Winning with target betting is easier, quicker and just plain better than all the alternatives. For the others, it's mostly impossible.

_
When the contest is between progressive betting and the only alternatives (flat/fixed or random betting), it's no contest at all: progressive betting wins, the other methods do not.

And since this has always been as much a mathematical challenge as a practical one, tailoring my version of progressive betting to the needs of the underfunded player seeking to beat the odds during occasional weekend trips to Las Vegas has never been a priority.

One simple truth I never lose sight of is that my application of the demonstrably sound principle I call target betting (the rules that I apply from first bet to last in each recovery series) cannot be claimed to be the optimum approach.

There may well be a better way to do this, and I am confident that if I fail to find it before my final visit to a casino, someone else will, and hopefully they will tell the rest of the world about it for free.

Why not sell my ideas rather than giving them away?

It is not because, as some of my critics have suggested, my ideas are worth even less than I charge for them.

It's because for me, this has always been about exposing as myth an axiom that I always felt served the gambling industry far better than the people whose wallets the casinos suck dry.

More than 30 years ago, I experimented with the simplest, most basic form of progressive betting in several Las Vegas casinos, and in every case encountered impressively efficient interference by pit staff.

Drunks, neophytes and other suckers were committing fiscal self-destruction all around me, and I was the only one singled out for friendly advice about how best to preserve my bankroll and save myself from certain ruin.

Why are all these nice people so afraid of a betting method that they say is a danger only to me and my money? I wondered, since fear (or at best, self-interest) seemed to me the only reason they would take me under their wing while leaving everyone else to their own devices.

In the years since, gambling industry representatives (many disguised as truth-seeking academic mathematicians) have either denied that casino staff will ever step in to stop progressive betting, or have patiently offered up implausible explanations for a policy that anyone will encounter within minutes of starting a Small Martingale.

Some examples:

1. Anyone dumb enough to try double-up or Martingale betting has obviously never wagered in a casino before and is in serious need of advice and counsel. Interesting, but implausible. Pit people in reality never offer advice unless asked, at which point they are usually courteous but non-committal, often starting out with, "The book says..." if the questions are about blackjack, or "Some people like this bet because..." Drunks hurling their money down the drain are only cautioned or removed from a layout if they upset other players by hurling something else, or knocking over drinks. Idiots who play or bet badly but don't ask questions are invariably left alone.
2. Pit staff know that a double-up player can do very well for a short period of time but will always crash and burn eventually. They are just being friendly when they advise against the use of this suicidal betting method. And pigs play poker sty-lishly! The entire gambling industry is geared to relieving players of their bankrolls as quickly and quietly as possible, while constantly reminding them that losing is "fun." The notion that a betting method that is certain to fail would be blocked is beyond silly, but no one is ever allowed to bet double-up without house interference. Casinos are constantly devising new long-odds side bets as sucker bait to bolster the relatively low house edge at blackjack and baccarat, and adding non-traditional table games that make roulette and pai-gow poker seem like easy money. If the Martingale was a surefire loser for gamblers, casinos everywhere would be promoting it as an "Exciting New Feature!!!" and printing new layouts to highlight it. Instead, pit staff respond to it like vampires to bright sunlight (not that I am suggesting that those nice people are bloodsuckers, mind you).
   
3. A progression will always fail because once the bet exceeds the table limit, prior losses cannot be recovered, and casino staff feel you should know the risks you face. This is one of my favorites, because it betrays how little the experts think of the rest of us. A $5 opening bet at a $5-$500 layout will bump up against the table limit after 7 consecutive losses requiring an 8th bet of $640. It doesn't matter that a losing streak that long is less than a 1.0% probability: it happens. A Martingale bettor who has a bankroll that is up to the challenge (quite likely, because he never loses if he is allowed to play) simply takes his business to a layout with a higher table limit (say, $100-$5,000) and continues betting at the required level. One win, and he starts the process all over again. If he is playing blackjack and he draws a natural, he's in clover! Given a house limit of $25,000 a double-up player will have to lose 13 bets in a row to hit the "green ceiling" and that's just a 1/8192 probability. And he's not dead yet...although that's a topic for another time.
   
4. If double-up really was a winning method, more players would use it. No one does because it's suicide, and casinos discourage anyone who plays irresponsibly. This is one of the biggest of the big lies that gamblers are asked to swallow whole. And most do. In fact, anyone who has ever spent more than a few hours at casino table games will have seen "Martingalers" at work, probably without recognizing them. They are the annoying people who place two or three bets, lose, and move on, leaving people who have been glued to their seats for hours wondering why their game has been so rudely disrupted (or so they believe). It happens a lot in a busy casino when empty seats are hard to come by and dealers and pit personnel have too much going on to monitor any one player's movements. The rule is three bets at the most at any one layout, then on to the next game. Casinos try to thwart Martingalers by prohibiting "entry" between shuffles at blackjack and baccarat, but that's just a minor inconvenience. Craps and roulette tables are never restricted, and field bets at craps have special appeal because of the 2x payouts for 2 and 12, which used to be 2x and 3x before the accountants that devised 6-5 payouts for naturals at blackjack did a little more dirty work.
5. Progressions are a bad idea because the ancient laws of mathematics state that any amount bet against a negative outcome must eventually have a negative outcome. Pythagoras and his peers and successors were and still are in essence stating a rule confirmed by logic, which is that because negative expectation will ultimately result in more player losses than wins, more money lost than won is an inevitable consequence. And as long as bets are of a fixed or randomly selected value, a long term win is highly unlikely. However, a progression is not random. Bet values are determined by the immediately prior outcome, and while that outcome is random and subject to the negative expectation for the game, the response to it never varies. A Martingale is a bad idea not because it does not win consistently but because it is too obvious. It requires camouflage to avoid quick detection, and that is what target betting is all about.
   

My conclusion long ago was that constant re-doubling is impractical in spite of the satisfaction gained from repeatedly recovering prior losses in a single bet.

Waiting out a losing streak by freezing or reducing the wager and then going for a one-bet turnaround seemed like a mathematically-supportable alternative, primarily because in most table games, the house's chances of winning a given bet are only marginally better than they player's.

Put another way, while each bet at a game with a 2.0% house edge faces negative odds of 49-51, there is no such thing as a fractional win or loss: you either beat the negative number, or you don't.

All of my blackjack and baccarat spreadsheet models track the performance against the same sample of outcomes of both a standard double-up method (the Small Martingale) and a variation that I call SM-Plus which modifies the progression to deliver a bigger win from drawn-out recoveries.

Against the blackjack outcomes (78,000 and counting) the standard double-up had one "bust" in 18,972 series, the pumped-up version had 3 busts in 18,055 series, and target betting had...no busts at all.

Here's the SM, SM+ and target betting summary for the blackjack trial to date.


(Click on the image to enlarge it)
The baccarat trial is especially relevant in this context because the data sets were supplied by two verifiable sources that are independent of each other and (more important) independent of me.

There were well over 300,000 rounds of baccarat in all, equivalent to almost three years of play for a very dedicated player putting in 30 hours a week with two days off each week but no vacation time.

Here's a summary of how a simple Martingale performed, along with data for the more aggressive double-up method, and for target betting.


(Click on the image to enlarge it)
I guess it's possible to make this stuff up, but why? The results achieved have been so consistent (predictable is another way to put it) that anyone applying the rules of these different approaches to target betting fairly and accurately is certain to see very similar numbers.

The other question always begged by results like these is how much better any disciplined betting strategy might do with human intervention allowed, meaning that prolonged negative trends might (or might not) have been avoided if defensive action had been taken.

High-speed simulations of any kind, my own included, require the wholly unwarranted assumption that a player in the early stages of one of those deadly downturns that we all know can occur (those of us who actually place bets in casinos, at least) would NOT back away from a punishing situation and resume play somewhere else. There are some certifiable masochists out there, I know, but I am not one of them.

The conventional academic argument is that since each outcome is independently subject to the same measure of negative expectation, attempts to escape a negative trend can have no long term benefit.

It may be true that a player who bets fixed or random amounts is as likely to get into more trouble after a move as he is to see an end to the negative trend that made him flee.

But for a target bettor, all that is needed is to get out of trouble is two consecutive wins, and the decision to bail out of a bad run is as much about morale as it is about math.

The math, though, supports preemptive "damage control" when a recovery begins to drag out uncomfortably, because the great majority of series (well over 60%) are over in six bets or less, and a tiny percentage drag on for 10 rounds or more.

As the Chinaman said, "A long losing streak must always begin with a short one, and it is better to lose a little than a lot."

Worth noting is that in less than 80,000 rounds of blackjack, target betting "won" (how I wish those quote marks were not necessary!) almost as much as it did in almost four times as many baccarat bets, confirming that blackjack is clearly the optimum table game for this strategy.

Here's the latest BST session...

(Click on the image to enlarge it)
An important reminder: The only person likely to make money out of this blog is you, Dear Reader. There's nothing to buy, ever, and your soul is safe (from me, at least). Test my ideas and use them or don't. It's up to you.
_