## Blackjack Insider Newsletter, March 2005, #62Craps for Profit: The Math of Dice Control By Dan Pronovost
Can anyone make money playing Craps?! Some readers of "
Before I answer this question (in this, and a continuing series of upcoming articles), let me start by saying that this is a very controversial subject, and will raise the shackles of many 'experts' (maybe even you, fine reader!). But before you judge too quickly, please be fair, and read the analysis presented here, and to be continued in future newsletters. So… to answer this question (and lay down them fightin' words): Jumping ahead… These ongoing articles will be 'stand alone', meaning that you do not need to use or have the
Just download this exe, save it on your Windows computer, and run it. The software is shareware, which means you can try it out for free. The documentation is over 100 pages, including everything you need to know and covers basically everything we'll talk about in these articles. The Theory of Dice Control This is intended as a brief summary Dice setters attempt to control the physical throw of the dice in such a way as to influence the outcome of the dice. This skill, when used consciously at different points in the game, generates a non-random distribution of outcomes, which the shooter hopes reverses the casino's edge in the game to the player's favor. To understand the physics of dice control, let's look at an actual craps table: Figure 1: Axes of rotation on a craps table With these labels, we can see that a shooter will be throwing the dice along the
A typical controlled shooter is attempting to cause the dice to rotate only along the Z axis. In theory, any spin in the Y or X axis can introduce unexpected bounces and a less controlled outcome. With a spin in only the Z axis, the Now that we understand the basic physics of dice control, we can see that the actual As well as limiting the spin of the dice to the Z axis, extremely proficient controlled shooters also try and fix the rate of spin for both dice to be the same. This can further reduce the dice outcomes for advantage play. For example, with a 22/44 or Using a hard way set again, suppose a controlled shooter achieves Z axis control but not rotation rate. In theory, the possible outcomes are the sixteen permutations of the four on-axis sides: 22, 23, 24, 25, 32, 33, 34, 35, 42, 43, 44, 45, 52, 53, 54, and 55. Notice that there are passing outcomes that sum to seven, as well as failures (61, 16). This will come into play when we talk about the statistics of dice setting, and the best way to determine if a skilled shooter is influencing the outcomes. In the next sections, we discuss two ways of determining if a shooter is in fact influencing the dice outcomes: SRR (Seven to Rolls Ratio) and the new SRR - Seven to Rolls Ratio Ok… you claim to be an expert dice controller, and making millions at craps. Good for you! Now, how do we The most common statistical analysis of the game of craps to date is the SRR:
Figure 3: Dice outcomes for a random shooter The above table for a dice controller will be quite different, but the number we concentrate on is the number of seven outcomes. On the come out roll, we want to maximize the number of sevens (i.e. have the highest possible SRR fraction, or lowest SRR proportion value), and on any point roll we want to minimize the number of sevens (i.e. have the lowest possible SRR fraction, or highest SRR proportion value). In With the above approach, we can convert various SRR ratios to actual player edges. In - Shooter uses a controlled throw on the come out roll that minimizes their SRR to 1:5.5.
- Shooter uses a controlled throw on all point rolls that maximizes their SRR to 1:6.5.
- Zero odds game, with flat pass line bets only.
**Player edge**: +3.43% (using 100 million craps rounds, where each round is a single bet. 342 million rolls in this case).
While it is possible to determine the player edge mathematically with different SRR values in the case of simple flat pass line bets, things get more complicated when you add unusual bets and rules (vigs, odds, uneven payouts, etc.) It is interesting to observe that the actual dice set is not relevant when simulating SRR shooters. The SRR is a direct result of their technique and set, not the other way around. But SRR shooters are no different from any dice setter: the principles of axis rotation discussed previously apply. Also, the actual dice sums, while very relevant to computing player edge, are not directly Enter Pro Test©: a better dice control metric We've seen in the previous section that the seven to rolls ratio, while somewhat intuitive and useful for calculating player edge, is not the best possible measure of dice setting skill. This results from the fact that sevens can be both 'good' and 'bad', meaning that they occur when we both achieve and fail z-axis control. This weakens the statistical utility of SRR for determining player dice setting skill. Let's take a fresh statistical look at dice control, starting with the basic physics principles described in the earlier. Z-axis rotation First and foremost, dice setters are trying to limit the dice rotation to the z-axis. This simply means that neither of the outside numbers shows up in the outcome. Hence, there are 4 times 4 = 16 possible outcomes that succeed in rotating in the Z-axis only. With a hardway set, this means each die outcome is one of: 2, 3, 4 and 5. Secondly, a good dice setter tries to control the number of face rotations or Thirdly, dice setters attempt to try to limit the number of Thinking in practical terms, how do we know if a throw has stayed on z-axis rotation for any given dice set? Or, how do we know how many face rotations or pitches occurred on those successes? While it is very clear with a hardway dice set, other sets will lead to ambiguous results unless the dice are clearly marked (or colored) and the starting dice set recorded. For the purposes of the Pro Test, we A random shooter should achieve 16 z-axis controlled outcomes on average for every 36 rolls. Of these "If I roll the dice a bunch of times and observe a certain number of z-axis controlled shots, what is the probability of this occurring randomly?" This fancy looking question is really the mathematical equivalent of asking
In our next episode… introducing Pro Test©! Now that we have a better understanding of the physics of dice control, and the meaning of the current SRR analysis method, we can strive to come up with a better and more accurate statistical model for dice control. In next month's article, we'll introduce the Once again, for those who are curious, you can download the software and read the documentation. Pro Test©, as well as everything we'll cover in this series of articles, is completely and thoroughly presented there. See our web site: www.SmartCraps.com. Learning about dice control… Ok… maybe we've raised your curiosity about dice control. Time to buy the book, and make millions, right? Wrong: dice control is a Dice control takes practice. And then, a whole bunch more practice. And then, you have to learn how to transfer that skill into the much more difficult realm of the casino floor. And then you're going to have good days and bad days, when you're "hot" or "cold" (not luck… but days when your dice influence skill is good or bad). If you want to get serious about dice control, be prepared to make a different and much larger time commitment compared to blackjack. There are a few "hands-on" courses for dice control, the first of which I'd recommend is "Golden Touch Craps" by Frank Scoblete and partners (www.GoldenTouchCraps.com). There are also some good (and bad) books, ranging from general interest to precise details. My favorites are "Get the Edge at Craps" by 'Sharpshooter' (deep with good math coverage), and "The Craps Undergound" by Frank Scoblete (a great dialogue from an experienced dice control and seasoned veteran). There are other great texts, and no insult is meant by their exclusion! Search amazon.com or check your favorite gambling store.
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