Leapyfrog,

You can find a rationale behind the plan on this web page. You might prefer one or more of the other plans discussed. The author doesn't like it either. 

I agree with the good doctor.

If you're interested in laying and are thinking about a staking plan, you could do worse than Maria's method.

Thank you very much muggins! 

Probability is a notoriously counter-intuitive subject. People are in general very bad at it, that's why the casino carpets are so thick.

XXVV's idea that intuition is "reason to the Nth degree" is interesting, but I think that only applies in certain scenarios, and surely roulette isn't one of them. There's no substitute for a properly researched method based on mathematics and logic.

Maybe someone can do us all a favor here?

The book is available as a free download-
http://horseraceratings.wordpress.com/2012/10/05/the-punters-revenge-free-online/

You need to join this Yahoo group and the book is in the "Files" folder:

https://groups.yahoo.com/neo/groups/hoof-ratings/info

I would do it myself but I can't seem to open a Yahoo account. I've tried several times but you're required to give a mobile phone no, then they send you a validation code in a text. Problem is, I never seem to get the code, maybe I have the wrong kind of phone or something. 

So if anyone has a Yahoo account or can open one more easily than I can, the book is available. But please upload it here!

Thanks in advance to some kind person. 

Quote from: Mathemagician on September 11, 2014, 04:49:37 PM
As it has never happened it can't be independent.

Peter, I can't see the logic of this at all.

If what you say is true, then you could also say something similar for blackjack. I don't know what the record is for the number of consecutive blackjacks dealt from a shoe is, but let's call it x, then you could say, "x + 1 blackjacks have never happened, therefore outcomes are not independent." But blackjack is already a dependent game for the simple reason that as cards are removed from the shoe, the probability of the next hand changes, assuming the cards are not replaced, and of course an analogous situation does not exist in roulette; a pocket is not removed from the wheel after the ball falls into it, and this is what is meant by independence, nothing to do with the number of events either blackjack or roulette has generated, which would be an issue of bias.

Hello Peter,

I was just looking at the first few pages of your book on amazon, and I'm a bit puzzled:

QuoteSceptics will tell you every spin is independent of what's happened before.
This isn't true, a ball has landed on red 28 times it has never landed 29
times. So much for each spin being a singular event!

I'm not sure what you mean by this.   

An entertaining preface to the classic book "The Theory of Gambling and Statistical Logic", by Richard A. Epstein (2nd Revised Ed. 2009). I particularly liked the bit about mathematicians in lunatic asylums. Enjoy.

After publication of the revised edition of this work (1977), I smugly presumed
that the fundamentals of Gambling Theory had been fully accounted for — an
attitude comparable to that attributed to the U.S. Patent Offi ce at the end of the
19th century: " Everything worth inventing has already been invented. "

In the more than 30 years since, progress in the fi eld of gambling has not
faltered. Improved computational facilities have led to the solution of games
hitherto deemed unsolvable — most notably, Checkers. Such solutions have a
regenerative effect, creating more problems that demand yet further solutions.
Computer simulations have provided numerical answers to problems that
remain resistant to closed-form solutions. Abstract branches of mathematics
have been awakened and applied to gambling issues. And, of paramount sig-
nifi cance, Parrondo's Paradox has advanced the startling notion that two losing
ventures can be combined to form a winning prospect.

Reader and author are equally admonished: Never bet against the future .

Gambling remains a near universal pastime. Perhaps more people with less
knowledge succumb to its lure than to any other sedentary avocation. As Balzac
averred, " the gambling passion lurks at the bottom of every heart. " It fi nds out-
lets in business, war, politics; in the formal overtures of the gambling casinos;
and in the less ceremonious exchanges among individuals of differing opinions.

To some, the nature of gambling appears illusive, only dimly perceivable
through a curtain of numbers. To others, it inspires a quasi-religious emo-
tion: true believers are governed by mystical forces such as " luck, " " fate, " and
" chance. " To yet others, gambling is the algorithmic Circe in whose embrace
lies the roadmap to El Dorado: the " foolproof " system. Even mathematicians
have fallen prey to the clever casuistry of gambling fallacies. Special wards
in lunatic asylums could well be populated with mathematicians who have
attempted to predict random events from fi nite data samples.

It is, then, the intent of this book to dissipate the mystery, myths, and mis-
conceptions that abound in the realm of gambling and statistical phenomena.

The mathematical theory of gambling enjoys a distinguished pedigree. For
several centuries, gamblers ' pastimes provided both the impetus and the only
concrete basis for the development of the concepts and methods of probabil-
ity theory. Today, games of chance are used to isolate, in pure form, the logi-
cal structures underlying real-life systems, while games of skill provide testing
grounds for the study of multistage decision processes in practical contexts. We
can readily confi rm A.M. Turing's conviction that games constitute an ideal
model system leading toward the development of machine intelligence.

It is also intended that a unifi ed and complete theory be advanced. Thus,
it is necessary to establish formally the fundamental principles underlying the
phenomena of gambling before citing examples illustrating their behavior. A
majority of the requisite mathematical exposition for this goal has been elabo-
rated and is available in the technical literature. Where defi ciencies remain, we
have attempted to forge the missing links.

The broad mathematical disciplines associated with the theory of gam-
bling are Probability Theory and Statistics, which are usually applied to those
contests involving a statistical opponent ( " nature " ), and Game Theory, which
is pertinent to confl ict among " intelligent " contestants. To comprehend the
operation of these disciplines normally requires only an understanding of the
elementary mathematical tools (e.g., basic calculus). In only a few isolated
instances do rigorous proofs of certain fundamental principles dictate a descent
into the pit of more abstract and esoteric mathematics (such as, Set Theory).

If this book is successful, readers previously susceptible to the extensive
folklore of gambling will view the subject in a more rational light; readers pre-
viously acquainted with the essentials of Gambling Theory will possess a more
secure footing. The profi ts to be reaped from this knowledge strongly depend
on the individual. To any moderately intelligent person, it is self-evident that
the interests controlling the operations of gambling casinos are not engaged
in philanthropy. Furthermore, each of the principal games of chance or skill
has been thoroughly analyzed by competent statisticians. Any inherent weak-
ness, any obvious loophole, would have been uncovered long ago; and any of
the multitude of miraculous " systems " that deserved their supernal reputation
would have long since pauperized every gambling establishment in existence.

The systems that promise something for nothing inevitably produce nothing for
something.

It will also be self-evident that the laws of chance cannot be suspended
despite all earnest supplications to the whim of Tyche or genufl ections before the
deities of the Craps table. Such noumena cast small shadows on the real axis.

In the real world there is no " easy way " to ensure a fi nancial profi t at the
recognized games of chance or skill; if there were, the rules of play would
soon be changed. An effort to understand the mathematics validating each
game, however, can produce a highly gratifying result. At least, it is gratifying
to rationalize that we would rather lose intelligently than win ignorantly.

Albalaha,

I concur. In fact, the "eye in the sky" is there as much for casino staff as for the punters, more so, perhaps. As for dealer signature, there is some evidence that this phenomenon does occur, but that's a very different proposition from the claim that dealers can hit sectors at will. It would be interesting to set up some controlled experiment though, or maybe some members here have their own roulette wheel and can try it?

Hi Gizmotron,

There was another thread by BEAT-THE-WHEEL ( which mysteriously disappeared ) in which he posted a sequence of wins and losses - 30 straight losses followed by 9 straight wins - and challenged the forum to find a solution. A very unlikely scenario, but easy enough to beat with the reverse martingale. All losses would be cleared and 1 unit profit made after only 5 consecutive wins. Are you suggesting that something like that can win consistently if you bet the same as the last decision ( which would have you winning every streak )?

Hi sqzbox,

QuoteOn a single number -
odds = 35 to 1, or 36 for 1.
Probability = 1 in 37.

Totally different things.

Odds here refer to the payout. Unfortunately the use of the term "odds" isn't consistent, as is observed in the Wikipedia article on Odds. I quote

Quote
Odds are a numerical expression, always consisting of a pair of numbers, used in both gambling and statistics. In statistics, Odds for reflect the likelihood that a particular event will take place. Odds against reflect the likelihood that a particular event will not take place. Unfortunately, the usages of the term among statisticians and probabilists on the one hand, versus in the gambling world on the other hand, are not consistent with each other (with the exception of horse racing).^[1][2] Conventionally, gambling odds are expressed in the form "X to Y", where X and Y are numbers, and it is implied that the odds are odds against the event on which the gambler is considering wagering. In both gambling and statistics, the 'odds' are a numerical expression of how likely is some possible future event. In gambling, odds represent the ratio between the amounts staked by parties to a wager or bet.^[3] Thus, odds of 6 to 1 mean the first party (normally a bookmaker) is staking six times the amount that the second party is. Thus, gambling odds of '6 to 1' mean that there are six possible outcomes in which the event will not take place to every one where it will. In other words, the probability that X will not happen is six times the probability that it will.

It remains true, though, that you can express probabilities as odds and vice-versa, without any ambiguity. In fact, it seems advantageous to express probabilities as odds in the world of casino gambling because it's easier to see what the house advantage is (but of course, the casinos probably wouldn't want that). It's not obvious that being paid at 35-1 and a probability of 1/37 shows that the house has an edge, but expressed as odds, it is. In my example of a dozen bet, for example, the odds (probability of a win) are 25-12 against, but you are paid 2-1 or 24-12 on a win. Now it's clear that the bet is not a fair one.

I always assumed that "chance" and "probability" refer to the same thing. Just goes to show that not defining your terms leads to confusion.

Odds are another way of expressing probabilities, and vice-versa.  Bookies usually use odds, but you can convert from one to the other easily.
   
You can have "odds against" or "odds in favour". The odds against is the ratio of the probability (chance!) of failure to the probability of success. The chance (probability!) of a dozen bet winning, for example, is 12/37, which is the success. The chance of failure is 25/37 because there are 25 "chances" to lose. So the odds against are 25/37 divided by 12/37. The 37's cancel out, and you're left with odds against of 25-12, or as it's sometimes written, 25:12, a bit more than 2-1.

If you want to express it as odds in favour of, just reverse the previous odds, so you get 12-25 in favour.