Why Casino Craps Can’t Be Beaten

[Editor’s Note: The following in-depth treatment of dice setting in craps is written by the author of Blackjack for Blood, one of the all-time classic how-to blackjack books, still relevant and popular more than 30 years since it was first published. Bryce Carlson is one of the most successful pro blackjack players active in the game today and in this post, he focuses his keen attention on the controversy of controlling the outcome of tossing dice on the crap table.]

Blackjack, especially winning blackjack, is a game for introverts — a little OCD and a touch of Asperger’s wouldn’t hurt, either. It just takes a special person to sit at the tables for endless hours, counting down the game, all the while mesmerized by the circus of whirling cards and dancing chips. Yeah, it takes a special person, and it’s not for everyone.

So, it’s not surprising that many people prefer craps. The variety of bets, the boisterous comradery, the sense of team success when a point is made, and the shared commiseration when the shooter 7s out, all make for a really fun game. The problem is they can also make for a really expensive game, too. This problem has led many researchers — some legit, some not — to try to develop winning strategies for craps based on dice control, just as researchers have developed winning strategies for blackjack based on card counting.

Now, all this research has resulted in a number of supposedly winning craps systems that are sold in books and videos, and in pricey weekend seminars available wherever casino craps is played. But do any of these systems actually work? Well — spoiler alert — the answer is no, they don’t.

But why? Why don’t they work? They all involve setting the dice in special ways, then throwing them in a specific, practiced toss that, if done correctly, should definitely yield an edge for the shooter. So, what’s the problem? The problem, as revealed by slow-motion videos of dice “pros” in action, is that the inevitable slightly uneven release of the dice that occurs with every toss, compounded by contact with the back-wall pyramids, cause the dice to chaotically twist and spin to such a degree that randomness cannot be overcome, even with the most practiced throw. The precision necessary is way beyond any human capability, and the required contact with the back-wall pyramids ensures a random result. So, there you have it, and if you’re willing to take my word for it, you can now set this article aside and head back to the blackjack tables. But if it’s proof you want, and if you’re willing to dive deep, then take a deep breath and read on …

If only Isaac Newton had been right, if only he’d been right, then maybe, just maybe, there might really be such a thing as Advantage Play casino craps. But he wasn’t, and there isn’t. And therein lies a fascinating tale that is worth a little trip down history lane.

For, you see, at its core, the potential to beat craps comes down to the nature of kinetic energy. But Newton didn’t believe in energy, kinetic or otherwise. For him there was no such thing! For Newton, there was mass and there was motion. And that was it. Newton knew that unless acted upon by an outside force bodies in motion stayed in motion, and bodies at rest stayed at rest. So, Newton reasoned that when an outside force acted on a body at rest to create motion it had to impart an “impetus” to the body which overcame the body’s inherent inertia. This force imparted an impetus, P, sufficient to move a mass, m, to a velocity, v. Hence, the impetus (now called “momentum”) must be equal to the product of the mass times the velocity, or P = mv. And that was all there was to it. But Newton, perhaps the greatest genius of all time, had a bitter rival of almost equal genius. His name was Gottfried Leibniz. And Leibniz had a different idea. He thought there was more to motion than momentum. He said there was also a “vis viva” or “life force,” proportional to the square of the velocity, that a mass acquires when it’s accelerated to a given velocity with respect to another inertial frame. Newton countered by mocking the whole idea of a putative so-called “life force” as superstitious nonsense, and sarcastically asked Leibniz if perhaps the laying on of hands were necessary to impart this special force to masses, and, if so, did it come by the power of God or perhaps Beelzebub. Leibniz replied that, like everything else, it came by the power of God, and if Newton doubted that perhaps he should take it up with the Pope, or maybe the Archbishop of Canterbury. Oops. Touché Leibniz. And so back and forth it went, year after year, such that during their lifetimes this bitter little tête-à-tête remained unabated, undecided and unresolved — just one more schlong slam in a long list of schlong slams by two of the greatest minds and brittlest egos in the entire history of great minds and brittle egos.

And then, in 1738, several years after both Newton and Leibniz had died, along came a rather comely young minx by the name of Mme Gabrielle Émilie du Châtelet. Now, Mme du Châtelet, who happened to be the wife of the Marquis du Châtelet, was not only a libertine deluxe of impressive imagination, but she was also the mistress of Voltaire, several of his friends, and a gifted young woman who somehow amid all the frolicking found time to be an accomplished natural philosopher, as well. This was definitely not your everyday wench, royalty or not. Now, Mme du Châtelet was a keen student of both Leibniz and Newton (in fact her French translation of Newton’s Principia is still the standard), and she marveled that this dispute regarding the fundamental nature of masses in motion had gone on for decades without a resolution. So, she decided to set up an experiment to settle the matter once and for all. She reasoned that in an inelastic collision of a rigid undeformable mass with a non-rigid deformable one all of Newton’s momentum or Leibniz’s vis viva would be absorbed by the deformable mass, and the degree of deformation would determine who was right. So she set up a simple but elegant experiment in which a small iron cannonball was dropped from a height of several feet into a bucket of potter’s clay and the depth of the depression left by the ball was measured. Then, using Newton’s gravity equations, she dropped the ball from a greater height, such that the velocity at impact was calculated to be exactly twice the velocity of the first drop, and, again, measured the depth of the depression left by the ball. She then reasoned that since Newton’s “impetus” was linear (mv) and Leibniz’s “vis viva” was exponential (mv^2), if the second depression were twice as deep as the first one, then Newton was right. But, if the second depression were four times as deep as the first one, then Leibniz would be right. So, she performed the experiment and measured the results and, voilà, the second depression was, indeed, four times as deep as the first one. Leibniz had been right all along. Poor Leibniz, he had waited a lifetime to beat Newton at something important, and when he finally did he wasn’t alive to enjoy it. Sometimes, the gods really do have a twisted sense of humor. Anyway, today we call Leibniz’s vis viva “kinetic energy,” and we describe it by the equation E = (1/2)mv^2. Leibniz would be proud.

Okay, so why is it so important that Newton was wrong and Leibniz was right? It’s important because it says that a small change in velocity results in a large change in kinetic energy, which means that when, say, two dice are thrown simultaneously with only a small difference in initial velocity, the differences in their behavior at impact will be large. Very large. Processes in nature tend to either damp or amp as they propagate through space and time. In those that damp, small differences in initial conditions (the Δ of the initial complex Lagrangians) become even smaller over time. But in those that amp, small differences in initial conditions grow large over time. And because kinetic energy is an exponential function of the square of velocity, tossing dice at craps is an amping process, whereby small differences in initial conditions result in large chaotic differences in the final results.

Now, over the last five years, a number of serious, legitimate researchers, including Stanford Wong, myself, and others, have sought to determine the truth about so-called AP craps. Some of these researchers have hoped to show that craps could be beaten, and some have just been intellectually curious. But, regardless of motive, all of them have diligently searched for the truth. Now, because simulations of precision shooting at casino craps are not feasible, these researchers have generally utilized carefully monitored casino sessions of statistically significant duration with recognized “professional” p-shooters, as well as slow-motion videos of such experts throwing the dice on regulation craps tables, to obtain valid useful data. The results of such studies have been telling. Virtually without exception, with the monitored “professional” p-shooters the larger the number of trials the more random the results appear, with each die face (and the 7s to rolls ratio) converging on a random frequency of 1 in 6. And with the slow-motion videos, it is obvious to everyone viewing them that, no matter how good the throw might look at normal speed, in slow motion it is apparent that a huge amount of uncontrollable randomizing occurs. In fact, in February, 2009, Wong stated in a post on the bj21.com craps page, in referring to the results of slow-motion video studies of skillful throws, “The truth is, there is much bouncing around, even in dice tosses that look great at real-time speed. Watching slow-mo video of dice tosses can be discouraging, and can be harmful to sales of dice books and to sales of dice-tossing instruction.” No one viewing such videos would ever disagree with that. So, while it is true that no one study is ever completely conclusive, over a five-year period the evidence has piled up as study after study by capable researchers has consistently pointed to only one conclusion: Real-world casino craps cannot be legitimately beaten — by anyone, anywhere, at any time. And the exponential, amping nature of kinetic energy is the fundamental reason why.

To see this more clearly consider this analogy: Suppose a world-class MLB pitcher were told to throw curve balls one after another such that each successive pair of curve balls must be thrown at the same speed to within a small fraction of a mile per hour, and have the same curving trajectory within a small fraction of an inch. No pitcher could ever do this, or would ever even want to, for that matter. It’s not humanly possible. But that is exactly the kind of control a p-shooter would have to have to have any chance of influencing the dice at all. And even if it were possible, which it isn’t, it STILL wouldn’t be enough! Why? Consider this: The theory of so-called AP craps is built on two plausible-sounding conjectures. The first one, promoted by Frank Scoblete and Golden Touch Craps, says that if the dice are set properly, thrown on axis with synchronicity, and just “kiss” the pyramid-studded back wall lightly after landing, it is possible to exert a sufficient degree of control of the dice to achieve a positive ev. We’ll call this the GTC conjecture. The second one, promoted by Wong, says that if the dice are set properly, and initially thrown on axis with synchronicity, even if they do hit the pyramid-studded back wall hard, a degree of “correlation” between the two dice can survive that is sufficient to achieve a positive ev. We’ll call this the Wong conjecture.

Let’s consider the GTC conjecture first. On the face of it, it sounds reasonable. It’s definitely a plausible-sounding conjecture. If the dice are set properly, and stay on axis with synchronicity right to the end, there is no question that sufficient control to achieve a positive ev would result. That’s why it’s so seductive. It sounds doable, if difficult. It sounds like all it takes is practice. But, as it turns out, it takes a hell of a lot more than that. Slow-motion studies of expert throws have repeatedly shown that even if the dice apparently remain on axis with synchronicity right down to the landing (something extraordinarily difficult to do), if the dice differ by even 0.25” in their rotational synchronicity at landing then, because of the exponential amping nature of kinetic energy, the combination of elastic (rebounding) and inelastic (skidding) collisions with the table will impart a huge amount of different rotations across the x, y, and z axes (pitch, roll, and yaw) between the two dice. Such tosses look great at normal speed, but in slow motion, even on a relatively “dead” table surface, their true random nature can be seen and measured. As with a pitcher trying to throw successive pairs of identical curve balls, the precision necessary to do it with dice is beyond human capability. Period. And that’s not even counting the pyramid-studded back wall! When you factor in the pyramids, the whole concept becomes laughable.

Now, let’s take a look at the last best hope for AP casino craps, namely, the Wong conjecture. Wong is a bright fellow, and he recognized from his early dice studies that maintaining on-axis synchronicity was a pipe dream. So, still hopeful that craps could be beaten, he developed a more sophisticated theory that posits that, although the dice do not remain on axis with synchronicity after contact with the table and back-wall pyramids, there is a surviving correlation between the two dice’s rotations that can potentially reduce double-pitch 7s resulting in a positive ev for the player. Specifically, Wong asserted that although the pyramids scramble pitch, roll and yaw such that the axis that each die finally assumes will be effectively randomized, a surviving correlation between the two dice may still remain because (1) the law of conservation of energy, (2) the assertion that both dice start off with the same initial kinetic energy, and (3) the assertion that translational kinetic energy is not preferentially converted into rotational kinetic energy mean the number of rotations the two dice undergo across their x, y, and z axes, respectively, will remain closely correlated. In Wong’s own words: “Ideally, the dice are still on axis and have equal speed and equal rotation when they hit the pyramids. The pyramids then randomize the axis of rotation of each die, and reduce the energy of each die approximately equally. As they leave the wall the dice have random and independent axes of rotation, but will rotate approximately the same number of times before coming to rest. Being approximately identical in position and motion when they hit the pyramids, and then rotating approximately the same number of times after hitting the pyramids, the end result should be a scarcity of double pitches.”

Now, for Wong’s double-pitch avoidance conjecture to be potentially valid, the correlated rotation assumption, above, is particularly important with respect to pitch. This is because if pitch between the two dice remains largely correlated (though not necessarily on axis), then, even though induced roll and yaw are effectively randomized (though still correlated), double pitches resulting in 7s should, as Wong asserts, occur less often than random.

Unfortunately, however, whatever its theoretical validity, in practice there are two fatal flaws with Wong’s conjecture. The first one is the fallacy that both dice start off synchronized with the same initial kinetic energy. They don’t. Numerous empirical studies have shown that there is always a slight difference in the initial velocities and axial alignments of the two dice and, as previously discussed, because of the exponential amping nature of kinetic energy, these small differences result in big differences in the final results. And secondly, and just as important, the assertion that pitch remains largely correlated during the toss because translational kinetic energy is either not converted into rotational kinetic energy, or, if it is, it is converted to the same degree in both dice, is manifestly false. This is easily verified when slow-motion videos of expert tosses on regulation craps tables are examined and analyzed. For example, one die, say, bounces up from the table and squarely hits the base of one of the pyramids and rebounds back with little to no conversion of translational kinetic energy into rotational kinetic energy; the other die, however, bounces up and hits another pyramid, say, a little off center or a little higher up from its base and a significant amount of translational kinetic energy gets converted into (primarily roll and yaw) rotational kinetic energy. Anyone watching slow-motion videos of expert throws knows that this kind of scenario occurs on virtually every toss, and when it does any surviving rotational correlation potentially reducing double-pitch 7s is lost to randomness because one die ends up with significantly less translational kinetic energy than the other die, which results in less pitch rotation (and more roll/yaw rotation and skidding) than the other die when it lands and rolls to a final random result.
So, with pitch, roll, yaw and rotational/translational kinetic energy effectively randomized by the table and the back-wall pyramids, the assumptions underpinning Wong’s correlation conjecture, just as with the GTC on-axis conjecture, do not stand up to either theoretical analysis or the empirical evidence, and, consequently, no surviving correlation between the two dice reducing double-pitch 7s can be assumed to survive a legal toss in real-world casino craps. And, again, extensive empirical studies over a five-year period back this conclusion up.

And finally, in April 2011, in a tacit admission that he had been wrong in believing casino craps could be legitimately beaten, Wong removed craps from the list of “Beatable Casino Games” on his popular bj21.com website, and also removed the “Craps” discussion page from his site, as well. In addition, a few months later, in October 2011, in an interview about craps on Bob Dancer’s popular KLAV radio program, “Gambling With an Edge,” Wong admitted that, instead of craps, “if you want to get serious about making money from casinos … get into blackjack or get into video poker or get into poker.” That pretty much says it all.

So, blame it on Leibniz, blame it on God, or blame it on the exponential amping nature of kinetic energy, but real-world casino craps cannot be beaten. Period. But, hey, cheer up, maybe in another universe, far, far away Newton was actually right ;-).

Now, compare this modern casino game to the primitive WWII-era “blanket-roll” game, where the consensus is that a highly-skilled virtuoso p-shooter could, indeed, potentially gain a winning edge. What is apparent in such a comparison is that the two things that prevent beating the modern casino game — namely, the exponential amping nature of kinetic energy, and the randomizing power of the back-wall pyramids — were absent or neutralized in the blanket-roll game. In the blanket-roll game there were no back-wall pyramids, and the soft, relatively high-friction army-style blanket was perfect for burning off kinetic energy very rapidly, thus effectively neutralizing kinetic energy’s amping nature. This makes for two very different games, one potentially beatable, and the other not. They say casinos are born at night, but clearly not last night, as they have very effectively eliminated the exploitable weaknesses in the primitive blanket-roll game.

Now, even though all this means that so-called AP casino craps is left without any credible operational theory or supporting evidence, whatsoever, justifying a belief in its validity, I know none of it is going to have the slightest effect on the so-called AP craps gurus. They’ll just keep on beatin’ the drums, pounding out that voodoo vibe for their faithful fans who are all too happy for a rationalization, any rationalization, to justify their inveterate gambling habits. And does any of it prove beyond a shadow of a doubt that casino craps can’t be beaten? No, it doesn’t. We’ll probably never have that kind of proof. But it does prove beyond a reasonable doubt that casino craps is unbeatable, and in an existential world that is enough for reasonable men. So, as for me, I’ll leave the snake oil to the snakes.