Anyone who walks into a casino hoping to win more bets than he loses is probably going to be disappointed.
But that is exactly how most gamblers approach the challenge of beating odds that they know from the start are against them.
It doesn't make much sense, does it?
It is a demonstrable mathematical fact that if you bet the same amount each time, or choose your bet values randomly, you will eventually fall prey to the house advantage, more likely sooner than later.
And even if you apply money management to the process, responding appropriately to trends for and against you and restricting bet values to a limited proportion of your bankroll, you won't win in the end.
You will simply get to play a little longer.
Casinos are not in the business of money management...player management is their game, and they do what they do so subtly that most gamblers believe that the choices they make are entirely their own.
For example, before a casino in my Nevada neighborhood burned down a year or so ago, its blackjack tables offered a betting spread of $2 to $200.
When it reopened, its fancy new layouts all had table limits of $5 to $100.
To the vast majority of punters, table (or spread limits) are a matter of supreme indifference.
Most people do not spread their bets wider than 1-5, and the bigger their bankroll and their opening bet, the tighter their spread is likely to be.
It is possible for them to make a little money if the house advantage maintains its predicted level for a while and if they press while they are ahead and pull back during a downturn.
They will be in trouble when the house gets a few bets ahead, because they will need an equal number of wins to recover, and because of the game's bias, that may not happen in time to save their meager bankroll.
By imposing table limits, casinos exploit the fact that most players are reluctant to quit a game during a losing streak, especially if the joint is jumping on a Saturday night, and finding another seat might take a while.
So for nearly all of the players who returned to that rebuilt casino in Nevada, their only complaint is likely to be that $2 bets are no longer permitted, not that the maximum spread has dropped to 1-20 from 1-100.
I do not have access to the books at Topaz Lodge, of course, but I can promise you that the house win per player numbers at its blackjack tables are up, in spite of a slump in casino traffic.
The reason is quite simply that $25 players can now only spread 1-4 instead of 1-8, and while spreads that tight are sure to lose in the end, the prospect of a late lucky streak has been summarily halved.
Gamblers are creatures of habit and highly predictable, and casinos depend on their knowledge of human behavior to maximize their profits.
"System" is a word that in the gambling context has become a pejorative, conjuring up images of snake-oil salesmen and the gullible fools they prey upon to profit from their evil schemes.
Outside of casinos, the word is more likely to connote discipline, orderliness, good sense and professionalism, and sundry other attributes.
Inside casinos, only the management is systematic, secure in the knowledge that mathematics, perhaps the most orderly discipline in the known universe, will smooth out minor fluctuations in player behavior and the ups and downs of fate and fortune and deliver a profit at the end of the day.
It comes down to this: a player who does not bet systematically will lose.
It may not happen today or tomorrow, but it will happen in time, as surely as 2+2-5 is a negative number.
And in spite of that undeniable truth, 99.99% of all gamblers will tell you that there is no system known to man that can beat the house advantage.
Here is a different look at the latest pencil log from my BST blackjack trial:
The big numbers in the BST screenshots should come as no surprise by now, and I have stopped providing breakdowns of each step along the way to a final win because by now the point should have been made.
What may surprise some of you is that throughout the session, losing series, defined here as recoveries achieved in spite of more bets lost than won, are in the majority.
It should not come as a shock, but too many people are inclined to assume that luck is the only factor that can make you a winner in a casino, and it simply is not so.
Since none of us can ever know ahead of time if the very next bet is going to win or lose, systematic betting is our only option.
Call it money management if you like - call it grzignflumpf, even - but however you may choose to gussy up or disguise it, a "system" is what is needed here.
Casinos know this and are constantly on the alert for players who do not bet (and lose) the way they are "supposed to."
Table limits are one way to reign in players who may have the means and the inclination to "bet the farm" in the midst of a punishing losing streak and recover all their prior losses in a single bet.
Another is to come down hard on punters who are "foolish" enough to revert to the best known - and thanks to the gambling business, most reviled - system of them all, the double up, double down or the Martingale.
Unless we believe in luck, along with Santa Claus, the Tooth Fairy, and other invisible benefactors, we all know that over time we are going to lose more bets than we win.
It that were not so, there would be no casinos.
It therefore follows that the only way we can win in the end is to rake in more money from a smaller number of winning bets than we give up from a greater number of losing bets.
A Martingale does the job very well: -1, -2, -4, -8, +16 delivers a 1-unit or +3.2% win against a house advantage of -3/5 = 60%, average win 16u, average loss 4u.
A Martingale also happens to be unplayable in a casino, except by professionals who spend their time in motion, losing no more than three bets in any one location before moving on in search of the single win that will give them a profit.
They find themselves out on the sidewalk from time to time, but they don't care: there is always another casino just a few steps away.
Nor do they care that "the math" is apparently against them: they are grateful that all but a tiny percentage of gamblers believe that to be so, leaving the field open to them.
Consider an opening bet of $5 and a relatively modest baccarat table limit of $15,000 (the current green ceiling at Harrahs Stateline), then the fact that 12 consecutive losses will be needed before the next bet in the progression ($20,480) will be unplayable.
Now think about the odds against 12 consecutive losses: roughly 0.002% or 2% of 1% or 1 in 4,016.
Next, consider that if our "Martingaler" places and wins a $15,000 bet at baccarat, he is $5,480 "in the hole."
End of story? Of course not! His chances of winning that first $15,000 bet are a little less than 50-50 (49.3 to 50.7), meaning that he will probably lose. But what he now has to ask himself is how likely it is that he can get just two bets ahead of the house ($30,000 less $10,240) after falling 12 bets behind.
Thanks to the house advantage, a force that pulls both ways, those chances are better than good.
The so-called Gambler's Fallacy is the assumption that because an inordinate number of bets have been lost, a win is somehow more probable at this moment than it would be otherwise.
When applied to individual bets, the delusion is well-named as a fallacious disregard of the negative odds that apply equally to every bet, regardless of what went before.
But our Martingaler has just lost 12 bets in a row, then won a single wager, indicating a house advantage for the sequence of -11/13 = 85%.
The known house edge for baccarat is about 1.4%, so how "probable" is it that the house will stay 11 bets ahead indefinitely?
Not very.
It is at this point that a large bankroll becomes essential to the task of eliminating the negative effects of the house advantage.
I have had many a mathematician scold me with a reminder that in theory, an egregious imbalance like the example above need never be offset sufficiently to enable a progressive bettor to recover his losses.
But I have yet to be provided with a real-play example of the house edge running amok without eventually returning to compliance with negative expectation for the game.
There is a good reason for that: It can't happen.
It can take a while, but the house edge cannot stay at 85% (or even close) forever. Remember, we are not betting the farm on a complete counter-swing of the pendulum, just one or two wins.
Mythematicians love to trot out runaway sims to "prove" their specious prophecies, so it seems fair that I offer one of my own, an Excel RNG that signals HELP! when the house edge exceeds 50% and SAVED! when paired wins occur.
For a Martingaler who is betting below his green ceiling, a single win is enough to recover prior losses. For a target player, it sometimes (about a third of the time) takes TWO, otherwise one is all that is needed.
Ask me nicely, and I will send you the file. Meantime, here are a couple of out-takes, and the formulas are at the bottom of this post.
Mythematicians, the guys who will defend the power of the house advantage no matter what, concern themselves with what is possible rather than what is probable, arguing that if a given betting method can fail even once in 50,000 bets, it should not be trusted at all.
In casinos, all manner of wondrous outcomes are possible, but not probable, and the probable outweighs the possible by a percentage just great enough to hand the house a profit at game over.
For example, a royal flush is possible on a $5 video poker machine, paying out $20,000 and making the lucky winner very happy.
But on average, at least $21,500 will have to be fed into the machine for every $20,000 paid out, making the house even happier.
And more than 98% of the people who play that machine between jackpots will take out considerably less money than they "contributed."
The HELP! SAVED! file is no more representative of an actual game of baccarat than any other runaway sim, but it serves to illustrate the important difference between what's possible and what is probable.
Once in a great while, a serious threat to the bankroll will emerge. But the greater likelihood is that by then, so much money will have been won that the potential damage from the exposure has been reduced or eliminated.
The sim features a Martingale rather than target betting as I prescribe it, but it confirms that if only paranoid pit personnel would permit double-up to be played, even that simple strategy will consistently overturn the house advantage.
Any pit boss you talk to will confirm that progressive betting of any kind, and the Martingale in particular, cannot possibly win in the long run.
But if your response to that is, "OK, then you won't mind if I give it a try," you will quickly learn that what he says is not what he believes.
The standard retort to any defense of a progression is that it risks too much to win too little, a nonsense criticism that would be meaningful only if it did not apply at least as much to every other method of betting, and to the house's exposure, too.
Think about it: the house permits players to bet whatever they want within the limits discussed earlier, anticipating a "hold" that can be less than 2% of total action.
In truth, the house's share of the churn is much higher than the predicted edge for table games, ranging from 1% at blackjack to 5.26% at roulette, but that's because most players bet as if they want to lose.
A player who can walk away with his bankroll intact, plus 2% of his action, does not have a whole lot to complain about - but systems "debunkers" pretend otherwise in defense of an agenda that is never clear.
The Martingale can be said to win "just $5" when a losing streak finally ends with a turnaround win, but it doesn't: It wins all prior losses PLUS $5.
If you are tempted to venture a Martingale, I recommend varying it a little to boost the bottom line: 5, 10, 20, 50, 100, 200 500, 1000, 2000, 5000 and so on.
But do not get too attached to this approach. You will not be allowed to play it for long!
I have been relentlessly scrutinized and harassed over the years, more often than not with a charm that is skin-deep, and that hardly makes sense from an industry that claims to welcome progressive betting.
Before Caesars Tahoe banned me from its blackjack tables (unaware that target betting works almost as well at baccarat, craps and roulette, among other games) my wife and I were invited to a dinner show.
We had been seated barely five minutes when the Maitre D' brought another couple to our booth, explaining that the show was fully-booked and since we had been comped, our help would be appreciated. It was a large booth, so why not?
Almost before he had settled in his seat, our new table-mate introduced himself as "Tony" and boasted that he and his wife were there because of the huge sums he bet at baccarat in the casino's salle privee.
He was, he said, a high roller.
"So, what system do you use?" he asked, with no further preamble. "Mine is really simple: After I win, I bet five chips, after I lose I bet one, and because I never bet less than $500, I am happy if I get only one chip ahead per shoe."
I replied that I preferred blackjack to baccarat, and that I did not have a system - I was just lucky, I guess.
The same question was asked repeatedly - gently, but firmly - through dinner and the show that followed, and my answer was always the same.
Why on earth would a player with a "winning system" be interested in how someone else stayed ahead of the game?
He wouldn't, of course.
But the house would want to know.
For the record, Tony's "system" is a total disaster. Target betting is not.
Here are the primary cell conditionals for the HELP/SAVED simulation:
(A1)=IF(RAND()<=0.49,1,-1)
(B1)=+A1
(C1)=+B1
(D1)=+B1/C1
(E1)=IF(AND(D1>=50%,C1>=10),"HELP!","")
(F2)=IF(AND(B2<0,A2>0,A1>0),"SAVED!","")
(G1)=IF(AND(G1<0,H1<0),A2*MIN(15000,ABS(G1)*2),A2*5)
(H2)=IF(H1<0,G2+H1,G2)
(I2)=IF(AND(H1<0,H2>0),1,"")
That will get you started with a DIY version of my sim.
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.
_ale
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