A friend sent me a computer application *Baccarat Advantage* (baccaratadvantage.com), a black box which outputs bet placement instructions based on inputted Banker and Player hand total values.

The creator of *Baccarat Advantage* calls himself “Dr. Jacob Steinberg,” and claims to have achieved a positive expectation after running 1 million live shoes through his program. Because a user of the program only accesses the program’s interface, where he enters the total hand values and receives the outputted betting instructions, the actual method of determining the bet placement is never revealed, and he can only use the application to play at online casinos, never at physical, brick-and-mortar casinos. In addition to the purchase price, Dr. Steinberg also requires his customers to share a percentage of their winnings from using the program, and the exact purchase price depends on what percentage the customer agrees to pay. In this way, he justifies selling the program, since he can in principle exponentially increase his income through his customers’ winnings while never actually revealing to them the exact method of his supposed holy grail.

Despite what Dr. Steinberg claims, my tests of his *Baccarat Advantage* objectively demonstrate that it quickly yields negative expectancies, and if he really did win a million live shoes with the method in his program, those shoes must have been unbelievably favorably biased to it. On the surface, his procedure appears to utilize information from hand totals and not just the (mathematically doomed to fail) pattern of P/B wins. Thus, there is a faint glimmer of card-counting potential, though the program does not fully account for the values of each card. However, whatever his method is, my tests show that it consistently yields negative expectancies and can no better win at baccarat than any other method tested to date.

A picture of the *Baccarat Advantage* user interface:

Upon activating the program, a brief splash window encourages the player with an affirmative tagline, *Because winning feels so good*. Play commences as follows: At the beginning of each shoe, the user enters the first four hand totals of the first two decisions in the “Second-to-Last Hand” and “Last Hand” rows. The program then outputs a bet placement instruction in the “Now Bet” row. The user then presses the “Won,” “Tie,” or “Lost” button according to the result of the bet, upon which the values in the “Last Hand” row moves up to the “Second-to-Last Hand” row, clearing the “Last Hand” row and making it available for fresh input. He then enters the next set of hand totals in the now emptied “Last Hand” row and repeats the process. After the end of each shoe, the “Reset” button is pressed, all the input boxes clear, and the process begins again for the next shoe.

There are two money management options: 1) Flat Betting and 2) Progression Betting. Based on $1 units, flat betting requires a $50 bankroll, while progression betting requires a $164 bankroll. The progression (as seen in the picture above) is a simple 7-level Martingale, padded at certain levels to cover Banker commissions. Flat betting is described as a “slow winner,” but requiring “lower bankroll,” while progressive betting is touted as an “infallible, quick winner,” but requiring “higher bankroll.” Either way, Dr. Steinberg claims his method consistently beats the house edge and is the only true (and easy) way to win baccarat.

For the most part, the program consistently outputs the same bet placement instructions per set of inputs. I write, “for the most part,” because there were some minor glitches which would sometimes result in the same set of inputs resulting in different bet placement instructions. The apparent glitches may occur when one changes an inputted value, and then back to the original value again, whereupon the opposite bet placement instruction would sometimes appear. This is clearly an operational bug on the part of the programmer, assuming there is supposed to be a one-to-one correspondence between unique input values and output bet placement instructions. Otherwise, the program appeared to be consistent enough for the most part to be tested against data sets of baccarat shoes.

To examine the long term performance of Dr. Steinberg’s baccarat black box, I created a script to automate the inputting and reading of the outputted bet placement instructions for 12,100 baccarat shoes. Roughly 3-4 shoes per minute could thus be accurately inputted and analyzed, and the entire testing took place over several days and nights. My automation script performs exactly what a human would do, entering the total hand values decision by decision, reading the outputted bet placement instructions, pressing the “Won,” Tie,” or “Lost” button according to the result of the bet, and pressing “Reset” after the end of the shoe before starting the next one. For the testing, I used the Flat Bet mode, since no progression will be able to consistently help a method which cannot win flat betting. For verification, I sent the data output to my friend, who double-checked and confirmed he was getting the same outputted bet placements from the program.

A sample of the data output follows:

1st column: shoe number

2nd column: decision number

3rd column: Banker hand total

4th column: Player hand total

5th column: decision P/B/T winner

6th column: *Baccarat Advantage* outputted bet placement

1 1 5 2 B - 1 2 1 3 P - 1 3 9 5 B P 1 4 3 8 P P 1 5 6 2 B B 1 6 5 5 T B 1 7 0 9 P - 1 8 8 7 B B 1 9 9 5 B B 1 10 0 6 P P 1 11 5 9 P B 1 12 6 6 T P 1 13 9 2 B - 1 14 6 7 P P 1 15 9 3 B P 1 16 0 5 P P 1 17 0 0 T P 1 18 2 1 B - 1 19 0 9 P P 1 20 5 8 P B 1 21 6 8 P P 1 22 7 9 P P 1 23 0 9 P P 1 24 8 1 B B 1 25 9 5 B B 1 26 8 6 B B 1 27 6 9 P B 1 28 1 9 P B 1 29 6 5 B B 1 30 3 8 P B 1 31 0 5 P B 1 32 3 9 P B 1 33 0 9 P B 1 34 8 4 B B 1 35 3 7 P B 1 36 8 6 B P 1 37 9 7 B B 1 38 3 8 P B 1 39 5 9 P B 1 40 4 6 P P 1 41 8 8 T P 1 42 3 9 P B 1 43 9 2 B B 1 44 7 5 B P 1 45 9 6 B B 1 46 0 2 P P 1 47 1 7 P P 1 48 9 0 B B 1 49 9 6 B P 1 50 8 0 B B 1 51 2 2 T P 1 52 4 7 P B 1 53 8 8 T B 1 54 9 5 B B 1 55 5 6 P P 1 56 9 6 B P 1 57 5 8 P P 1 58 4 4 T B 1 59 7 6 B B 1 60 6 5 B P 1 61 0 9 P P 1 62 1 7 P B 1 63 0 8 P P 1 64 1 6 P B 1 65 0 9 P P 1 66 8 6 B B 1 67 6 6 T B 1 68 4 6 P P 1 69 4 3 B B 1 70 0 9 P B 1 71 5 1 B B 1 72 3 4 P B 1 73 4 2 B P 1 74 4 8 P P 1 75 8 7 B B 1 76 7 8 P B 1 77 2 2 T P 1 78 9 4 B P 1 79 8 6 B P 1 80 6 6 T B 1 81 6 4 B P 1 82 3 7 P P

Notice that sometimes the program does not bet after a Tie, and sometimes it does.

The numerical and graphical results of the testing are presented in Simulation Series 31 Results. Three sets of data were examined, each one consisting of slightly different Banker (B) and Player (P) compositions. As the following plots show, the qualitative behavior of the *Baccarat Advantage* Player’s Advantages (P.A.’s, the net units won after commissions divided by the total amount bet) depend on the B/P compositions of the data set, though all are consistently negative.

Data Set 1 had a slightly lower-than-average numbers of Bankers, 50.61% Bs and 49.39% Ps (not counting Ties). In this set, the P.A.’s of the *Baccarat Advantage* bet placements are always consistently worse than the expectancies for B, while the P.A.’s of the opposite of the *Baccarat Advantage* bet placements are always consistently better than those of P. (Because of the lower-than-average numbers of Bs in Set 1, the expectancies for B is always *more negative* than that of P.) The following plot which graphs the evolution of the P.A.’s over the numbers of shoes tested shows that in Set 1, *Baccarat Advantage* P.A.’s (*blue* for the program’s output, and *red* for the opposite of the program’s output) mostly lie to the outside of the Banker and Player P.A.s (*yellow* for B, and *green* for P).

Data Set 2 has slightly more Bs overall than Data Set 1, 50.69% Bs and 49.31% Ps (not counting Ties), which is closer to what are the “average” proportions. As the following plot shows, the blue and red *Baccarat Advantage* P.A. lines begin to fall in-between the yellow and green Banker and Player P.A. lines.

Data Set 3 has 50.83% Bs and 49.17% Ps (not counting Ties), which is more Bs than “average,” and for the most part, the *Baccarat Advantage* P.A.’s are always comparable to or no better than the standard B/P expectancies. Thus, in the plot below, the blue and red lines are mostly contained within the yellow and green lines. In various, brief stretches, the *Baccarat Advantage* P.A’s became slightly more positive that that of B, and the opposite bet placement’s P.A.’s correspondingly became slightly worse than P, which is the opposite of what occurred in Data Set 1.

Notice that the line of symmetry between the opposing pairs in the above P.A. graphs is about half way between -1.0 and -1.5. This line of symmetry is due to the built-in tilt of the game in the house’s favor, and the fact that it is negative is the reason why “just bet opposite” a losing method does not win either. In a perfectly fair 50/50 game, the line of symmetry would be at exactly P.A.=0, meaning in such a zero-expectancy game in the long run, you always have equal chances of being net positive or negative, and on average, break-even. However, in baccarat, the house’s edge skews everything in the house’s favor, and you expect to always be net negative in the long run, no matter how you play. In other words, if you can’t consistently win a perfectly fair 50/50, zero-expectancy game in the long run, you have even less mathematical hope of winning a negative expectancy game in the long run.

Despite the above qualitative differences due to B and P compositions in the shoe, the resulting P.A.s are always negative, and the *Baccarat Advantage* method itself loses all data sets quite unceremoniously, as the following plots of the net score versus shoe clearly show:

I did not test *Baccarat Advantage’s* progression mode systematically, but I compared a few shoes to demonstrate that the bet placement output from the program in progression mode is exactly the same as in flat bet mode; only the bet amount differs according to a win or loss, and the progression is the straightforward 7-level Martingale.

Just for fun, I let my automation script run through a small data set in the progression betting mode. In these runs, the required bet amounts would bust past the 7 levels of the progression every few dozen shoes, and a rather sad pop-up box would announce, “Sorry, you have lost. Start over.” Tracking the exact results of the 7-level progression over my testing results would have been a routine exercise, but completely not worth the time or effort.

In conclusion, my tests show that Dr. Steinberg’s *Baccarat Advantage* yields standard negative expectations and is quantitatively no different than any other baccarat method I have tested, except that in certain situations when the B/P compositions are above or below average, the P.A.’s of the *Baccarat Advantage* bet placements or its opposite are slightly more positive than expected when always betting B or P. Unfortunately, the slight improvements in odds in these situations are not enough to be profitably exploited.

*Baccarat Advantage* is a black box that is at best broken and at worst bogus.