The most significant error in this paper comes from the boundary conditions the authors assumed when they obtained Johnson’s average daily theoretical win (ADT) for one day of play. They stated, without justification, that Don Johnson would either play 720 hands or quit after having lost $500,000. These are highly non-optimal boundary conditions. Based on these boundary conditions, the authors determine an ADT of about $41,000. In fact, the optimal boundary conditions are (approximately) for Don Johnson to quit after having either won $2.4M or lost $2.6M. These quit points lead to an ADT of about $125k, with an average of about 480 hands required to hit a boundary point.

In personal communications, Johnson stated that my results above are consistent with those obtained by his mathematicians. He also stated that based on other more intangible table conditions he sometimes exceeded these quit points. Such aberrations included, for example, error-prone dealers.

Another serious problem with the author’s results comes from the distribution the authors use to model blackjack. The author’s distribution pays the values 0, 1, -1 and 1.5 based on a 1 unit initial wager, with probabilities 0.0982, 0.0483, 0.3893 and 0.4623. This distribution gives a house edge of 0.25% with a standard deviation of 0.9809. In the actual blackjack game that Johnson played, outcomes cover the entire range from winning 8 units to losing 8 units, after splits, doubles and surrender are taken into consideration. The correct house edge is 0.263% with a standard deviation of 1.1417. It follows that the authors used a distribution whose standard deviation was substantially smaller than the actual standard deviation for blackjack.

A player’s ADT playing against a loss rebate is proportional to the standard deviation of the game. Underestimating the standard deviation is another cause that led to the authors to underestimate Don Johnson’s overall win-rate. It appears the authors did not investigate the exact blackjack rules that Don Johnson played against. Had they made this effort, the authors could have gotten the correct distribution for their blackjack simulations with a simple Google search, which would have led them to the wizardofodds.com website. This search would have led them to use an accurate blackjack model.

There are other sources of positive expected value that the authors did not consider. In addition to Johnson’s ADT of $125k from a correct loss rebate strategy, Johnson was also given $50k per day in “show up money.” He also claimed to work hard to create conditions where the dealers made errors. When I heard Don Johnson speak at the World Game Protection Conference in Las Vegas in 2013, he stated that he coaxed about two or three errors per day from the dealers. That’s at least another $200k per day. These additional sources yield about an ADT of about $375k per day. Playing 40 days (as the authors assumed), it follows that Don Johnson’s overall results were completely in line with expectation. Indeed, 40x$375k = $15M.

I am surprised that the authors did not do a simple Google search on “Don Johnson blackjack.” If they had, then they would have found my work. For nearly a year, my results have been in the top 5 under the Google search “Don Johnson blackjack.” I have written a number of articles on Don Johnson as well as on the general theory of beating loss rebates. In the last few months, I have proved and published a series of theorems that I call the “Loss Rebate Theorems.” These allow a direct spread sheet solution that does not require Monte Carlo modeling.

The authors simulated 500,000″ Don Johnsons” with incorrect boundary conditions and an incorrect blackjack model. I simulated billions of “Don Johnsons” using a variety of quit points and the exact blackjack distribution corresponding to the specific game Johnson played. My simulated results were confirmed by the values produced by my Loss Rebate Theorems. I then confirmed my results were consistent with Johnson’s actual strategy by direct communication with him.

The authors state that “In the end, it is likely the case that his (Johnson’s) net winnings over the five-month period were overstated.” The truth is that Don Johnson won at a rate that was consistent with his expectation. The authors conclude that “there is a role for probabilistic fact checking at high-end periodicals.” They are right.

I invite the readers to visit my blog, http://www.apheat.net, and read my articles on loss rebates and Don Johnson.

]]>I am wondering whether you have considered incorporating value of information analysis to see where narrowing uncertainty might improve the decision.

Also did you attempt calibration of experts for estimating probabilities (see Doug Hubbard’s book How to Measure Anything) and if so I am interested in your experience.

]]>You said

“symbolic data analysis can be considered a method for Big Data.”

I agree completely. You could say also that it is a method for the cloud and the open source data.

I have appreciate much your paper; I hope you will join our next workshop on SDA in Taiwan june 2014.

Best

Edwin Diday Prof Paris Dauphine University. ]]>

First lets remember that correlation is not causation. The article states “The more people who are killed by guns in a state, the lower will be life expectancy in that state.” Well, of course, because life expectancy and death by any means are inversely related anyway. One could say that the more it rains in a state the higher the humidity and pretty much nail the prediction. That says nothing about causation. There are also a number of counterfactuals in your graphics. Montana, for example has a high 8th grade reading score which the author equates to “ignorance” (I’m not sure how reading and ignorance are established as equivalent but I will go with it for now), and yet has a “high” firearm death rate but a moderate life expectancy. Part of the problem is that many of the “red” states are rural and agricultural in nature — look at the reading scores graphic and you can see a definite North-South difference. The differences are spurrious when you take into account that there are more hunters living in the rural mountain West and Southern areas and more people from urban populations who come to those areas to hunt while on vacation. The gun deaths seen in those locations are not necessarily locals either — many people who vacation and go hunting from urban areas are not as well educated or familiar with firearms and either hurt themselves or others due to their “ignorance” of local laws and hunting regulations.

There are so many logical leaps in this article that it almost comes across as intentional humor. The subject matter is not well researched, nor are potential confounds accounted for in the presentation. This seems to be a one-sided attempt at using pseudo-stats and graphics to sway public opinion in a particular direction.

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