Is on-line gambling close to being like the real thing?
The obvious answer
to this question is no. However, due to the ease of accessibility, the
popularity of on-line gambling is staggering. I recently was engaged in an
on-line chat with on-line players that became... well, hostile as I presented
flaws of computer generated play with "random results" for on-line games.
Are "Random Number
Generators" capable of simulating real life games like blackjack, craps,
roulette, and poker? Even deeper, can RNG's be programmed and manipulated for
desired results? I left out slot machines because they are operated by RNG's
both on-line and in the casino. My question arises after receiving two hands of
four of a kind, two full houses, a nut flush, a straight and several hands with
three of a kind all within the same hour of play. How could this be? For my
answer, I went to my "knows all, explains all guy", Mike In Hawaii.
Gears and
Wheels…
By Mike In Hawaii
Bear with me for a moment.
In World War II the Germans created a cipher
machine. It was very German. It was a thing of mechanical beauty and
awe-inspiring. It consisted of a number of interlocking geared wheels with
scrambled wires and contacts and even a further patch panel where you could
change even more of its wiring. Every time you pressed a key to encrypt a
letter, the machine moved and re-wired itself before the next letter.
The average human looking at this thing and its
impressive statistics on how many key presses it would take before it would
repeat itself with a given cipher key setting, and being shown its inner
workings, would be dumfounded. It made the average mind implode with its
complexity and beauty. Each time you pressed a wheel, it performed like a flea
circus act.
It was certainly a masterful mechanical random
number generator applied to the problem of encrypting text messages in an
unbreakably sophisticated fashion.
But there were three things wrong with this
picture and that proved to be very important.
First, it was a machine. After all was said and
done it was gears and wheels. Machines are predictable. They cannot be
otherwise.
Second, it was used by humans. Humans are very
predictable, and error prone. They make mistakes. Such as sending out a long
encrypted message and then realizing they used yesterday’s cipher key and
immediately re-sending it re-encrypted with today’s cipher key before their
supervisor catches them. This does not sound like much, but this is the sort of
mistake that in the right hands gets a lot of people killed.
Third, it was not being watched by ordinary
people, but by geniuses. People so smart
in their unique way they needed special handling, almost like mental patients.
They lived in an alternate universe and saw things others could not see. They
did things with math no one had ever dreamed of before.
Between it being a machine, and thus
predictable, having its mechanical purity contaminated by human error and being
watched by special people who only needed a tiny clue, it failed. Even worse,
the Germans could not imagine it could fail, so they kept on using it. Even as
evidence mounted that it had been compromised. They blamed the security leaks on
everything else but the machine. It was inconceivable this masterpiece was
compromised.
Ah, so what does this have to do with Craps,
and gambling?
Anything we are interested in?
Gambling and random numbers or random events
are heavily interlocked. If an outcome were predictable, then gambling ceases to
be gambling.
Gambling is very illegal in Hawaii, some of the
most draconian anti-gambling laws in the nation; make it one of two
anti-gambling super states.
Still I ran Chess Tournaments for surprisingly
large amounts of cash, where each entrant would buy in, play the tournament and
then the prize money would be distributed out based on a pay table for first,
second and third etc.
Sound familiar? Very much like a Texas Hold’em
tournament at Binions.
The difference is that while poker is still
considered a random game of chance, and thus gambling, chess is considered a
game of skill and therefore not gambling. One can argue over that, and indeed
many do allege that poker is a game of skill, just like chess, and thus should
not be gambling, legal or illegal. But poker does include a randomizer, the
shuffle and deal of the cards. Chess does not. So a line gets drawn.
Any mechanical action such as shuffling cards,
turning a roulette wheel, throwing dice, are all subject to random number
failures which have been exploited by shrewd gamblers and followed by upgrades
in Casinos to improve the chances that such things are done more randomly. A
modern super card shuffler is an example.
The above WWII example and Casinos come
together at this point. Especially today, more and more of the randomization at
Casinos are being done by RNG’s or Random Number Generators.
How random is it Johnny?
Good question. There are two basic problems.
Generating random numbers and testing random numbers to see if they are really
random. Both are amazingly difficult.
It is a bit like the surprising problem in
optics. While it is not that hard to grind a very precise mirror or even a lens
in your basement for a home-made telescope, grinding an optical flat, a piece of
glass that is extremely flat across its entire surface, is tremendously
difficult and demanding.
We talk about a series of numbers being “white”
as in white noise. We are not talking about prejudice here, just the opposite.
We are talking about all possible outcomes being generated with exactly the same
expectation. If we take an alleged random number generator and collect enough
sample numbers from it, we ought to be able to see it produce each possible
outcome the correct percentage of the time.
So if the outcomes are either 1 or 2, heads or
tails, odd or even, then we would expect it to produce one half the time, and
two half the time. The problem is how many trials do we need? Oh boy, that nails
it. A lot of trials as it turns out.
Are we going to be happy with plus or minus 1%
confidence? If we get 51% of one and 49% of the other are we going to be happy?
Probably not. 1% is a fair percentage of the
house advantage in many games. The only way to test it to a higher precision is
to collect more trials.
Here is the big rub. If we collected 1,000
trials of two equally likely outcomes, say heads and tails, and decided we need
more precision, more confidence, in order to double our confidence in the
results we have to square the number of trials.
To double our confidence we would not need
2,000 trials. We would need 1,000,000 trials. (Gasp!). [He must be making this
up.]
To increase confidence ten-fold or one stinking
decimal place, we would need many more trials collected. Wait for it…
You need 1,000 raised to the tenth power, which
is the size of number normally used only by astronomers. Short version, this
gets out of hand very fast.
It gets worse. When you throw dice, there are
not two outcomes, there are 36. As the number of outcomes increases the number
of required trials to get each to have something approximating the right answer
(for number of occurrences of each) goes way up also. So 1,000 may not be enough
to even get you started. I find for 36 outcomes “sensible” starts at about 1
million trials.
So along comes someone with their “Super
Incredible Reverse Big Red and Double Up on Sevens with Two Place Bets on the
Dark Side Guaranteed Gold System for Massive Profits at Craps.”
How do you test it? First you are up against 36
possible outcomes on each roll of the dice, and then you are up against the
complex mechanics of the betting system, which introduces even more possible
tree branches and multiplies the total outcomes. Quickly you get to where
millions of trials are required to even start to get 1% confidence in any of the
numbers generated.
All assuming you could generate the quality
random numbers in the first place. At the very core of such a test would be a
random number generator. If it is defective, everything else is defective.
Garbage In = Garbage Out (as we like to say).
But, put lipstick on that pig, make a full
color Pie Chart, load it into PowerPoint, which is the greatest mass hypnosis
tool ever invented, and you can sell that bacon as pure gold. And you can have
the “math” to “prove” it.
How? Well any sensible number of trials is
going to produce data that is of such low confidence that each test run’s output
will change significantly and scatter results all over the place. Just keep
doing it until you eventually get the “answer” you want.
The number of trials to actually prove it would
be huge and you would need a very good random number generator. The number of
trials to accidentally get the “correct” answer is not large at all. In fact it
is easier with fewer trials. Just pick some number like 5,000 that the average
Joe is going to imagine is a large number for this purpose.
If you just want “an answer” that matches your
allegation by accident, you can just keep testing until the “right” one pops
out. Enshrine that Crap (pun) in Excel and work a lot on the color graphics for
the PowerPoint presentation of your “proof”. Suddenly the proper selection of
colors for psychological impact is more important than your stinking garbage
data, with one of those Christmas tree car deodorizers as optional equipment.
Now we come back to it. Any computer software
random number generator is NOT random! Period! End of discussion.
It is a machine, well an emulation of a
machine, with virtual gears and wheels. They are correctly called pseudo-random
number generators. True, a good one takes a long time to repeat and is
relatively “white” over a very long sample, but it is still a pattern generator.
True the very best ones are “close enough for Government work”, or your local
ATM.
Is Anything Really Random?
There are few things that are considered
actually “random”. Probably the best of these is radioactive decay. If you have
a radioisotope and you watch it with a detector such as perhaps a Geiger
counter, there is no way currently known which can predict when the next
“click”, the next radioactive decay, is going to happen.
So you might take a pseudo-random software
random number generator of high quality and run it very fast all the time,
locked on. Hook it to a Geiger Counter contaminated by some radioisotope so it
clicks a lot, and each time it clicks, grab the output at that instant of the
pseudo-random number generator. The random clicks “encrypt” the output of the
pseudo-random number generator a second time. The result is about as good as we
know how to make a string of true random numbers.
Too esoteric? Not really. Ever heard of slot
machines?
Modern ones do exactly this, but instead of a
radioactive Geiger counter they use the human player. They run their
pseudo-random number generators very fast and wait for a pull on the handle. The
instant they detect a pull, they grab whatever number is up next.
The outcome is now certain. All the spinning
wheels, real or simulated, or whatever other motion and flashing needs to be
done is just a little show, a few seconds of entertainment for the player before
revealing the answer.
The human does the final “encrypting” because
they cannot pull a handle reproducibly compared to the speed of the clock on the
pseudo-random number generator running inside the slot machine, or video poker
machine, or whatever.
There are even websites which crank out random
numbers based on this procedure, clocked a second time by the arrival of cosmic
rays or decaying radioactive sources. So a high quality set of random numbers
can be obtained for all the testing that needs to be done with them.
But even after your random numbers are “in
order”; there is no getting around the number of trials required. Or the fact
that number goes up very fast with the number of possible outcomes.
Or the real killer, what is needed to increase
confidence in the answer generated. Just one silly decimal point, going from a
confidence of a lousy 1% to something potentially useful like 0.1% takes not ten
times as many trials. It takes however many trials you got 1% confidence with
raised to the tenth power.
Opps, a Fly in the Ointment!
Let’s look at a specific case. You are playing
poker online. Let’s assume it is a decent website with every reason to expect it
is free of tampering, well run and as legitimate as playing in a top of the line
casino. You get four of a kind, Jacks. The very next hand you get four of a
kind, Nines. What is going on!
When you take a data set, a number of trials
that is way too small, normal statistics are right out the window. If you are
looking at only about 100 poker hands, that number compared to what would be
required to produce “proper statistical distribution of hands” is so invisibly
small, that you might capture outrageous variations from statistical chance.
Such as back to back four of a kind hands. Or 100 hands with no pair, zip, high
card only, all 100 of them.
Your first reaction in the above case might be
to think there is something wrong with the random number generator. In fact in
the old days of DOS it had a random number generator that stank so bad in its
BASIC that any attempt to create a game with it was laughable. Now days even
software pseudo-random number generators can be very good. My personal favorite
is the DES encryption run in cipher feedback mode.
But we still have to deal with what I call God
Math (with a capital M) [To Infinity and Beyond!] and real world pedestrian
math, lower case.
Any time we participate in a gambling session
the one thing we can count on is that our sample, our personal number of trials,
will be tiny compared to what is needed to see distributions of results anywhere
near those fancy statistics to many decimal places which God Math can crank out
for an infinity of trials.
So while statistics may say that four of a kind
is a very rare hand, with a small sample it is a bit like earthquake prediction.
If someone gets up every morning and predicts there will be an earthquake in Los
Angeles today, there will inevitably come a day when he is unfortunately right.
I played limit Hold’em at the Bellagio. I had a
pocket pair, but I figured someone would raise before the flop so I just called.
Sure enough, about four seats down, someone raised. So I re-raised and he raised
again to the limit. The flop came 10, 10, Ace, and I just checked. He bet and I
raised. He re-raised and I raised again.
Everyone else got very far out of the way. We
were obviously both sure what was going on. He had pocket Aces and had a full
house with Aces over tens. He figured that I had Ace/10 and held tens over Aces
and he had me way over a barrel. We both had what I call “Titanic” hands. There
is no getting away from them. Someone is going down with the ship.
I had two pair, both tens. At the Turn card we
bet and raised each other to the limit. At the River we bet and raised each
other to the limit. He threw down his pocket Aces so hard they bounced on the
felt and the dealer was half way through pushing over the chips when I carefully
turned over my cards face up for the dealer to see. The dealer did a double take
and slowly raked back all those chips and shoved them over to me. One player
confused asked, “What’s going on?” Another player answered, “Four of a kind”.
Where is a bad beat jackpot when a table needs one?
As little as I get to play, something like that
should never have happened in my lifetime. To get four of a kind AND the perfect
setup where any novice could cash in to the limit of the law is rare indeed.
Trying to prove something by collecting trials
is tricky. The number of trials needed to make a sensible and believable
statement is nearly always quite large. The results from a sensible number of
trials are almost certain to be garbage.
As the complexity of what is being tested goes
up, the number of trials needed goes up as well, quickly surpassing anything
humanly possible. By the time you take the 36 ways dice can fall, add a bunch of
if then else statements on top of that to simulate even a relatively simple
betting system, and even using a decent pseudo-random number generator, a
computer is going to have to crank on it for a very long time to get anything
believable.
This is where Monte Carlo testing falls down.
At the number of trials required to get the results to settle down to a useable
accuracy and precision.
Going at it the other way, attempting to use
God Math to calculate the value of a Craps betting system to infinity and
beyond, can be very daunting with all its paths and branches, probabilities for
each branch and so forth, coupled with the changing rules for the come out and
the chasing points phase. If you can do it, without error, double-checked and
checked again, then you have something as we say “suitable for framing”.
But ultimately to prove that something works
you need to generate good data. Good data needs to have less noise than the
required accuracy needed for proof. If you need to prove something is happening
51% of the time plus or minus 0.1%, the noise in the data needs to be reduced to
less than 0.1%. Or you need to do it not with trials and Monte Carlo
simulations, but with God Math where answers can be obtained to any required
number of decimal places. Sometimes that is easy to set up. Other times it can
be quit difficult.
Sometimes you cannot create a computerized
Monte Carlo version at all. Take precision dice shooting or dice influencing. By
its very nature a human has to throw the dice and he or she can only throw so
many times in a row, so many times per minute. There is a sharp limit on how
many trials can be collected. And it is WAY too few! So we can argue about dice
control until the cows come home.
For me I took another approach. I reasoned out
how dice control could work at the physical level and proved to myself that the
skill involved was learnable. I even calculated what would be the result on the
bottom line if various amounts of control were possible. Reaching the point
where I consider it something every Craps player should do. Learn to shoot the
dice correctly, consistently, calmly and with control. There is a chance it will
make a difference and it certainly is going to help you keep your head in the
game.
Beyond that, I don’t think anyone will ever
prove scientifically that they can control the dice in a legal fashion to a
useful and reproducible extent. So I am happy to take it on faith.
But when someone announces they threw the dice
several hundred times and got an abnormal amount of Sevens or whatever, my
reaction is “so what?”
I would be far more interested in watching
someone quickly produce a beautiful controlled, smooth throw several hundred
times in a row. That I would believe in.
So What Can Be Said?
In any gambling session the one thing you can
count on is that you will see so few trials that the statistics will almost
certainly be skewed, possibly dramatically.
Four of a kind, twice, back to back is just the
sort of thing that will happen to someone. More importantly, anyone who will sit
still long enough is going to hear about it. You don’t hear about the hundreds
of thousands of times it did not happen to other people.
Statistics calculated to three decimal places
are fun to know and tell. Just don’t be surprised if the “impossible” happens.
Be it four the hard way eight out of ten throws in a row, four of a kind back to
back, two royal flushes on a video poker in a single hour or someone holding the
dice for an hour and a half.
The reaction should not be “What are the odds
against that!” it should be “That was bound to happen somewhere to someone and I
got to see it!”
If lightning did not strike occasionally
gambling would be a lot less fun.
Oh, yes, beware of anyone misusing lipstick…
On The Coat Tales of a
Gambler
Episode 24 - Home for The
Holidays… Part II
After the night in Phenix City, we slept late before heading on to Atlanta for
the cockfights. Vic had never been to cockfights and while we were driving,
Scarpone answered Vic’s questions as well as explained how the game was played
with the betting of cash. Between Vic and Scarpone, they had about 55 grand. I
know all this sounds unbelievable and it just goes to the extent and extreme of
illegal gambling that went on at the time. Most of the players at a cockfight
appeared as ordinary looking guys wearing overalls, some worth millions and
betting thousands on two chickens fighting to the death. It was crazy times for
sure and amazing amounts of money traded hands in the rural countryside, in some
remote barn. The fighting roosters were prized as family pets. At the same time,
this blood sport was an “all-in” kind of game. Two fowl would enter the arena,
but only one (usually) would survive. Sometimes even the eventual winner would
not live long enough for all the bets to be settled. It was brutal and hard to
imagine how frenzied people became at cockfights.
The cockfight was not actually held in Atlanta. Scarpone had me drive to
Griffin, Georgia, the birth place of Doc Holliday. There is a Doc Holliday
Museum in Griffin. I visited it a few years back when I last toured the south on
my way to Carolina. Scarpone’s contact was in Griffin and after we arrived,
Scarpone gave him a call. The contact told us to wait for him at the Holliday
Café; it would take him about a half an hour to drive to the café.
We waited at the café over coffee and home made pecan pie. A black sedan pulled
up and a man wearing a black fedora got out. The man lit up a smoke and leaned
against the front fender of the car. That was our signal. We finished up the
coffee. Scarpone settled the check while Vic and I headed for the Lincoln.
Before getting back into the car, Scarpone briefly spoke with the man in the
hat. Once in the Lincoln, Scarpone told me to follow the other car, but that I
was to wait a few minutes. While we sat there, Scarpone told me that we would
drive north to Ellis Road and then turn left. The contact would be waiting on
Ellis Road and from there we’d follow him on to the town of Vaughn.
It was early afternoon when we arrived in Vaughn. The cockfights usually began
under the cloak of darkness and could last long into the night or even the early
hours of the next day. There was still plenty of daylight to find our way to the
location. We stopped at gas station in Vaughn. The contact man got out of his
car and came over to Scarpone’s side of the car. He said that he was going to
leave his car at the gas station and jump in the backseat with us to lead us the
rest of the way to the farm. The cockfights were well organized and secret. Word
of mouth was relied upon to for the location. Only known gamblers were informed.
Holding the contests after dark was another way of keeping a low profile on
otherwise quiet back country roads. Car pooling, with pickups loaded with
gamblers in the beds of the trucks, was part of the cover too.
I was directed to drive north on a dirt road. After a few miles, the contact man
told me to watch for an old tractor in the ditch. Just past the tractor, there
would be a driveway to the right. The driveway was long and rowed with trees.
After several minutes we emerged from the trees to a large barn and farm house.
I parked the car in field behind the barn. Getting out from the car, I heard the
contact man’s last words to me, “I hope you can find your way back?”
We were not too early. Already a large crowd of people had arrived. The field
was filled with other cars and a lot of trucks. Wire cages were in the back of
several of the trucks. In the cages were the contestants for the night’s fight.
Along the side of the barn, a barbeque had been set up with a table of food. You
could pay five bucks and eat all night. There was also booze for sale, though
most of the attendees brought their own. None of it was labeled.
Roosters are territorial by nature. That old expression, one too many roosters
in the hen house us a truism. It does not take much for roosters to go at one
another. Never the less, in addition to their aggressive nature to jump up and
fly at one another, and tear with their sharp beaks, the natural spurs on the
rooster are fitted with raisers. The rooster’s long sharp spurs are potent
weapons alone, but with the addition of steel blades tied to their legs, it
assures for a bloody fight to the death.
Cockfight gambling on is simple. There is nothing like a racing forum with a
chicken’s history of successful bouts. You basically pick a bird to win and bet
your money. The more money that is bet the more you win. Sometimes you bet with
the guy next to you, sometimes there is someone that bankrolls the whole
shebang. Because of the nature of the sport, there is usually not an odds on
favorite. Simply stated, the birds usually do not live long enough to gain a
reputation. There is always a winner and there is always a loser. The loser
never survives and often the winner never recovers to fight again. So, it is an
even money bet and reading this, you may wonder how it would be different from a
coin toss.
Once the fighting began, Vic and Scarpone were in the thick of it betting
between $1000 and $5000 a fight depending upon winning or losing the previous
bet. The handlers of the roosters would enter the ring with their fighter.
Before they released the birds, the handlers would rile up the fighters into a
heightened state of maddened aggression. They would blow cigar smoke at the
birds and while still holding the birds, shove them at one another teasing an
attack. Once the crazed birds were at their peak of madness, they were released.
Jumping up at one another, flapping wings, kicking and pecking, it was over in a
matter of seconds. The bets were settled and the handlers prepared another pair
of cocks for the next event. Cockfights were extremely noisy and it seemed that
the excitement of it all perpetuated the din and insanity as the night
progressed. Though, I suppose, the abundance of alcohol contributed in part.
Scarpone won about ten grand that night. Vic won even more. Again, there is no
skill to gambling on roosters, just pick one and go. Vic was a wealthy man and
had the huevos as well as the money to gamble. As it turned out, this particular
event was bankrolled by the Atlanta Mafia. Scarpone’s contact man was a
“wise-guy” with the Atlanta mob. Scarpone’s invitation to the cockfight came
from a mob guy, Frantinelli.” Scarpone often gambled with Frantinelli.
Frantinelli thought Scarpone was Sicilian because of his nick-name and I suppose
with his Latin heritage, he could be mistaken for Sicilian. There was more to
the invitation for Scarpone than just a cockfight. Frantinelli wanted Scarpone
to consider a partnership in illegal gambling, bootlegging, and drugs.
The Atlanta mob wanted to move into Southern Alabama. Specifically, they wanted
business in Montgomery and Mobile. Scarpone was known to the boys from Atlanta
to be a professional gambler and they wanted a savvy front man, someone local to
help them set up their connections. It was not a secret that the cops and judges
in Southern Alabama were on the take. The Atlanta Mafia hoped that by bringing
in Scarpone, he could help the mob with greasing the right palms of the
politicians in Alabama.
Although Scarpone held a mild interest in Frantinelli’s proposal, it was later
withdrawn when Frantinelli learned that Scarpone was Spanish, not Sicilian. I
remember Scarpone saying to me that it was just as well. He was a loner at heart
and when it came to business, Scarpone wanted to call the shots and he
especially did not want to be in a position of perhaps being shot at.
On The Coat Tales of a Gambler, continues…
