on crooked dice (made to look like casino dice) so a cheat can differentiate them from a set of straight dice.
Since the 1970's, and the move to corporate owned casinos, it has become more and more common for casino dice to have serial numbers printed on them. The number is 3 or 4 numeric digits, possibly with letters and dashes, usually printed on the 6-spot but can be found on any face except the 1-spot. This number denotes the issue and is used to prevent them being switched for crooked dice. Another security check sometimes used is having key letters printed on the underneath of spots which can only be viewed by looking through the transparent die. The casino's name, sometimes location, and/or logo will often be printed on the dice too using a metallic foil. The 1-spot usually bares the casino's name while the 2-spot may have the logo.
The most common size today is 3/4 inch but the size can vary with 5/8 inch and 11/16 inch the next most common sizes.
Casino dice were made of cellulose nitrate, starting around the 1920s, but sometime around the 1950s the manufacturers switched to cellulose acetate which is more durable. Very old casino dice have often started to crystallise and will have turned yellowish around the edges. This crystallisation is caused by age and exposure to moisture and ultra-violet light. A completely crystallised die will disintegrate if pressure is applied.
Casino dice can be readily bought. However many cheap casino dice are in fact rejects that haven't met the manufacturers standards or used dice that have been cancelled by their casino. Both rejects and used dice will have been defaced in some way.
Manufacturers call rejects culls. These are factory marked with a hot pin in the centre of the 4-spot or hot stamped with a number of 'X' or star symbols or just simply stamped with the word "VOID". Some manufacturers stamp a gold "O" onto the four spot.
Used dice may be bought as souvenirs from many casinos although some refuse to let them go. When a die is taken out of play it will be cancelled. It could be that a hole is drilled through it or a crescent or circle is pressed into one side with a vice. Sometimes a gold bar is hot stamped on the six-spot. A sharp pointed metal scribe is often used to press a small shallow mark into a face. Some older dice were scratched or had a date or initials marked on them. By state law Atlantic City casinos must drill all the way through their used dice.
If you want true perfect dice then pay the extra for a stick. A stick is a number of dice that are still in their sealed pack as delivered by the manufacturer.
Crooked Dice
With so much money riding on the roll of a die it's no surprise that crooks try to influence the outcome. Here you can learn all about the methods the cheats use to win your money...
Crooked dice are not a recent development. The Indian Hindu Sanskrit, Mahabbarata, the first documented reference to dice, mentions crooked dice and examples have been found in ancient sites in the Orient, South America and the Middle East.
Dice that are fair are known as straight or square dice, perfects or levels. Terms for crooked dice are numerous and there are a number of methods for gaffing dice. Crooked dice do not behave in the same manner on every throw but they do change the odds and so are known as percentage or P.C. dice.
A dice mechanic will substitute crooked or gaffed dice for the real ones and can quickly switch them back once they have gained their advantage. Slight of hand may be used or the switch will take place when the dice are out of sight. Crooked gambling houses used to employ stickmen for Craps who would switch the dice when signalled. Today the major casinos are honest and have no reason too cheat. An expert switcher will almost be impossible to spot. If you suspect a switch has taken place then you could examine the dice yourself. Remember the dice you are playing with may not be the dice that started the game and cheats will switch the dice back and forth as it suits them. A cheat may even let another player take his crooked dice away, just writing his loss off as part of his scam. This means there could be crooked dice in circulation that no one is aware of.
Craps is where the money is so crooks and cheats target this game the most. Passers are crooked dice that favour passes and not the 7, or craps on the come out throw. Missouts are crooked dice that favour the 7 and not the points.
Loaded dice or weight will be heavier on one side. The extra weight may be lead, gold or platinum so it only takes a small amount to change the odds. The weight is often placed nearer one corner or edge rather than at the centre of one face. Transparent dice do not prevent loading because the actual spots can contain the weight. Check if the spots are deeper on some sides than others, although this is no guarantee because a well made gaffed dice will look straight and even. To test for loaded dice simply repeatedly drop the die in a glass of water. It should sink and if a particular number always faces up the die is loaded. The pivot test is one where you hold the die between your thumb and finger by diagonally opposite corners. If the die is loaded it will tend to turn downward as you lightly hold it.
Floats or floaters don't have extra weight added but weight taken away so they become lighter. They are hollow inside and the gap is placed off centre to bias the dice. They are known as floaters because they will often float, with the hollow side up, when placed in water.
Tapping dice or tappers are dice with a hollow dumb-bell shaped chamber inside. The hollow chamber is filled with mercury. When the mercury is in the end of the chamber near the centre of the die it is fair. But when the cheat wants the die to be biased he will tap the die so the mercury runs to the other end and weight one corner. Some tappers use the same principal but with a weight that slides up and down the chamber on a fine wire. These may have a ratchet mechanism to hold it in place until the die is tapped and may have a rubber bumper to prevent any noise. Obviously these dice must be opaque. Tappers are not used often because of their unreliability. To test for these, tap the die on all it's corners and use the loaded die tests.
Shapes are dice that are not true cubes. Shapes may be convex or concave on some sides or edges or a side may have been shaved down.
Bevels are shapes with one or more convex sides. These dice will be more likely to roll off the convex sides and on to a flat one.
Suction dice have a concave side which can create a slight vacuum when rolled on a hard flat surface. On a rough surface the dice tend to stop on the concave side when a flat side would keep on rolling. These dice favour the opposite side of the concave one.
Trip dice have edge work and flat sides. Dice are manufactured with different types of edge. There are different ways to machine the edge of a die and if all the edges are machined the same way the die is fair. Trip dice will have differing edges. They tend to wear after use and need to be replaced by the cheat quite often.
Cut-edge dice are trip dice that have an edge shaved at an angle of 45 degrees while the others may be at 60 degrees which effects the roll.
Raised-edge dice are trip dice with a lip on some sides. These sides have more surface area and also grip when rolled on cloth.
Dice with razor-edge work have different edges. Dice can be razor edged on some sides and turned or rounded on others so the die will roll off the rounded edges and grip on flat ones.
Split-edge or Saw-tooth edge work is serrating some edges of the dice with tiny cuts. The idea is these edges will grip. The bias is hard to ascertain and these dice are said to be worthless to a cheat.
Bricks or flats are shapes that have one side shaved down so the four adjoining sides are made smaller and have less surface area. The shaved side and its opposite face will be the more likely outcome. Six-ace flats will favour the 1 and 6 sides and work against the shooter in a game of Craps. Flat passers are a pair of dice cut down to favour 3-4 and 6-1 so totals of 4, 5, 9 and 10 occur more often (point numbers in Craps). Barred dice is another term used for these.
Bevels can be held together or pressed on to a flat surface. If they rock back and forth you know the die's face is convex. Try running your finger over the sides of the die feeling for lips or edges. Remember to check all sides of a die to determine if it is a shape. There are devices used by casinos called micrometers that measure the sides of dice extremely accurately. Sometimes shapes and loaded dice are combined, with both defects so minute that spotting them is difficult. Different methods of shaping and gaffing dice can also be combined to produce such things as razor edge convexes, bevelled suction shapes, etc. An obviously mis-shaped or loaded die is said to have very strong work that won't pass in fast company.
Raised spots are supposed to cause the dice to roll off that side. The spots aren't finished properly and these are used by amateur cheats. They can be easily felt and are not as effective as other crooked dice.
Capped dice are shaved down on some sides and then have the material replaced by a layer of material that matches in look but differs in elasticity. The dice tend to bounce off these sides and settle on one not doctored. The join should be invisible all though wear and heat may show it up after time. Use your finger nail or something sharp to feel the resiliency of all sides. Liquid capping is the painting of dice with a solution that dries to get the same effect. This isn't worth doing because the substance becomes sticky in players hands and picks up dirt.
You will often see dice players blowing on the dice for good luck. Another way to cheat is to paint sides of the dice with a clear sticky substance which can be activated by the moisture in the cheats breath causing the dice to have a tendency to stick to the throwing surface.
Slick dice are polished on some sides while the other sides are roughened. This is supposed to make the dice slide to a stop on the smooth side and roll off a rough one. This bias is negligible but is hard to spot because even straight dice can become rough after a lot of use.
Bristles are dice gaffed with a pin. The pin is inserted into the centre spot of the 5 side, only slightly protruding, and will hold if rolled on a cloth or baize surface. They are known as bristles because pig or horse bristles were used. It is an extremely old method of gaffing dice. Outmoded and not used by professional cheats because of the likely hood of being discovered.
Mis-spotted dice with duplicate numbers on opposing faces are called tops and bottoms. Other terms for these dice are tops, mis-spots, horses or tees (T's). A gamblers term for these is busters. These can easily be identified simply by examining all the faces of the die. Remember all opposing sides must add up to 7. These dice are not as instantly recognisable as you may think because only three sides of a die are visible at any one time.
Double number dice have two sides of the same number, double deuces will have two 2 spots and no 5. A pair of dice with duplicate sides of 1, 5, 6 and 3, 4, 5 will never produce a total of 2, 3, 7 or 12, the only numbers that can lose in Craps. High-low splitters are marked twice with 1, 2, 3 on one die and 4, 5, 6 on the other. These produce a lot of 7's and a crooked house would switch them in when some one has made a heavy bet on the field in a Craps game. Door pops are a pair of dice that only ever come up 7 or 11. One die is spotted with 6's and 2's the other is all 5's on every side and only a complete idiot would fall for these. Games that require high numbers to win, like Backgammon or High Dice, can be played with high number dice that have two 4's, 5's and 6's. Low number dice have two 1s, 2s and 3s.
Electric dice are metallic on one side or have metal slugs in the spots on one side. These are used with an electromagnet under the playing surface. Greedy Chuck-A-Luck operators sometimes use them under the counter or chuck cage and special Craps tables were manufactured to incorporate the magnet. Electric dice are not as commonly used as they once were due to the fact that many dice players carried a magnet to test for them. If a die sticks to a magnet then without doubt it is crooked. Gambling venues that use electromagnets are known as juice joints or wire joints. These are not strictly speaking percentage dice because when the magnet is on the outcome is certain.
Crooked dice may be unconventionally spotted so a cheat can differentiate between them and a set of straight dice when switching them back and forth from a game.
If playing dice for money you should play with transparent dice to reduce the chances of using crooked ones. Casinos always use these dice and today's major casinos are respectable, professional operations and have no need to cheat. Don't play with strangers but rather stick to a friendly game with people you know well and trust. Should you ever find that you are in a crooked dice game the best advice is to cut your losses and take no further part. Even if you are positive the game is rigged the situation could rapidly turn ugly if you were to accuse some one.
Casinos don't take any chances when it comes to profit so they don't use just any dice when thousands of dollars are riding on a roll.
Casino dice are called perfect or precision dice because of the way they are made. They are as close to being perfect true cubes as possible, measured to within a fraction of a millimetre, manufactured so each die has an absolutely equal chance of landing on any one of its six faces.
Casino dice are specially hand made to within a tolerance of 0.0005 of an inch. The spots are drilled and filled with material that is equal in weight to the material removed. Usually sides are flush and edges sharp. They are predominantly transparent red but can come in other colours like green, purple or blue. Spots are usually solid but a number of different designs can be found.
It is believed all casino dice should have the same conventional arrangement of faces and spots. They're right handed so that if the 1-spot is face up and the 2-spot is turned to face the left then the 3-spot is to the right of it with all opposing sides adding up to 7. If the 1 spot is face up then the 3-spot runs diagonally up from the left and the 2-spot runs diagonally down from the left. A different orientation of the spots is sometimes used on crooked dice (made to look like casino dice) so a cheat can differentiate them from a set of straight dice.
Since the 1970's, and the move to corporate owned casinos, it has become more and more common for casino dice to have serial numbers printed on them. The number is 3 or 4 numeric digits, possibly with letters and dashes, usually printed on the 6-spot but can be found on any face except the 1-spot. This number denotes the issue and is used to prevent them being switched for crooked dice. Another security check sometimes used is having key letters printed on the underneath of spots which can only be viewed by looking through the transparent die. The casino's name, sometimes location, and/or logo will often be printed on the dice too using a metallic foil. The 1-spot usually bares the casino's name while the 2-spot may have the logo.
The most common size today is 3/4 inch but the size can vary with 5/8 inch and 11/16 inch the next most common sizes.
Casino dice were made of cellulose nitrate, starting around the 1920s, but sometime around the 1950s the manufacturers switched to cellulose acetate which is more durable. Very old casino dice have often started to crystallise and will have turned yellowish around the edges. This crystallisation is caused by age and exposure to moisture and ultra-violet light. A completely crystallised die will disintegrate if pressure is applied.
Casino dice can be readily bought. However many cheap casino dice are in fact rejects that haven't met the manufacturers standards or used dice that have been cancelled by their casino. Both rejects and used dice will have been defaced in some way.
Manufacturers call rejects culls. These are factory marked with a hot pin in the centre of the 4-spot or hot stamped with a number of 'X' or star symbols or just simply stamped with the word "VOID". Some manufacturers stamp a gold "O" onto the four spot.
Used dice may be bought as souvenirs from many casinos although some refuse to let them go. When a die is taken out of play it will be cancelled. It could be that a hole is drilled through it or a crescent or circle is pressed into one side with a vice. Sometimes a gold bar is hot stamped on the six-spot. A sharp pointed metal scribe is often used to press a small shallow mark into a face. Some older dice were scratched or had a date or initials marked on them. By state law Atlantic City casinos must drill all the way through their used dice.
If you want true perfect dice then pay the extra for a stick. A stick is a number of dice that are still in their sealed pack as delivered by the manufacturer.
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