Hand Lengths in Craps:
A Closer Look at Monster Rolls
By Dan Pronovost
Dan Pronovost is the owner and president of DeepNet Technologies, makers of a wide range of gambling training products and software. Their web site are: www.HandheldBlackjack.com and www.SmartCraps.com and all products are available for free trial download. Dan is the creator of the new card counting system Speed Count, which is being taught by Henry Tamburin and Frank Scoblete in the Golden Touch Blackjack two day courses: www.GoldenTouchBlackjack.com.
This is a continuation of on-going articles on the game of craps and advantage dice control. As with prior articles, we are using new and powerful mathematical tools to analyze craps, now available in our software Smart Craps. This article refers to Pro Test and other statistical metrics described in our prior articles to date. If you haven't yet read these articles, you probably should to understand what follows:
- Craps article #1: www.bjinsider.com/newsletter_62_dice.shtml
- Craps article #2: www.bjinsider.com/newsletter_63_dice.shtml
- Craps article #3: www.bjinsider.com/newsletter_64_craps.shtml
- Craps article #4: www.bjinsider.com/newsletter_65_craps.shtml
Hand Length in Craps
In June, I wrote an article that basically showed that hand length in craps (the number of rolls that you keep the dice at one time) is a very poor metric for determining if someone is influencing the dice outcomes (see www.bjinsider.com/newsletter_65_craps.shtml). We learned that while on the surface it seems pretty amazing when a shooter holds the dice for 1/2 hour or more (i.e., a long 40+ roll), these events by themselves are not good evidence of dice control. Pro Test, the tuned dice control metric used in our Smart Craps software, is by far a more accurate test and requires as few as 100 to 500 rolls to prove with statistical confidence that a person is indeed influencing dice outcomes.
But after this article was published, Frank Scoblete (a well-known dice controller and contributor to Blackjack Insider) provided me with some very detailed hand length data, asking for some analysis. Frank has already supplied me with personal Pro Test roll data in the past, and passed with the best scores I've ever seen (his roll set data represents 'godly' level of dice control skill, as I've been quoted saying a few times). Frank has meticulously kept records of his casino craps sessions, including total number of outings and exceptionally long hands.
Having analyzed hand length (# of rolls from come out to sevening out) in general for craps and found it to be a poor metric of influence, I was skeptical and tried to put him off… but he persisted and gave me all the detailed data I required. Well, having failed to find a way to ask for something he couldn't provide, I was left with no choice but to look more closely at the data.
And indeed, it was another case of bumping into the trees in the mathematical forest, as I like to say! With sufficient, complete and unbiased data, hand length can be an interesting and compelling variable to study in craps.
How to Properly Study Hand in Length in Craps
In our last article, we basically surmised the following reasons why hand length is not the best metric for determining dice influence:
- The probability of getting a 'monster roll' (50+ rolls holding the dice in craps) is pretty rare for both a random shooter and skilled shooter. By using the Smart Craps simulator, we found that a random shooter had a 0.09% chance of a 50+ roll, while a very skilled dice controller had a 0.14% chance. Even a 'godly' level of skill (like Frank's) meant a meager 0.44% chance of having a 50+ hand. When looking for good statistical measures, it's very important to make sure that the metric should show a disparity in results between the control variable and hypothesized influencing factor. While the difference above is not zero, it is not as great as a direct influence measure like Pro Test.
- Any statistical test needs to be unbiased and fair. This means establishing beforehand how many trials you will perform, recording them all, and ensuring all data is included and none is excluded. A report of "I had just had three back to back monster rolls!" is meaningless by itself. We need lots of hands, which really means months or years of data potentially.
- A claim of dice influence by passing a Pro Test in 200 to 500 rolls is easy to test and very plausible. The subject can be re-tested in a reasonable amount of time, effecting a trustworthy experiment. It is impossible to setup experimental conditions to record hundreds of hands (each containing many rolls): the best we can do is use, say, a year's worth of session data for a dice controller, and trust it was recorded properly and fairly.
- Any claim of monster rolls has to be plausible for some expected level of skill. If some claim of number of monster rolls means the odds of it happening is rare for even the most skilled shooter, then we have to be skeptical that the data is fair and unbiased.
The challenges above make statistically testing hand length challenging, but not impossible. Enter Frank's hand length data…
A Year's Worth of Casino Session Data
Initially, Frank e-mailed me the innocent question, "Here are six hand lengths: 50, 52, 55, 57, 60 and 89. Would this shooter be the same as a random shooter with these hands?"
Thinking back to my hand length article, I noted that we would need to know how many hands were rolled, ensure that the data was for an unbiased trial period, and basically needed to match all the difficult metrics I noted above.
To which Frank replied politely, "These [hands] all occurred in a single year so the 948 is like a prescribed number since the year began at one point and ended at another point." He had told me initially that he had had 948 hands in that period of six 50+ hands, but I had missed that point. Combined with the fact that these represented no more or less that one year's complete data, I felt satisfied that this met my requirements for fair and unbiased trial data. Of course, I couldn't personally validate the data, but it represented live casino sessions with many witnesses, which was good enough for me.
To study this data, I started with the same statistical technique we use with Pro Test in Smart Craps: what is the probability that a random shooter will have 6 or more 50+ monster rolls in 948 hands? We answer this using the same mathematical tools that we use for Pro Test: the Bernoulli equation (see www.bjinsider.com/newsletter_63_dice.shtml). A random shooter has 0.09% chance of a 50+ hand, so we can apply the equation to find out the probability of 6 or more such hands in 948 trials. The envelope please (drumroll)… 0.02564% is the winner!
So far so good… there is less than 1% chance that a random shooter could achieve Frank's results for number of 50+ hands in one year. But how likely or unlikely is it for Frank, as a very skilled shooter, to achieve these results? We need to confirm that it is not absurdly rare for a very skilled shooter to achieve six or more 50+ hands in 948 trials.
To test this, I used the Pro Test data Frank had previously supplied me. His results show an exceptional skill level (5% to 15% potential positive edge, depending on how he sets the dice and bets). With his data, the chance of having a single 50+ monster roll is 0.44%. Using the Bernoulli equation, we can also find out his odds of having six or more 50+ monster rolls in 948 hands: 24.18693%. This is not surprising, since the expected number would be 948 * 0.0044 = 4.2. So, it is plausible for Frank to have 6 or more 50+ monster rolls in one year.
So, there is far less than 1% chance that a random shooter could have this many (or more) monster 50+ rolls, and it's totally plausible with Frank's already confirmed skill level that it could indeed happen. Excluding the possibility of hands not being recorded or a biased sample set, we have compelling statistical evidence of dice control from hand length data!
If should be noted though that at a less 'godly' level of dice control skill, using Pro Test results from other expert skilled shooters, the probability of six or more 50+ monster rolls is only 0.24456%, which would make us skeptical of the data. The only reason we can comfortably apply our statistical test in the first place is because we had in advance sufficient Pro Test data to confirm a sufficiently high level of dice control skill to collaborate the hand length results.
Case closed on Monster Rolls: Not Guilty By Way of Plausible Explanation.