Showing posts with label win-loss pattern. Show all posts
Showing posts with label win-loss pattern. Show all posts

Thursday, April 30, 2009

"Just who are you preaching to? Even if your ideas about beating the house edge made sense (and they don't), no one could afford to use them!"

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This is a criticism I hear from time to time, and my only answer to it is that making money is never cheap, except in everyone's dreams.

Setting up a business on fabled Main Street, for example, requires a huge outlay on premises, remodeling and inventory, just for starters, and often profits are not seen for years.

Building a casino costs billions these days, and since some players manage to win now and then (sometimes in the millions) the house has to keep huge sums handy to cover downturns and stay ahead.

There is no mathematically supportable way to beat the odds at games of chance without occasional risk, and betting a wide spread is inevitably expensive before it can be profitable.

Your own data show occasional enormous losses that wipe out hundreds of hours worth of winnings. That kind of disaster could happen any time, possibly in successive sessions. That means that your strategy could be suicidal. Admit it: you are working for the gambling industry.

Casino table games are all about probability. It is possible for target betting to lose because its win rate is less than 100%. But it is not probable.

In simple terms, you are looking at favorable odds of far more than 5,000 to 1 if you bet progressively using the target betting rules, and the odds against two successive losses are therefore at least 25 million to 1.

It has always seemed strange to me that the so-called systems debunkers whom I often refer to as mythematicians insist that if a betting strategy can lose just once, it must be worthless.

The house has the best system of them all, a passive strategy that encourages players to bet and behave in a certain way, but does not force them to put money on the table or tell them how much to wager. But even the house loses occasionally.

What happens with target betting is that even in the face of occasional "high exposure," profits come in rapidly and consistently, just as they do for the house.

Sometimes, winning is harder than usual, just as it is for the house.

And once in a very great while, the team has to take a hit, just like the house.

All of the figures posted here and elsewhere in support of target betting are honest and accurate, and all of them demonstrate that very infrequent setbacks are quickly recovered.

Your chances of being killed in a car crash in the U.S.A. are estimated at around 20,000 to 1 against. Does that guarantee that you will be road kill before the end of your 20,000th trip? Of course not!

What you get from auto safety data is much the same as the message derived from target betting trials, and that is that your risk of crashing and burning is too insignificant to preclude either driving a car or betting in a casino!

That assumes, of course, that you drive safely and sensibly on the road, and that you defy the odds in a casino by using target betting to win consistently.

Sounds like you never heard that insanity is doing the same thing over and over again and expecting a different result. Your "proof" is not proof at all because your data are subjective and suspect at worst, and anecdotal and irrelevant at best. You can't use prior outcomes to develop a betting strategy that will work against future outcomes.

I am comforted that insanity is never defined as doing the same thing again and again and expecting the same result, which is what I do with each new target betting trial.

It is also why I recommend to those who are rightly at first skeptical about my ideas that they don't take my word for anything, but instead apply my method to "future outcomes."

They will quickly learn that they have nothing to fear, and much to gain.

It makes no sense to dismiss past outcomes as non-representative.

Even casinos do not do that!

A new game or a rule change to an old game might initially be tested against what I always refer to as runaway sims because they totally eliminate human control and restraint.

But that is never more than a first step.

A casino will insist that a new game must be tested against real players in actual "gaming" conditions before it has a chance of being introduced to the floor.

The gambling industry knows very well that people do not play like computerized robots, and that sims therefore cannot accurately reflect reality.

Face it, no one with the kind of money you say is needed to make target betting work would put it at risk the way you want them to. Gamblers may not be the smartest people on the planet, but they are not the stupidest either. They know that if you want to win, you have to protect your bankroll. You say the opposite.

"Conservative" betting is almost as dangerous to a player (please, let's not call him a gambler) as greed, which is Punter's Enemy #1 in a casino.

The house always wants people to bet conservatively because the math says that they are more likely to lose that way.

The ideal player, from a casino's point of view, is someone who bets a narrow spread (never more than 1 to 10), pulls back when he is losing, and responds timidly to a potential winning streak.

Table limits (spread limits) exist entirely to encourage players to be cautious in their betting habits, so that when they start losing, it is far more difficult for them to bet their way out of the hole.

It is a very simple matter for arithmetic to demonstrate the folly of narrow spreads, and you can be sure that the gambling industry knows that.

Nothing that I have published here or elsewhere in the dozen years since I first posted the principles of target betting for free on the Internet is new to the casino business.

Casino operators know very well that progressive betting is the only way to consistently and reliably overcome the house advantage, and they go to extraordinary lengths to discourage it.

I tell the "experts" that they should try progressive betting for themselves before helping the gambling industry disseminate more deliberate disinformation about how it can't possibly work.

It does work, and casinos hate it.

As for high rollers, most of them have survived expensive lessons on the hazards of trying to "buy the pot."

Big bets alone can never guarantee success at games of chance, and "whales" earned that nickname from the gambling business not because of the size of their bankrolls, but because they keep on taking a dive, then resurfacing for another go-around.

Las Vegas casinos love to put out press releases about the huge sums won by a high roller in from Hong Kong or the land down under. But you will never see publicity about a "whale" who dumped $10,000,000 at baccarat (or whatever) before limping home.

That's because winners bring in losers; losers are bad news, except for the bottom line.

Money alone will not beat the house advantage.

Money and a plan - a plan I call target betting - will always get the job done.

Losses will occur. But winnings will always exceed losses.

As I keep saying, the only way to stay ahead in a casino is to win more when you win than you lose when you lose.

There is nothing revolutionary (or insane!) about that idea: It is wholly logical, sensible and scientific.

If you keep on winning back your losses in fewer bets than it took you to fall behind in the first place, the house edge becomes meaningless.

So...here are the latest BST blackjack results. More of the same old same old!


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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Friday, April 10, 2009

The conventional wisdom says a million wins don't matter and losses are all that counts. True, but false at the same time!

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A mathematician arguing for the YCW (you can't win) philosophy will tell you with a straight face that progressive betting can never be profitable because more bets lost than won must always result in more money lost than won.

No amount of evidence to the contrary will be considered acceptable, in the same way that for centuries, the conventional wisdom dismissed data showing that Planet Earth was not flat.

It is of course completely rational to warn against a betting strategy that will occasionally suffer a catastrophic loss that will always wipe out all prior profits and bankrupt the player.

But progressive betting will only match that caveat if the method is applied the way the casinos and their house-trained experts want it to be, in real play or in computer simulations.

That means that the player must keep on betting through prolonged downturns, and meekly throw in the towel whenever his next bet is prohibited by the prevailing table limit.

The ideal gambler is, in the view of all casino operators and the mythematicians who promote the gambling industry's ordained right to the contents of all our wallets, an impetuous spendthrift who comes to the table with an inadequate bankroll. He then bets a very narrow spread, and sheds first his inhibitions under the influence of "free" booze, then his stash.

It is theoretically reasonable to suggest that since target betting my way lost just once in some 70,000 recoveries, that loss might have occurred in the very first session, and therefore the method is potentially too hazardous to merit consideration.

It is theoretically equally reasonable to argue that since 1 in 70,000 American motorists will be killed or seriously injured in a road accident on any given day, the car in your garage is potentially unsafe at any speed and you would therefore be ill-advised to drive it ever again.

I cannot refute a statistically supported recommendation that the only certain way to win in a casino is to keep all your money in your pocket and, better yet, never step across the threshold.

But short of an outright ban on gambling, the evidence shows that progressive betting is a better way to win than any of the alternatives.

Those of you who come to agree with me after a few hundred hours of cautious exploration and practice (I certainly do not expect you to take my word for anything!) will learn that target betting can be modified in all sorts of ways to suit your gambling personality and your resources.

In fact, the more modifications you develop, mixing and matching them as you see fit, the less likely you are to be identified by casino pit personnel as a player who wins "too often" and should be stopped.

Elsewhere in this blog is data that show that even the much-derided Martingale or double-up betting method (-1, -2, -4, +8 etc.) demolishes the house advantage in the almost 400,000 real-time, real-play outcomes that are the subject of the current trial.

Played right, double-up can be a powerful antidote to the house edge. If the casino you have selected allows you to play it at all, that is.

Target betting with my rules applied is far harder to spot, and the modifications that I recommend or that individual players will develop for themselves make it even more effective in the real world.

Here's the latest BST data set:

(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.
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Tuesday, April 7, 2009

There's no escaping the fact that math rules in the casino. And it's also easy to see that mathematics does not rule out progressive betting.

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The consistent success of target betting or any method that breaks the fixed or random mold is assured by the fact that outcomes in games of chance are collectively predictable.

In blackjack, for example, a reasonably representative sample (say, more than 1,000) will confirm that pushes occur about 9% of the time, player naturals bring in a little extra from about 4% of all hands, and doubles and splits governed by strict basic strategy play will win about 20% more often than they lose.

You can also be sure that paired wins or losses will occur about half as often as isolated wins or losses, triples will be encountered roughly half as often again, and so on.

"Roughly" and "about" are words that academic mathematicians hate to hear, but the smaller the sample of outcomes, the harder it is to predict what will happen with absolute certainty.

Luckily for the target player, absolute certainty is absolutely unnecessary.

Regular readers will know that I say with monotonous regularity that If you can win more when you win than you lose when you lose, then losing more often than you win won't hurt you.

A picture is worth a thousand numbers, so here's a summary for the 100,000-plus baccarat rounds supplied by Lorenzo Rodriguez and Zumma Publishing:-

(Click on the image to enlarge it)

The first thing to notice is that after a single crash-n-burn and 13,640 successful recoveries, the AWB/ALB number is a relatively unimpressive 104%, but still enough to deliver an overall profit.
The overall HA/AV for this set was 1.6%, which is high for baccarat but not desperately so.
Two out of three recoveries were achieved with a single win, although as negative expectation required, more recovery/turnaround attempts were lost than won (the house had a 1.16% edge in that area).
Series requiring 10 or more rounds to recover were less than 9.0% or 1 in 11 and 62% of all series were wrapped up in five bets or fewer.
The average bet value was high according to some at $592 but bets of $1,000 were required only 4.4% of the time (less than 1 in 20).


Many a mythematician might be inclined to dismiss 114,000 rounds as anecdotal or non-representative, so keep in mind that the sample is equal to well over a year of play for a fulltime baccarat fanatic.

Also keep in mind that according to the same self-styled (and often house-trained) "experts" the results you see above are impossible.

Now please consider a much larger sample of baccarat outcomes, more than 200,000 supplied by Lee Jones, a systems promoter who can verify their accuracy and with whom I have no connection (he might even consider me a most unwelcome competitor since I don't charge for my ideas and his are for sale).

(Click on the image to enlarge it)

The AWB/ALB product is higher at 109% vs. a more standard house edge of 1.18% and the average bet value is way down at $352 ($592) but the rest of the numbers in the summary closely resemble those for the smaller and quite separate sample from the Zumma books via Lorenzo Rodriguez:

EOS 1-5 62.5% (62%)
EOS 6-10 29% (29.3%)
EOS 10+ 8.5% (8.7%)
Positive series 35% (35%)
Neutral series (29%) (28%)
Negative series (36%) (36%)
1-win EOS 66% (66%)
EOS wins/tries 49.1% (49%)
Bets of $1,000+ 3.6% (4.4%)


The biggest difference between the two baccarat samples lies in the final target betting win (2.86% for the larger data set vs. 0.16%). The reason, of course, is that the first sample included a bust, one that was triggered by such a precipitous plunge that only the "robot" at the heart of every runaway sim would have sat through it!

Baccarat holds far fewer surprises (good or bad) than blackjack, but the stats for the first 75,000-plus outcomes in the BST blackjack trial are remarkably similar to the baccarat numbers, except for a much higher win percentage for target betting and a dramatic jump in the AWB/ALB product:-

(Click on the image to enlarge it)


And here are data for double-up (a Small Martingale) against the baccarat outcomes. The "win one unit" original version has the double disadvantage of being easily spotted and blocked, and a slow win rate that means that a single "bust" would wipe out years of profits.

(Click on the image to enlarge it)

We are now looking at close to 400,000 "real play" outcomes, which is a representative sample according to any objective, sensible standards.

We can see that ruin (the loss of our $1,000,000 bankroll) is a rare occurrence indeed, and that in spite of a single crash-n-burn, target's notional profit at this point is closing in on $4 million

Spread is the critical factor, we have learned. A spread of less than 1-1,000 is doomed, in the long run.

We do not have a monopoly on that knowledge: the casinos are well aware of the danger to their bottom line posed by progressive bettors with a disciplined plan and a fat bankroll behind them. They and will do whatever it takes to thwart them.

Obviously, a player confined to a single casino or, worse, to a handful of table options, can never hope to spread from 1-5,000 (the recommended optimum) or even 1-1,000, in the same place.

The solution to that is an over-abundance of patience, and strong legs. Spreading from $5-$100 (1-20) from the opening of a new series is plausible, but after that, 1-5 is the limit to aim for ($100-$500, $500-$2,500, $2,500-$10,000 and $10,000-$25,000, for example).

One player flying solo might find the range hard to achieve under ever-increasing casino staff scrutiny, and tough as it sometimes is to run smoothly, team-work is probably the answer.

For now, all we are concerned with is "The Math." And it is on our side.

If you doubt it, here are new numbers from the BST trial (I just began batch #16):


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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Monday, March 30, 2009

The million-dollar question: Is damage control just another gambler's fallacy, or can ruin be avoided intuitively?

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Human intuition or decision making is the critical element that the You Can't Win brigade omits from the runaway simulations they use to "prove" that the house advantage at games of chance is ultimately unbeatable.

They also eliminate cards, dice, wheels, tables, money, dealers and real time, and then pretend that a high-speed computer simulation based on a random number generator (RNG) is "exactly the same as a real game."

Once upon a time, I was able to ask who would be gullible enough to bet actual cash against a game that used RNG output to simulate blackjack, baccarat or roulette, and I was confident that the answer was clear.

Then the casinos came out with giant flat-screen TVs featuring curvaceously UN-flat, life-sized "dealers" and slots for suckers to push their money into. And by golly, some people do play these so-called games, lured perhaps by cleavage that they can drool over without getting their faces slapped.

The mythematical defense of sims is that at some point, a fatal negative pattern of losses and wins will occur in real play that is exactly like output from a RNG, and vice versa, and ruin will be unavoidable.

It is, as I have said before, like arguing that a car that crashes with no driver at the wheel and with the gas pedal and brakes disabled is inherently unsafe.

Sorry, guys, but gambling is a human activity and the human element really does matter.

Simulations are useful only because they run at very high speeds, saving a huge amount of real-time research, and can give some indication of how a new game (or a method of betting) will perform.

But when the Wizard of Odds and other experts sponsored by the gambling industry claim that casinos rely on simulations to evaluate new games or rule changes to old ones, they are being deliberately disingenuous.

Sims have a role to play, but is always a preliminary one.

Casinos know very well that the only tests that really matter have to be conducted out on the floor, and nothing new ever gets the green light until it has been exhaustively evaluated under real-play conditions.

I have gone to great trouble over the years to amass as many blocks of outcomes from actual play as I can, and target betting has so far recorded only one million-dollar crash-and-burn in more than 500,000 rounds of baccarat and blackjack (more than five years of play for a full time gambler, if such an animal still exists).

The pattern that caused target betting to crash and burn looked like this...


If you were to see a "deadman's drop" like this in real play, one that went on to give the house a 33.33% edge in 114 bets in which 34 more wagers went south than didn't, you would not wait for rock bottom.

You know for sure that if you were sitting at a baccarat or blackjack table and the shoe turned that vicious that fast, you would decide it was time to take a break long before your bankroll was in serious jeopardy.

As it happens, this spectacular nosedive followed eight consecutive wins that raked in $1,090 in profits before the ninth bet, for $500, lost.

For years, my rule for blackjack has been to keep redoubling during an opening win progression until the bet hits $200, add $100 each time if the winning streak continues, and accept a loss of $500 or more as EOS, happy to end the series with $590+ in extra chips, and fall back to a minimum opening bet at a different layout.

Blackjack is the perfect game for target betting because "natural" pay-offs that exceed the value of the original bet (adding 50% or I'm not playing!) and well-timed splits and double-downs make it much more profitable than baccarat.

To make up the difference, I set the win progression cut-off much higher at $1,000 vs. baccarat, and that made the rules set vulnerable in just this one instance out of more than 60,000 successful recoveries.

The first baccarat trial, bust-free after 37,062 recoveries, delivered a virtual profit of $1.97 million and retired the original $1 million buy-in. The second baccarat series had one bust in 18,446 series and earned a little more than $110,000 (better than a break-even but not by much!). The current blackjack trials stand at a funny-money win to date of $1.75 million and counting. That's a total win of almost $4 million for five years' work, chickenfeed for a CEO but a big improvement on negative expectation.

It would be easy for me to change the baccarat results to eliminate the "bust" then claim that target betting was unbeaten against hundreds of thousands of real-play rounds.

But that would be cheating, and I don't believe in that (not because I am a saint, but because it is simply not necessary!).

For the record, changing the win progression rule to match my blackjack strategy would have turned a baccarat crash-n-burn into a win equal to 5.0% of the action for that same data set.

House-trained academics have a notion that systems promoters always have an excuse when their method crashes in ruins, and eliminate the problem simply by changing the rules.

So target betting's single loss of its bankroll stands in my book, reducing my method's win rate from 100% to -1/69,272 recovered series = 99.9985564%.

I generally claim a 99.992% win rate for my betting method, equal to favorable odds of 12,500 to 1. If I am in a cautious mood, I fall all the way down to 5,000 to 1 in a player's favor, figuring that even that has to be preferable to negative odds of 495 to 505 if you're a little lucky and play blackjack well.

And then there's the obvious wisdom of not claiming a 100% win rate, but instead encouraging the casinos and their tame experts to go public over and over again with "proof" that target betting cannot beat a runaway sim and is therefore worthless.

Let's face it, if gambling industry brainiacs can show for certain that the strategy is worthless, then they have no legal argument for banning its use in their casinos.

As for the ability of a thinking human being to recognize potential danger before it becomes deadly and take steps to avoid it, "simsters" know well that evasive, self-protecting tactics are difficult (meaning inconvenient) to model.

I have done it with what I call an interactive sim, which relies on the famously unreliable Windows RNG to spew out losses and wins with a randomness that may be questionable, but is at least out of my control beyond my insertion of a clear house edge of 1.4%.

In real play, several factors are likely to prompt a player to quit a series before recovery, then resume betting at the appropriate level elsewhere. A sim can't imitate boredom, hunger, fatigue or a need to pee, among other human responses, but table limits play a key role and they can be factored in.

The way it works is that the sim starts and ends series after series as a "live" player would, but the spreadsheet platform enables a human to scroll down, identify a spread limit trigger, and respond to it.

The job is done by "freezing" all of the outcomes or rounds up to that point, then refreshing the RNG to simulate play continuing at a different layout.

This is done whenever a spread limit trigger arises, and my assumption is first that at a $5 table, a $100 bet is as high as a real player would be able to go without attracting unwanted attention. After that, the rule is a spread of 1-5: lose a $500 bet after starting out with a minimum wager at a $100 table, and move on, then a $2,500 bet, and so on.

Series very rarely drag on for long (the average EOS comes in less than six bets) so this is not nearly as complicated or tedious a procedure as it sounds.

The point is that flesh-and-blood players do not suffer the kind of downturns that the robot at the heart of a runaway sim is required to ignore in order for the routine to "prove" that no betting method can ever beat the house advantage. It is simply not human nature to take a relentless beating when real money is at stake without taking appropriate evasive action.

Runaway sims are dishonest. But in some ways, that's not a bad thing for a cool, calm and disciplined player who knows how to beat the odds and win consistently.

Here's the latest BST blackjack data (playing the $500 win progression rule!).

(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.
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Friday, March 13, 2009

When the dealer keeps beating your 19+ hands, should you sit still and suck it up, or get the hell out of there?

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Your average academic mythemaniac has a simple answer: Save on shoe leather and stay where you are, because running away can't affect the long-term outcome.

There may be a grain of sad truth in that if you are a blackjack player who bets flat or within a very tight spread (1-5 is as tight as the proverbial duck's bum and many punters think they are being conservative and sensible if they narrow their spread still further).

The reality is that while paired wins are a constant, predictable feature of any house game's win/loss pattern (WLP), trends do occur that lock them out for a while.

Bailing out of the current game and taking your NB and LTD numbers elsewhere can never guarantee an improved WLP and the only way to find out if you made the right decision is to slide a substitute player into the seat you vacated and have him track the hands that came out of the shoe after you left.

All you can ever know for certain is that every deadly negative trend begins with a threatening pattern that gets steadily worse, and to avoid a potential (but not certain) disaster, you must take evasive action before you go broke.

Strategy debunkers love to use runaway sims to "prove" that there's no way to overcome the house advantage at casino table games, and the same tool demonstrates conclusively that paired wins occur about as often as paired losses.

When they stop happening, it is smart to back off and go hunting for a more comfortable WLP, even if the only certain benefit is to your peace of mind...your morale, if you like.

No one should ever gamble if they feel threatened or uncomfortable for any reason, so never hesitate to interrupt play whenever the mood strikes you, and resume it elsewhere when you're ready.

Here's the log from the last BST session in Batch #14.

(Click on the image to enlarge it)

If what you see here had occurred in the course of output from a runaway sim, the essential assumption would be that the "player" (meaning, in that context, the method) would keep on betting wildly without a care in the world, until the negative pattern ended or his money ran out.

In real life, human beans don't like being kicked in the head or stomped on with heavy boots or being robbed at (metaphorical) gunpoint, let alone all at the same time.

They take defensive action.

The most effective response to a house spike is to simply walk away, knowing that interrupting play for a while can never hurt the long-term outcome, which for the target bettor is yet another session win.

I have heard from some players who prefer to pull back to fixed minimum bets for a while, especially when they are in a busy casino on a wild weekend night and hate to give up their seat. I guess it can't hurt to take a breather by treading water when the pressure's on, and the effects of such a move (or non-move!) are hard to model accurately.

What matters is that no one with blood in his veins plays the way runaway sims require them to. It would, at best, be contrary to human nature.

Just remember the DBO rule: Don't. Bend. Over.

Above all, stay cool and calm and don't take a losing streak personally. It will end. And then, as always, you will come out ahead.

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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Tuesday, March 10, 2009

Waiting for the other shoe to drop could take a lifetime (and it may never happen at all!)

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The assumption that mythematicians like to cling on to and batter us about the head with is that if you are certain to lose more bets than you win in the long run then you must also be doomed to lose more money than you win.

They don't care that models and data summaries covering millions of outcomes with a clear overall house edge include countless thousands of profitable series that consisted of more losses than wins.

They just keep chanting that the sample, however large, was "not representative" and warn that at some point, the sum total of all losses must exceed the sum total of all wins. So, beware, insolent peasants, and be ready to pay your dues.

Here's the latest BST log:

Click on the image to enlarge it

It's true that from time to time, a win-loss pattern will set in that has a succession of isolated wins (wins immediately followed by one or more losses). And if the PB value is outside of your MSL ("do over") range, two wins separated by one loss will not save the day before the cavalry rides over the hill in the form of "twins" (two wins in succession!).

The horrors of long stretches in which the NB keeps jumping skyward with each failed EOS bet diminish dramatically as your confidence grows. But it never hurts to keep in mind that you are playing a game in which the odds are almost always against you.

As I explained in the summary, table limits usually extend the battle to climb out of the hole because without wiggle room in your bet values, the green ceiling forces you to keep betting the max until the WLP switches to a more positive trend.

But that assumes you do not have the option to back away from the layout that has put you in the hole, and resume play at a location where you can continue to strictly follow the target betting rules.

Here are the target betting bets applied by the spreadsheet model to the outcomes in the pencil log shown above. The final totals differ from the numbers at the bottom of the log because the recommended responses to dealer naturals and dealer 21s are not applied. I'll fix that at some point, but my purpose here is to keep on demonstrating that more lost bets does not translate to more lost dough!


Click on an image to enlarge it

The blocks of numbers in the spreadsheet line up with the checks and crosses etc. in the log, so if you print out the three images, it should be fairly easy to match them up.

As always, there were numerous turnarounds that delivered a profit from a negative situation, and overall, the house edge was almost 2.0% gross, confirming that more hands went south than north, so to speak.

The NET AV was +2.79%, demonstrating once again that properly-applied doubles/splits really do deliver a player advantage. We already knew that a 3-2 pay-off is better for the bottom line than a 1-1 pay-off!

Real math (as opposed to mythematics) is reassuringly predictable when it comes to data from games of chance. An analysis of recovered series will invariably show that one third contained fewer wins than losses, one third had an equal number of wins and losses, and one third had fewer losses than wins. Surprise!

The bigger the sample, the more precise the distribution becomes. This set (the outcomes from 090309) made a liar out of me, temporarily, with 45 positive series, 18 negatives, and 21 break-evens, but that's not the norm. The current trial sample (all bets against Ken Smith's BST app) are also out of whack (547/369/315) but the distribution will settle down eventually!

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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