The data in this study indicates that it is extremely unlikely (less than 0.014% probability) that the observed experimental data is the product of a normal game of blackjack without alteration of the dealt cards. Although this study makes no claims as to the actual cause of this statistical abnormality, the results are consistent with the practice of 'dealings seconds' exactly when the dealer has a hand total from 12 to 16, and the player has a hand total of 16 or more.

The purpose of this study is to replicate his experiment and confirm or deny his conclusions.

The hypothesis to be tested is as follows:

Excluding an initial 45 rounds of blackjack played to perfect the data collection process, no further games or trials were played. No rounds are excluded from the collected data, nor was any other form of exclusion or intentional experimental bias introduced.

The table below shows the results from this trial for the hands matching the hypothesis:

The 'No bust' columns represent observed incidents of dealer hands where the third card dealt to the dealer did not cause the dealer to bust immediately. Note that this includes dealer hands where the dealer would later bust the hand (in four or more cards): the final state of the round is not relevant to this experiment. The 'Bust' columns represent dealer hands where the third dealt card caused the dealer have an immediate hard total greater than 21 (a bust).

We can easily compute the expected probability in a fair game of blackjack for a 'Bust' or 'No bust' result given any dealer hard hand combination. The following table summarizes these computed values (these are not experimental results):

This experiment can be analyzed using Bernoulli Trial methods. The probability of obtaining exactly x successes, each with probability p, in n trials is given by the following binomial distribution.

By summing this equation's values from 0 to the observed number of 'Bust' events, we derive the probability of the observed experimental results.

Using the above statistical approach, we can compute the probability of seeing the observed number of dealer 'Busts' or less (bold italic column):

An alternative cumulative analysis can be completed by combining the total bust dealer hands. 28 were observed when the player hand total was greater than or equal to 16, and 45.5 were expected. Given the fixed and independent expected probabilities for each hard hand, the standard deviation can be computed and used to determine the overall likelihood of so few busts. Using this aggregate method, the probability of the total observed number of busts when the player hand total is 16 or greater is 0.0144% (once in 6944).

The data in this study indicates that it is extremely unlikely (less than 0.014% probability) that the observed experimental data is the product of a normal game of blackjack without alteration of the dealt cards. Further experimentation would be necessary to provide evidence for any actual hidden playing tactic being employed. But the observed results are consistent with the blackjack technique of 'dealing seconds', whereby the dealer avoids taking the next shoe card when they know it will bust their hand, and instead take the second-next shoe card. This practice would cause the statistically abnormal low number of busts seen in this experiment. The lack of abnormality in the dealer hands when the player hand is valued less than 16 shows that it is exceedingly likely that some form of bias is being employed selectively.