Sims tell lies. We all know that. But when they say things you want to hear, they're so cool.
Opponents of any and all betting methods that challenge the supremacy of the house advantage in casino games of chance are crystal clear in their interpretation of the "laws" of mathematics.
If the actual value (AV) or house advantage (HA) applicable to a representative sample of outcomes is a negative percentage, then a player's losses against those outcomes will closely approximate his total action multiplied by the HA.
So 1,000 bets against a negative HA of 2.0% with an average bet value (ABV) of $10 will result in a loss of $200, give or take a chip or two.
There is no room for equivocation here: "Any amount bet against a negative expectation must have a negative result."
Luck can upset the house's applecart for a while, but it is a temporary phenomenon according to the law(s) of large numbers, and the axiom can be boiled down to three little words...you can't win.
That means that the following sim-generated results could not have happened:
They did happen, against outcomes supplied by a random number generator (RNG), with all five indicated progressive betting methods showing a profit after 1,000 rounds in spite of a very substantial house edge.
Last time, I posted a summary from 150,000 RNG outcomes that showed target betting well ahead of the game in defiance of the "laws" of arithmetic as interpreted by the gambling industry and its very smart experts.
And to be fair, their pessimistic view of a gambler's long-term prospects is logical as long as the punter bets fixed amounts or bets randomly.
If he bets progressively with a very specific target in sight, negative expectation will be thwarted at least 99.99% of the time, making results like those above and elsewhere on this blog commonplace.
The methods summarized here include the standard Small Martingale, which doubles the bet after any loss until a win is achieved, delivering a profit equal to the value of the opening bet, and a souped-up Martingale (-5, -10, -25, -50, -100, -250, +500) that gooses win values in proportion to an increase in overall risk.
Target betting heads the list, of course, with OG referring to a version of Oscar's Grind that departs from the rules laid out by Tom Ainslie in his book.
Mr. Ainslie claims that "Oscar" has been a steady winner for him year after year and is endorsed by one of gambling's premier mathematicians. But I have been far less lucky whenever I have applied it against one of those sims that systems debunkers love so much.
The OG shown above doubles the bet after a win, to a maximum value of the loss to date (LTD) plus one unit.
The Ainslie version adds one unit after a win, ensuring that recovery after a prolonged downturn will be long and arduous indeed.
Mr. Ainslie recommends abandoning a recovery attempt and starting over if the LTD hits 20 units (-$100 at a layout with a $5 minimum). That rule makes getting ahead a very iffy proposition.
OGT spices things up a little by making the win target not one measly unit, but 10% of the maximum loss in the current series. So if the method is $500 "in the hole" at one point, the win target is $50, and so on.
In each of the above summaries, EXP shows the amount each method "should have" lost in compliance with the HA x Action formula promoted by the gambling biz.
As you can see, it didn't happen, which is not to say that it never will.
The estimable Wizard of Odds, by far the most eloquent of all the casino shills plying their trade on the Internet, describes his decisive debunking of a betting strategy devised by a challenger with the lyrical name of Daniel Rainsong.
I have no knowledge of Mr. Rainsong's method and have been unable to track him down, but my guess is he wuz robbed.
The sim that beat him imposed a spread limit of 1,024 to 1, which might not have stymied Mr. Rainsong's strategy but would be a big problem for mine.
Mike "Wiz" Shackleford, self-billed as an international casino consultant, was able to offer Mr. Rainsong a seemingly generous house edge in his "billion bet sim" because he well knows that it is a deficiency in the critical combination of spread and bankroll, not the value of the HA below double digits, that seals a player's negative fate.
Hell's bells, he could have set the runaway sim's HA at zero and still have "beaten" the Rainsong method. But that, of course, would have given his game away.
Like many gambling industry insiders, the Wiz is well aware that inadequate bankrolls and tight spreads are the stuff that fat house wins are made of.
An even-money game (the sort that does not exist in any casino) would draw out the house's winning process a little longer, it's true. But it is short-term negative spikes against the player that put the wind up inexperienced players and wipe out piddling bankrolls, not gouge-level HAs.
The great joke in gambling is that most punters would be defeated by a game that actually gives them the edge!
That is why casinos routinely report game win percentages that far exceed the known HA for blackjack, baccarat, craps, roulette and the rest.
Think of the billboard slogan that suckers could be reading as they pedal-to-the-metal towards their certain doom in Las vegas: "We'll give you a player edge, but we'll STILL kick your ass."
Spread is the whole ball of wax for progressive betting or for ANY winning method, and a 1,024-1 limit is a deliberately deceptive gift to anyone claiming that the house edge is unbeatable.
It is a non-issue for most gamblers, for whom a 1-10 spread is too much excitement, as well as a guarantee that they will lose unless they get very, very lucky.
Casino operators have known since the beginning of time that capping the bet spread is the most effective way to protect the house edge.
That is why table limits ($5 to $500 at a blackjack layout, for example) exist, and why pit personnel are on the lookout for players who gradually escalate their bets until they achieve a turnaround win and then start over.
"The math" demands that the sooner you hit your upper limit, whether it is house-imposed or your choice, the more likely you are to fall victim to negative expectation.
Conversely, the more wiggle room you are permitted, the greater is the probability that you will be able to win more when you win than you lose when you lose, thereby overcoming the otherwise inexorable ill effect of losing more often than you win.
It is a challenge to work a casino with target betting, and it can only be done by keeping as low a profile as possible.
My policy has always been to spread no wider than 1 to 50 at a bottom tier casino (say, $5 to $250), and no wider than 1-5 at any one layout once the bet has reached $100.
Above the bottom level, the rule of thumb remains 1-5 at the current layout, and drops to 1-10 in any one casino.
The theoretical effect of this sliding scale is a whole lot of to and fro between layouts and casinos, but theory has a habit of evaporating when real life takes over.
Because the odds against you do not change much from deck to deck or game to game, a recovery series made problematic by "local" limits can be suspended until better conditions are available. But that will not happen often.
As your bankroll grows, it becomes easier to stay calm and confident when the pressure is on, and respond appropriately.
In spite of all of the Wiz's claims to the contrary, computer simulations are not a substitute for real play because they exclude the most critical component of gambling, the human element.
They also eliminate cards, dice, wheels, dealers and real time.
I have on occasion been accused of being an agent of the casinos because I offer players an alternative to losing that cannot possibly help them in the long run.
All I can say to that is that anyone claiming that games of chance cannot be beaten is a far more effective shill for the casinos than I could ever be.
Bet flat or bet randomly and you will lose.
Bet progressively according to the rules that I have been providing free of charge for more than a decade, and the odds will be dramatically in your favor rather than fractionally against you.
Either way, the arithmetic is very simple.
Against a game with a 2.0% house edge, you have a 49% chance of winning any bet and a 51% chance of losing it, whether you use target betting or not.
That means that each and every time you place an LTD+ bet in the hope of turning a losing series around, you will probably lose it.
But because your bet values keep changing to match the LTD (and because you either win or lose 100% of your bet, not some cockamamie amount in between) you can be confident that eventually, you will beat those negative odds.
On average, target betting with optimum parameters applied will turn a recovery series around in just over five rounds.
Both versions of the Martingale will do the job a little faster, but their greatest drawback is that they are unplayable in most casinos (pit staff will interfere with their use because they know they represent a real threat).
Tom Ainslie's inch-by-inch version of Oscar's Grind needs an average of 30 rounds to get out of the hole with the 20-unit bust limit omitted. It cuts that number by more than half with the limit in place, but struggles to make a profit, obliterating its gains with a succession of $100 bailouts.
Oscar's Grind could easily be a creation of the casino industry because the limits Mr. Ainslie advocates guarantee that it will fail while deluding the player into thinking that he is in control.
It is a progression, to be sure, but a halfhearted and nervous one that is no threat to the house advantage.
Capping the bet at $100 (assuming a $5 opener) will accelerate the bankroll's downfall and might even be more dangerous than betting random amounts within the same range and hoping for a little luck.
A veteran dealer at Caesars Palace in Las Vegas once told me that Frank Sinatra, a blackjack enthusiast who liked to take over an entire table, would stuff his pockets full of chips and walk away when he won but was not required to pay off his marker when he lost.
That, I admit, may be the best betting strategy I ever heard of. Target betting is the next best thing, far superior to any version of Oscar's Grind!
It all comes down to the comparative frequency of wins and losses, or the win-loss pattern (WLP), and the demonstrable mathematical truth that for both sides in the game, isolated wins are more common than streaks.
For a random player, the WLP whisks his fortunes back and forth like a falling leaf in a gentle breeze, a win here, two losses there, a win, a loss, two wins, three losses.
In essence, the target player bets against the house being able to sustain a winning streak, which is subtly different from putting his money on his own luck.
Most gamblers backing what they hope is a player winning streak do so diffidently, often failing to recover the chips they lost when the WLP went against them.
Target betting's primary objective is to recover past losses in fewer bets than it took to lose the money in the first place.
It is "axiomatic" that if the house cannot take a bite out of your bankroll by winning more often than you do, than the house has a problem.
When all of target betting's rules are in play, the strategy will recover prior losses with a single win more than 70 percent of the time (not as impressive as a Martingale's 100 percent, but usually not as dangerous or as obvious, either!).
Until the strategy's top limit bet value is reached, two consecutive wins will do the job.
Once the "max" is on the table, target betting is as much at the mercy of the house advantage as any other method.
But in order to get into a hole that deep, the method must have been battered by a spike in the house edge that will at some point have to be at least partially offset in order for the known laws of math to hold true.
Let's say that the house edge went haywire for a while, putting you 12 bets "behind" in in 30 rounds, for a series HA of -12/30 = -40.0%. Ouch! All of a sudden, you are at your limit, and the only thing that can save you from certain death is the size of your bankroll (and your intestinal fortitude).
How likely is it that the house spike will continue, or that the next few dozen hands will not contain enough player wins to get you out of the hole? Not very.
Negative expectation for the game is, say, 2.0% (higher than blackjack, but easier to work with when it comes to arithmetic). We know that at some point in the future, the 12 bets you are now behind will be mixed in with upcoming wins and losses until the overall house edge for a sample beginning with the first bet in the current series drops from 40.0% to a number much closer to 2.0%.
In theory, the WLP could bounce gently to and fro without any significant streaks either way for the next 570 bets until the overall house edge settles at the level where it is "supposed" to be.
But that is very rarely the way things go in games of chance. Much more likely is a pattern resembling one of the three red-line charts shown above: more downs than ups, but enough ups to save the day for you and your bankroll.
For most players, falling just a handful of bets behind sets them on a slippery slope that cannot be escaped without a calculated exploitation of every potential winning streak.
Bumping the bet in response to every win will at times increase the speed of the downward slide. But it will also make a very rapid recovery possible.
I spend a lot of my casino time watching other players from a respectful distance, because seeing them succumb to a WLP that I know I could easily have beaten is almost as satisfying as winning myself.
Don't get me wrong, I get no pleasure at all from seeing strangers lose their money. But there is nothing I can do to help them, and monitoring their avoidable missteps at least provides one of us with a positive outcome!
If you want to win consistently, you first have to accept that over time, you are going to make more wrong bets than right ones, and decide what you are going to do about that.
If you are $50 behind and plan to stick with a bet value averaging $10, then you know you will need five more winning bets than losing ones in the near future just to break even again. How likely is that? Again...not very.
By freezing your bet after a loss, you are, in a sense, betting that the house will continue its winning streak for a while.
When you bump your bet value in response to a mid-recovery win, you are up against the same negative odds that apply to every bet but recognize that a ping-pong volley of bets of equal value is not going to get you out of the hole.
The great irony is that much of the time, betting as wide a spread as you can afford will put you at less risk than betting smaller amounts over and over again as you slowly slide deeper into the mire.
Along the way you have to set aside the standard gambler's dream of rich rewards for little risk, and think instead the way the house does.
Be happy to pocket a win that is just a few percentage points of your total action, remembering that that is how the bills get paid in the casino that surrounds you.
Don't be greedy, don't be noisy, don't get cocky and above all, keep your head down.
You will win far more money far more often than the average gambler. But that does not mean you are unbeatable.
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.
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