A Collection of Mathematical Gambling Systems
That Work at Home But Not in the Casinos


Frederick Lembeck


55 Bethune Street, #H-826
NY, NY 10014
(917) 406-6092


It won't hit you until you actually test first-hand one or both of the attached sample mathematical gambling systems, and realize they actually do work at home and on your desk, but not in any casino. (Trump haters will realize this is incriminating evidence and do cartwheels.)

The long-yearned-for hard evidence needed to expose the global casino industry's true criminal nature is at last at hand. (Can it be that Trump didn't make his billions from honest gaming but from swindling untold thousands of trusting, unsuspecting tourists with crooked gaming equipment? Not just him but all of the casino lords? This will now come out.)

But it won't hit you until you actually test first-hand one or both of the attached systems. Then you and G-d will walk together hand-in-hand, like friend with friend.

The author states loudly that he's NOT a Trump hater, he's merely a veteran police reporter doing a crime story. (See About The Author, below.) He's obviously no Trump fan but as far as the author is concerned the story is about the whole of the crooked casino industry worldwide, not just one particular casino owner. (If you own casino shares this would be the time to sell. Don't say no one warned you.)


2-3 months.


Initially the Trump haters, but as the worldwide public realizes it's true that the whole casino industry planet-wide actually is top-to-bottom crooked, interest will become global and gigantic. Some publisher somewhere is going to make money off this one. How nice it would be to have an agent who knows how to negotiate a proper advance.


There's some helluva history here.  Are The Casinos Crooked? began life in the late 1980's as Beat the House, which Al Hart of the Fox, Chase Agency sold to editor Wally Exman at Stein & Day.  Exman, speaking for Stein & Day, wouldn't allow Lembeck to say the casinos are crooked without proof, so he had to write the book not as evidence of casino dishonesty but merely as mathematical gambling systems that actually work.
Within eight weeks of the publicity flyers going out, innocent-sounding persons bought out Stein & Day.  But instead of merging it or consolidating it or spinning it off, or any of the usual things, they just shut it down -- blithely tossing the whole of their investment down the drain.  Stein & Day simply came to an end, taking Beat the House with it.
After several years of contemplation Lembeck decided to try again.  After Stein & Day ended Wally Exman became an agent.  He and Lembeck reconnected and Exman-as-agent sold Beat the House to editor Allan Wilson at Citadel Press.  Once again the editor, this time Wilson, wouldn't allow Lembeck to say the casinos are all crooked without proof, so once again Lembeck was forced to write the book not as evidence of casino dishonesty but merely as mathematical gambling systems that actually work.
Once again, shortly after the book was publicized, Citadel Press was bought out, this time by the respectable Kensington Publishing.  But instead of running the Citadel list they had just bought (and spent so much money on) Kensington simply dropped the whole of the Citadel Press list, including Beat the House.

Definitions of the world “paranoia” always include the word delusional.  For it to be paranoia it has to be delusional. But what if it's not delusional?  What if the casino lobby really is quietly derailing Lembeck's book?

In 2004, Lembeck made the decision to self-publish on Amazon.  Now if someone tried to buy the title out they'd have to buy it out from Lembeck himself.
In fact, the Amazon web page has been hacked to death a hundred times over.  If you go there you'll see the retail price of Beat the House, (the last time Lembeck checked, at least) was raised by hackers to over $900, an obviously absurd price.  The tampering is endless.  Sales of course have been obstructed.
- - - - - - - - - -

Lembeck now wants to recast the book entirely.  Instead of it being merely a collection of mathematical gambling systems which actually do work at home (but not in the casinos) he wants to find a fearless agent, editor and publisher (probably Trump haters, but Lembeck is indifferent to that) who will at last allow him to ask the question he's been forbidden to ask all these years:  Are The Casinos Crooked?

He's looking for an agent, editor and publisher with guts.  Honest people who want to blow the whistle on the entire global casino industry and expose its dishonesty before the whole human race.

But if it should turn out that Trump really did make his billions not from honest gaming but from swindling unsuspecting casino patrons with crooked equipment, then this should be made known to the world at last and kept secret no longer.

Given the history of the casino lobby buying out any publisher before the book's content can ever reach the public mind, Lembeck is now viewing the book's advance as being probably the only money he'll ever see. So he wants enough to retire on.  He's old already.  If your guy won't pay it, someone else will. When the casino lobby tries to remove the book from existence by buying out the publisher for $100M above his firm's actual value he'll more than earn back the petty change  he advanced to Lembeck.  Welcome to the Modern Age.


Frederick Lembeck was a math prodigy.  Before he was in kindergarten he was already solving multi-digital arithmetic problems in his head, dazzling the adults around him.  The systems in this book speak plainly enough about his math ability.  They're all modifications of traditional systems which normally didn't work in the casinos (they served only to improve the player's chances but never were able to overcome the built-in house edge) except that Lembeck figured out how to tweak them so that they do overcome the house edge, apparently the first person ever to do so.  (Except that in a real casino they still don't work, no matter how well they work at home.  Because the casinos are crooked.)

Lembeck began his journalism career as a police reporter (a job he loved) for The Observer, a small weekly in Oakland [Bergen County] New Jersey.  Because of his flair for writing he quickly became a Features Writer, and the excellence of his work earned him a place in New York's Westbeth Artists Community, where he still lives.  After relocating to New York he became a freelancer and once again his output brought an invitation, this time to join the world-renowned Overseas Press Club, where he got his first overseas assignment and where he remains a member to this day.  In addition to his anti-casino journalism he's currently at work on a screenplay, “Years of the Siege,” about a plot to overthrow Stalin, masterminded by the Leningrad General Staff during the city's 900-day Siege in the Second World War.  He lives in New York City, has never married and is an Air Force veteran. He has no opinions and likes everybody.


 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 


A Collection of Mathematical Gambling Systems
That Work at Home But Not in the Casinos

Chapter 1 – The Realization

The casinos are all crooked. Worldwide. This is a difficult realization for a lot of people. They see the towering, glittering casino and think to themselves, “C'mon, they wouldn't risk all this with a cheating scandal.” But in truth there's no risk at all. The casino lobby buys everyone and everything.

The people doing the actual swindling are the casino operating companies which the hotel owners hire to run their casinos. The hotel bosses don't try to operate the casinos themselves, they're hotel men, what do they know about running casinos? No, they hire a professional casino operating company and that's who's doing the swindling, the so-called “point holders,” the part-owners of the operating company. They're all in it together and they divide the profits together, to each according to how many points he holds.
Where in all this does Donald Trump fit in, you're wondering? It's unknown at the present time but it's expected that it'll come out if there's ever an honest investigation. Or maybe the casino lobby (read: casino gangsters) will just buy everyone off. Part of what should come out of any honest investigation will be the identities of all the crooked authorities and politicians, historically, who've been bought off already. It should be quite a list.
In any case, the truth is now in your hands, dear reader, mathematical gambling systems that work repeatedly and reliably on your dining room table but just plain never work in an actual casino. Don't waste serious money trying to make them work in a casino, you'll just get burned. If they let you win during that first visit when you're betting $1 bets it's only to sucker you into coming back later with $100 bets. (At which point you'll be skinned like a rabbit.)

They're crooks. The whole place is crooked. Just take a look at their faces. Some of the most polished phonies you'll ever see in your life.

Chapter 2 – Any Craps

This is probably not the place to get into a discussion of karma, since you're simply looking for a book of gambling systems that work, but if it's true that there are casinos out there using rigged tables, then the karmic implications are enormous. Could you imagine cheating the elderly out of their Social Security checks, what kind of entry that creates in the heavenly record books, not to mention luring emotionally-troubled compulsive gamblers into ever-deeper anguish and misery with trick tables. Could you imagine destroying a compulsive gambler's life like that, watching him deteriorate as he comes back again and again, and you all the while giving him a completely-phony warm welcome every time you see him, just for the sake of the money you can swindle him out of, knowing full well the whole time that somewhere back home probably an entire family is being destroyed by this person's emotional illness.

Can you imagine someone growing rich from such a thing? If ever there was such a thing as blood money, this would be it.

It's said that in Monte Carlo when a person commits suicide without any money in their pockets the police have orders to stuff some money in his pockets so people will think the victim killed himself because of world-weariness rather than gambling losses. Does hell have a pit deep enough for such tricksters? Is this how the Royal House of Monaco supports itself? How many suicides a year do Monte Carlo, Atlantic City and Las Vegas average?

The recent Las Vegas shooter, Stephen Paddock, killed more than fifty people so he could draw the world's attention to his suicide note which he photographed and posted online. But the world never got to read the note because the Las Vegas Sheriff's Office seized it then said there was no suicide note. This is the caliber of the vermin that enforce the law in Las Vegas. No better than Monte Carlo. This is why the casinos don't have to worry about a cheating scandal, because the so-called police and so-called Casino Control Commissions are as crooked as the casino operators. Everybody getting greased. Everybody, everybody, everybody. Once again, welcome to the Modern Age.
If there really is a G-d then the names of the slimeballs will finally become known someday. It'll have been worth the wait.

The compulsive gamblers would certainly be the most pitiful victims of a crooked casino, but they would probably be a relative minority. Probably most of the people victimized by such a house would be ordinary naïve citizens, honest people would would not know they'd been swindled until they heard about the scam years later. Even then it's likely some would not believe it was them but think it must apply to someone else.

- - - - - - - - - - - - - - -

Any Craps is the fastest of the systems in this book because you get a fresh bet with each new roll of the dice. No mathematical gambling system could ever be faster than this. It's also some hell of a moneymaker, as you'll see shortly. But only at home. Never in a casino.

The system is most easily demonstrated on the Any Craps bet in the center of the craps layout, found in any casino, but it can be played on any 7 to 1 bet anywhere.


When you bet Any Craps you’re betting on the shooter to throw a 2, 3 or 12 in the next roll of the dice. Mathematically it’s a true 8 to 1, paying 7 to 1. This means the house is cutting itself out a HUGE edge, better than 10%. But it doesn't matter. You can still beat them, at home at least. Math is all po
werful. Math is what tells the earth how to orbit the sun.

Your opening bet is the house minimum, whatever it is, usually just $1. Place your bet on one of the C's in the center of the craps layout, Figure 1, above. (At home use nickels, dimes and pennies for chips.)

1 - Any time you lose, you increase the bet by $1.
2 - Any time you win, you decrease the bet by $10.


So simple. Have a look.

Bet # Amount Decision Total Out Total In Profit
1 $1 L $1 -$1
2 2 L 3 -3
3 3 L 6 -6
4 4 L 10 -10
5 5 L 15 -15
6 6 L 21 -21
7 7 L 28 -28
8 8 W 36 $64 28
9 1 W 37 72 35
10 1 L 38 34
11 2 L 40 32
12 3 L 43 29
13 4 W 47 104 57
14 1 L 48 56
15 2 L 50 54
16 3 L 53 51
17 4 L 57 47
18 5 L 62 42
19 6 L 68 36
20 7 L 75 29
21 8 L 83 21
22 9 L 92 12
23 10 L 102 2
24 11 L 113 -9
25 12 L 125 -21
26 13 L 138 -34
27 14 L 152 -48
28 15 L 167 -63
29 16 W 183 282 49
30 6 L 189 43
31 7 L 196 36
32 8 L 204 28
33 9 W 213 304 91
34 1 L 214 90
35 2 L 216 88
36 3 L 219 85
37 4 L 223 81
38 5 L 228 76
39 6 L 234 70
40 7 L 241 63
41 8 L 249 55
42 9 L 258 46
43 10 L 268 36
44 11 L 279 25
45 12 W 291 400 98
46 2 L 293 96
47 3 L 296 99
48 4 L 300 95
49 5 L 305 90
50 6 L 311 84
51 7 W 318 456 $126

Simple indeed. But it works only at home, never in a casino. The crooks aren't going to let you walk off with their money. You can kiss that idea goodbye before you even get on the bus.

Why correct by $10 instead of $9 or $11 or some other number? Since the game gives the house a mathematical edge, WHICH IT GENUINELY DOES, you have to counter with a slick mathematical correction to overcome the house edge. This is actually quite easy. If you don't know math don't worry, I do.

The correction for all long shots is to decrease the bet after each win by the true odds, in this case 8, plus 2 extra to create a solid, reliable drift downward in your betting amounts. Since 8 + 2 = 10, the correction after each win in Any Craps is $10.
If the true odds were 10 to 1 the correction would be $12. If the true odds were 15 to 1 the correction would be $17, etc. On your kitchen table the demonstration will quickly soak up the whole of the House's capital. In the casino it’ll be the exact opposite, you won't win so much as bus fare home.

Why? Partly because of the wretchedness of the human state, no doubt, but mainly because the casinos are crooked. Every table in every house in every country in the world – crooked! The time has come to blow the whistle. If Trump is in on it then Trump fans better brace themselves.

Your homework is to play an hour's worth of very quick Any Craps progressions (and they will be quick, you'll see) just to see what kind of money you can rack up in an hour's time.

Once again, don't set limits in your test game. Since it's only for practice, run the progression all the way up to $100 or more if need be.

What will impress you this, even more than the amount you make, is the speed with which you make it. When you get done, pause and reflect that you made it all in a single hour. If only the casinos were honest how rich we could all be.

Chapter 3 – Half Peak

I first became interested in mathematical gambling systems when I read a magazine article on the subject and began to wonder if it might be possible to supplement my own modest income as a freelance writer with a little bit extra from the casinos. In particular, the article mentioned a system called D'Alembert, which fascinated me so thoroughly that I actually got on a bus to Atlantic City to try it out, my first time in a casino ever. It turned out I won $300 that first night playing D'Alembert, just by simple-mindedly standing at a craps table betting Don't Pass over and over again, but it was an experience I was never able to duplicate. In hindsight, knowing what I know now, I speculate the pit boss may have sized me up as a newcomer to mathematical gambling systems and tipped off the boxman to let me win a few hundred in the hopes that I'd figure I'd stumbled onto something and come back a week later with larger bills instead of singles. I wasn't as rich as I looked though, which saved me from being victimized. Playing a 50-50 bet I should have won at D'Alembert roughly 50 percent of the time. When you try it yourself, in a real casino, you'll see it doesn't work out that way.
That first night was the beginning of a journey that led to this book, but not in a straight line by any means. Only two nights later I lost the $300 playing D'Alembert again. It seemed to me at the time that I had hit a run of bad luck. Indeed, to all outward appearances, that was exactly what happened. My downfall, I thought, was a mere lack of capital. All I needed was enough to ride out the bad losing streaks and I'd be all set. After losing a couple hundred dollars more, this time my own money, I had to stop. I couldn't afford such losses. Freelance writers are as poor as mice.

Now I am one of these people who happens to believe there's an invisible God looking in on human affairs and even getting involved much of the time, so in my case I even went so far as to imagine my bad luck might be the Lord God Almighty Himself speaking through events, telling me to back off here, something's wrong. And so I did. He'd been telling me a lot of things all along the way but it wasn't until I'd felt a little pain that I was ready to listen. What He plainly was saying now was that He wasn't on my side in this one and that I should stay away from the casinos. It was not clear why. It seemed to me that if I had figured out a way to beat the house I should be allowed to profit from it. The Almighty, however, disagreed and only now do I understand why: I would profit from it all in good time, but evidently more important by far (from His point of view) was that the story be told, that the casino criminals' treachery be laid bare. This is something that might not have happened if I'd been allowed to milk the system quietly for millions.
From the safety and comfort of my New York City home, far from the perils and temptations of Atlantic City, I contemplated D'Alembert. It dawned on me then how similar it was to the price surfing that stock traders utilize and grow rich on. It was plain enough to me that the underlying principle had to have some kind of potential, butI couldn't understand why it should work on the stock exchanges, yet not in the casinos. Time and again I was averaging three losses for every two wins on a bet that should have been very nearly one to one. What a trusting soul I was.

Early in my search I discovered drift, a mathematical phenomenon that stems from the fact that losing streaks are always going to be a tiny bit longer than winning streaks, even at an honest table (as if there is such a thing), because the house always wins a tiny bit more often than you do. That in turn causes the amounts of your bets to drift ever higher, thus the term drift. I decided drift was the problem and conceived the Half Peak mechanism to compensate for it. (You just close out your progression at half your peak when a run of good luck carries you that far back down the scale, that's all, then start all over again with a brand new game all the way back down at your original starting point again.) But even Half Peak didn't work. It worked on paper and it worked on the kitchen table but it didn't work in the casinos and the reason was always the same: killer losing streaks that never even gave the Half Peak mechanism a chance to work.

I couldn't figure out what the problem was and once again I lacked the money to continue. A lucky thing for me. In the meantime my study of craps (and then roulette) led me to figure out other systems as well, such as Baby Hardways, Any Craps, Daddy Hardways and others, above all, Free Odds. Once again, they all worked beautifully on paper and on the kitchen table, but not in the casinos, and the explanation was unfailingly the same: bad luck completely beyond what the laws of probability would have predicted, or even believed possible.

I turned to more research. Deeper research. I had done research before but this time I was serious. I went to the New York Public Library, a holy place, and began digging into the major source material in the field. In particular I discovered John Scarne, now deceased, alas, the greatest gambling authority America has ever produced, and there in the back of his masterpiece Scarne's Guide to Casino Gambling, I found a chapter on rigged tables, spelling out the whole technology.

It was a revelation. It was from this that I realized there was a genuine possibility there might be rigged tables out there.

It was Scarne who taught me about the hitters and missers at craps, dice that always roll seven when the electromagnet is pressed and dice that never roll seven when the electromagnet is pressed. Scarne taught me how roulette wheels could be rigged, how blackjack and baccarat shoes could be fixed, and all the rest.

Simultaneously I bean to learn about how ownership is structured at the casino operating companies, that nobody gets to be a boxman (the guy in the tuxedo who runs the game) without being a point holder (part owner) of the casino operating company. The boxman isn't the same as the dealer, mind you. The dealer is a mere employee of the operating company, not a part owner. It's the boxman who pushes the electromagnet button, not the dealer.

Later, I read Bernard Baruch's autobiography and learned about his days in the Colorado silver rush as a young man, how he spotted a crooked roulette wheel in one of the casinos, of his subsequent run-in with the proprietors when he tried to make a little money by always betting the exact opposite of the way the big money was betting. It was Baruch's account that awoke me to the depth of the tradition of crooked gambling equipment in not just America's but the whole world's gaming industry, and my realization that not just sleazy houses but even some of the swanky carpet joints might be crooked. How would you know? How would you even suspect, without coming in with systems that work so well at home? Princess Grace was supposedly such a class act. How could her casino be crooked?

Later still, I was invited to a neighbor's cookout where I met another guest who told me he once was a bodyguard for one of the big-shot casino executives in Atlantic City, and when he heard the speculation I was entertaining, he told me it was true! In the casino where he worked, he said, underhanded business was in play, in addition to wired tables, but he refused to specify more than wired tables. He even tipped me off that activation can now be done by remote control, like a TV. Soon it'll be, “Alexa, sucker this fish big time.”

Was he right? Was this a reliable witness? What value should I assign to this man's information?

From this realization that crooked gaming might be rampant in the world came the realization that a book should address the matter. Had I been an ordinary fish I'd have just swallowed the losses and move on. But as a journalist I realized all this was a story. In the end I decided to tell the story exactly as it happened and then present the systems for the reader to try, to see for himself if they work or not. You'll discover they generally do, although even on your kitchen table you'll have losing streaks. Then you'll try them in a casino and discover they generally don't. You'll hit bad luck far outside the laws of probability. Maybe someday an aroused public will force a full congressional investigation. It'll depend on what the man on TV tells them to think. (They don't need G-d, they have the man on TV. The only reason G-d had to settle for being G-d is because He didn't have enough pull to get to be the man on TV. Man, ain't you woke?)


The System Itself

Half Peak is actually nothing more than D'Alembert with a single, very helpful modification added: the half-peak mechanism. The bets for playing Half Peak at craps, if you're curious to try, are called the “Pass Line” and the “Don't Pass Line.' You can see them in Figure 2, The Craps Layout.


They're the pair of parallel stripes running along the length of both sides of the green felt and curving up both ends of the table. They're the even-money bets, the ones you play Half Peak with. If you place your chips on the Pass Line you're betting on the shooter to win. If you place your chips on the Don't Pass Line you're betting on him to lose. Either way it's a 1 to 1 payoff. If, for example, you bet $5 and win the dealer gives you back your $5 plus $5 from the house. If you lose the house keeps your $5. That's all. (The actual rules of craps, for as much difference as it makes, are as as follows: a first throw of 7 or 11 wins, a first throw of 2, 3 or 12 loses, and a first throw of 4, 5, 6, 8, 9 or 10 can be won only by repeating the number before a seven appears.

Except that it's rigged. The boxman will switch on an electromagnet that makes the dice roll a 7 (or never roll a seven). Sorry, Fish, that's what you get for trusting a casino.
Half Peak works on any 1 to 1 bet, including Roulette, Baccarat and anything else. Not that it'll do you a lick of good, given that the casinos are all crooked.

The Half Peak formula is a pearl of simplicity: every time you win, you decrease your bet by one unit; every time you lose, you increase your bet by one unit. You start anywhere. Pick a number you think is lucky, say 11, and make that your opening bet. If the first bet wins, the second bet is 10. If the first bet loses, the second bet is 12. Then just repeat the process over and over again to infinity.

Consider what happens with every pair of wins and losses. If you bet 11 and lose, then bet 12 and win, you've shelled out 11 + 12 = 23 but taken in 2 x 12 = 24, a profit of exactly one unit. Likewise if you win the first bet, then lose the second, you've rolled out 11 + 10 = 21, but of course you won 2 x 11 = 22 on the first bet, so again the profit is exactly one unit. That's where the system's profitability comes from. Every pair of wins and losses generates exactly one unit. It doesn't matter if the pair is 11 and 12, 48 and 49, or 16,380 and 16,381, they all generate the same one unit.

The idea behind Half Peak is that if you place three hundred bets a night (about 3-4 hours worth in the case of craps, the fastest game), and they work out to be about a 50-50 split between wins and losses (which they generally will be over the long-term average), then you've won $150. And that's with $1 betting units. What happens if you switch to $10 betting units, or $100 betting units? Nor does it matter if the wins and losses alternate or if you get long runs of one or the other. It all works out the same. The only requirement is that the wins and losses average out roughly 50-50, which they inevitably do over a long enough period of time, on your kitchen table at least.
Let's take a look at an example.



Bet # Amount Decision Total Out Total In Profit
1 $11 L $11 -$11
2 12 L 23 -23
3 13 L 36 -36
4 14 W 50 $28 -22
5 13 L 63 -35
6 14 L 77 -49
7 15 W 92 58 -34
8 14 W 106 86 -20
9 13 L 119 -33
10 14 W 133 114 -19
11 13 W 146 140 -6
12 12 L 158 -18
13 13 W 171 166 -5
14 12 W 183 190 $7
(15) (11)

Table 2 is an account of an actual game of D'Alembert I played in one of the carpet joints in Atlantic City. I started with a bet of $11 and immediately hit a losing streak, losing five of my first six bets. At its worst I was $49 in the hole, and yet look what happened. Out of fourteen bets overall I won seven, lost seven and ended up with a net profit of precisely $7, or one half-unit per bet. I won and lost the same number of bets, yet ended up with a clear solid profit. Moreover, it would all have worked out exactly the same even if the wins and losses had all been reversed. Look at Table 3 please, a mirror image of Table 2 and see how it all works out the same.



Bet # Amount Decision Total Out Total In Profit
1 $11 W $11 $22 $11
2 10 W 21 42 21
3 9 W 30 60 30
4 8 L 38 22
5 9 W 47 78 31
6 8 W 55 94 39
7 7 L 62 32
8 8 L 70 24
9 9 W 79 112 33
10 8 L 87 25
11 9 L 96 16
12 10 W 106 $132 26
13 9 L 115 17
14 $10 L $125 $7
(15) (11)

This is a purely hypothetical D'Alembert game, exactly the opposite of the real-life game in Table 2, devised purely to illustrate that I would have won exactly the same $7 even if I had lost all the bets I actually won and won all the bets I actually lost. If you look at it as a balance sheet then Table 3 seems to be a more successful game that Table 2 because the severe losing streak at the beginning of Table 2 becomes a fabulous winning streak at the beginning of Table 3. And yet they both finish the same, with a profit of one-half unit per bet.

D'Alembert looks like a great system up close and it certainly is one of the best of the traditional systems, but unfortunately it has a serious problem called drift, an honest mathematical phenomenon that stems from the fact that over the long run the house is always going to win a tiny bit more often than you. In this case, it has nothing to do with a crooked house cheating you. Drift will happen even on your kitchen table. It's just in the nature of any game where the house has that built-in mathematical edge.

According to probability theory a casino wins 507 out of every 1000 bets and you win 493, on average. This in itself would be no problem: the one unit profit from every two bets can easily cover the cost of these 14 losses in a hypothetical run of 1,000 bets which produces a hypothetical $500 of profit. But because the house always wins a tiny bit more often than you do, even on your kitchen table, your losing streaks are always going to be a tiny bit longer than your winning streaks, which means the amounts of your bets will tend inevitably to get higher and higher as the tide of luck ebbs and flows. Thus if you were to open a game of D'Alembert with a bet of 50 units, in the first hour your bets might work their way up and down to, say, a high of 60 and a low of 40, but in the second hour they would have a disturbing tendency to be something more like 64 and 44. And in the third hour they could be even higher than that. After a while you'd find your bets averaging up around a hundred or so, and fifty would be a number you'd be lucky to see, if ever.

Obviously your progression has to have some way to correct for drift or you'll find yourself betting hundreds of units on every bet and see all your profits absorbed in financing these enormous bets.

The way to correct is to end your D'Alembert progression at Half your Peak when a winning streak finally carries you that far back down the scale, then start all over again with a brand-new game all the way back at the original starting number.

Now as a practical matter you aren't going to open a game of Half Peak with a bet of $50 because a hairy losing streak early on could send your bets up to $80 or $90 very quickly and soak up thousands of dollars of your capital, and you would have no guarantee that another hairy losing streak wasn't just around the corner. Double whammies like that could clean out the Emir of Kuwait, and these things do happen. In real life it's irrelevant because the casinos are all crooked anyway, but for demonstration purposes, don't start with too high a bet.

So you begin your game of Half Peak on a bet of $10. By and by drift will carry your progression up to a peak which is more than double your opening bet of $10. If you're lucky enough to work your way back down to half that peak, whatever it is, you quit and start a new game at $10.
For example, if you work your way up to a peak of $30, then half peak is $15; you quit as soon as you work your way back down to $15 and no further – game over, victory claimed. Then you start a fresh game at $10. You've corrected for drift by jumping $5 down the scale, from $15 to $10, a minor loss that you cheerfully accept as part of the cost of doing business, know it has saved you from the mathematical gangrene of drift.
Whatever your peak turns out to be, you quit as soon as you work your way back down to half of it. Even if bad luck carries your progression as high as $50, you quit as soon as you get back down to $25, then start a fresh game at $10. But you should get back down to half peak again sooner of later. Not in a casino of course, only on your kitchen table.
And that's it. That's how Half Peak is played. And it works. Does it ever. You're not gonna believe it even after you've seen it with your own eyes. Just don't be such an idiot as to think it's going to work in a casino.

Here's your fun homework assignment for this chapter, not only easy but lots of pleasure as well: get yourself a pocketful of quarters, dimes, nickels and pennies and play a game of Half Peak on your kitchen table just to see for yourself how the system works out. You could use any 1 to 1 bet. Use pennies to represent $1 chips, nickels to represent $5 chips, etc. Budget $50 for yourself and $50 for the house, to simulate $5000 capital each.

See who cleans out whom. See if the results are repeatable.

No you don't have to get together $100 in cash to run this test, just use IOU's. Your actual cash need here is probably no more than $3-5 worth of laundry change but please be accurate with the IOU's so that if by some miracle you should just happen to break the house, surprise surprise, you'll know you really did it.

This is a fundamental exercise. Its purpose is not so much to teach you Half Peak as to awaken you to the realization that the systems in this book actually do work.