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Gamblers' Fallacy versus Doctrine of Maturity of Chances

Wizard of Odds discusses one famous gamblers fallacy: DOCTRINE OF THE MATURITY OF THE CHANCES.

Posted by Chip ( on July 22, 2000; later updates.

In Reply to: Wizard of Odds: Phony Gambling Author Paid by Casinos posted by Ion Saliu on July 22, 2000.

: Chip : I already know a guy nick-named Wizard of Odds. His nickname is valid only insofar as related to mysticism. I think his correct nickname should be "Lizard of Odds": His odds-related knowledge belongs to the dinosaurs' era! He visited my website in 1998. He was so impressed that he included my page on Fundamental Formula of Gambling (FFG) in his Hot Links, or something like that.

Despite all the evidence I have supplied I continue to get challenges via e-mail from people who believe their gambling system is the exception to the rule and really does work. In mathematics rules do not have exceptions, if they did they wouldn't be a rule in the first place. Those with these claims always ask that I write a simulation program to prove their claim. I am not about to write free gambling programs to every Tom, Dick, and Harry with a casino betting system. If you still are a true believer then pay me $1000 and I will write an honest program to test any reasonable betting system. In the event that your gambling system does show a profit over millions of bets not only will I refund your money but I will publicly proclaim on my main page I was wrong and give you full credit for disproving every respectable book on probability ever written.

Boy this gets easier and easier. First thank you all for all of your e mails. I am truly humbled. Seems old ION isn't quite the hot shot he thinks. So let's set him up! You will not see me refer to Powerplay as a "system" as you refer to yours. I encourage all reading this to go to and reiterate Senior ION's tripe above. NONSENSE is preciously what your comments are. Mike Shakleford will eat you up and spit you out. Please folks, contact him and pressure ION the magnificent to submit the $1,000 for the gambling challenge. He sure wiggled good didn't he.

Let's go to another part of Mike's gambling site. Here is a question and his reply:
Q: Your analysis of various side bets like Streak, Pair Square and others was very interesting. Do you know how these new games get invented and established? Do the casinos employ guys like you to compute the probabilities? If so, are the games copyrighted in some way? Thanks. – Bob Pierce of Lake Charles, Louisiana.

A: I could talk about this all day. Part of my income is derived from analyzing games such as these. The gaming authorities require such analysis before a game can be licensed to play. Usually these games are invented by an individual or are owned by a gaming company. After the casino game owner receives a license it must go through a 30-day trial period. If the trial period went well the owner can then apply for a permanent license. The entire process is very slow and it is difficult to get a casino to be the guinea pig for the trial period. Casinos are actually quite risk averse in their business decisions. Yes, the game owner will usually seek a copyright to protect others from stealing the idea. Click here to learn more about my consulting services.

Now let's see. I(r)ON(head)is name calling a mathematical genius who is paid for analyzing games of chance. But, he is afraid of a $50 snake oil salesman. But wait let's go another step, on Mike's site. Ok ION, read it and start your bs meter running:
If you don't believe me here is what the Encyclopedia Britannica says under the subject of gambling:

"A common gamblers' fallacy called 'the doctrine of the maturity of the chances' (or 'Monte Carlo fallacy') falsely assumes that each play in a game of chance is not independent of the others and that a series of outcomes of one sort should be balanced in the short run by other possibilities. A number of 'systems' have been invented by gamblers based largely on this fallacy; casino operators are happy to encourage the use of such systems and to exploit any gambler's neglect of the strict rules of probability and independent plays."

Ok now notice the word gambling system and how it is in quotes. Who uses that word to promote, what a bargain, $50 system(s)? BTW, I think you might have to go to my last reply under the challenge, and explain how you are not going to cause the game of roulette to shut down.
How about 1 more, just for laughs. In this corner ION Saliu. His opponent, originally from Germany, Albert Einstein. Yes that's right, old Al said it is impossible to ever beat a fair game of roulette in the long run. So who are you going to bet on ladies and gentleman. As for me, I'll take Einstein and lay the points.

Ion, your in over your head. You shoot off your mouth and anyone who is knowledgeable about gambling in any serious manner can see that you are indeed a fool. I have been around for years and I'm still here. Your big thing is "Chip's afraid to play me.." Each time you harp on that you make a bigger moron out of yourself than the last time. Get a hold of some scholarly work on the subject of gambling, like Thorp's The Mathematics of Gambling, or something by Peter Griffin. Research gambling strategies like the Kelly Criterion. Your shtick is played out and boring. Your an adolescent trying to rebel against authority. So as I close, I expect you'll have a retort and make a bigger fool out of yourself. My playing partner, Playbig 2000, has been falling down laughing at you from the start. He was a member of Ken Uston's card counting blackjack teams in the 80's. I guess you want to challenge (yawn) him too. If you do, give him some time. He needs to finish unpacking at his new house, bought with money won playing baccarat. Thank you Bally's on behalf of Playbig gambling strategy. He has been contemplating posting here too. Don't forget to send in your $50 folks!!

Set up complete,


A famous gamblers fallacy is the doctrine of the maturity of chances.

Ion Saliu's note
But why does Wizard of Odds beg his website visitors to buy his "winning gambling systems"? Actually, even his "name" "The Wizard of Odds" is stolen from a 1970's TV show! Doesn't he say first that there is no winning gambling systems? That all gambling systems fail? If that's not schizophrenia, I don't know what is … Chip as well: No gambling system can win … yet his gambling systems won big at blackjack and baccarat and roulette!!

Gambler's fallacy and all, it's all about streaks — not only losing, but winning as well. We can notice in a vast majority of cases that most deviations from the norm (expected number of successes) fall within 1 standard deviation. The normal probability rule is very lax, or cautious … or generous, one might as well say! Read also: Demise of Gambler's Fallacy, Reversed Gambler's Fallacy.

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Wizard of Odds demolishes all gambling systems…except for his own winning gambling systems!

Set the record straight on Chip, his real name, criminal behavior, Powerplay roulette, baccarat - June 2004.

Read the doctrine of the maturity of the chances or Monte Carlo fallacy.

Roulette, Blackjack Systems Challenge, Testing in Casino is declined by all gambling gurus.

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The scheming Wizard of Odds wants authors pay big money for his phony testing.

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A gamblers' fallacy to remember is the doctrine of the maturity of chances.