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Reason #3 why the Wizard likes Bovada: Excellent Odds
In my opinion many online casinos are too stingy when setting the odds on their games. They think they will make more money that way but I believe they are misguided, because when players lose too quickly it's not fun, and those players might not come back.
Bovada is one of the few casinos that understands this. They offer generous odds to let you play longer and get you a better chance of winning. Among their generous offerings are FullPay Jacks or Better returning 99.54%, five other video poker games paying over 99%, singlezero roulette, and my favorite, Double Jackpot Poker, returning 99.63%!
Kudos to Bovada for not being afraid to give their players a good gamble.
Visit Bovada
Introduction
 If player has total of 1621 go to step 2, other wise play normally.
 If dealer's 2card total is 1216 then go to step 3, otherwise play normally.
 Peek at the next card in the deck, if it would bust dealer then burn it and take following card, otherwise give it to dealer.
 Take further cards as necessary to attain total of 17 or more, then score hand.
This is what would be known in a real casino as dealing seconds. I do not know what the game does if the player splits and my experiment ignores split hands.
It should be emphasized that I do not know if this code is legitimate.
The Experiment
Casino Bar Experiment Results
Dealer 2card Total  Bust on Third Card  

Yes  No  Total  
12  11  73  84 
13  13  48  61 
14  18  49  67 
15  21  40  61 
16  26  33  59 
total  89  243  332 
Assuming an infinite deck for the sake of simplicity it is easy to calculate the probability the dealer will bust with any given total of 1216. With a total of 12 there are 4 cards that will break the dealer and 9 that won't so the probability the next card will break the dealer is 4/13. Likewise the probability of busting on the next card with a total of 13 is 5/13, and so on. The next table shows the expected number of times the dealer should have busted in this experiment based on these probabilities and the number in the sample for each total from 12 to 16.
Casino Bar Experiment Results
Dealer 2card Total  Sample Total  Probability of Bust  Expected Busts 

12  84  30.77%  25.85 
13  61  38.46%  23.46 
14  67  46.15%  30.92 
15  61  53.85%  32.85 
16  59  61.54%  36.31 
total  332  149.38 
Analysis of Results
The variance of the binomial distribution, which this experiment follows, is n*p*q, where p is the probability of success and q is the probability of failure. The total variance is then 84*(4/13)*(9/13) + 61*(5/13)*(8/13) + 67*(6/13)*(7/13) + 61*(7/13)*(6/13) + 59*(5/13)*(8/13) = 78.11. The standard deviation is the square root of this number, or 8.84.
The difference between actual and expected dealer busts is 149.3889 = 60.38. This is 60.38/8.84=6.83 standard deviations below expectations. The probability of falling this far or more to the left of the bell curve is 1 in 238 billion. To put this in comparison the probability of hitting the Power Ball is 1 in 80,089,128. It would be 2976 times easier to win the power ball with one ticket than to have results this bad in a fair game.
Independent Tests
The GameMaster did his own independent test. Of the 223 hands in the GameMaster's sample where the player had 1621 and the dealer had a 2card total of 1216 the dealer should have busted on the third card 100.77 times, but in fact only busted 53 times. The probability of 53 or less busts is 1 in 43 billion. Should there be any doubts the GameMaster videotaped his play.
Dan Pronovost, the webmaster of Deep Net Technologies, did a smaller sample of 99 hands with a player total of 1621 and a potential dealer bust on the third card. His results show 45.54 expected busts and 28 actual busts, with a standard deviation of 4.84. The probability of observing 28 or less busts are 0.014%. I attribute this greater probability to a smaller sample size. To gather the 99 hands to meet the conditions of this experiment Dan played 500 total hands, and took a screen shot of every one. The details of his experiment can be found at deepnettech.com.
My friend M.N. also conducted various tests on the blackjack game of Casino Bar and their sister casino Casino on Air. The most convincing of which is the distribution of the dealer's third card when the dealer had a 2card total of 1216 and the player had 1721 at Casino Bar and 1621 at Casino on Air. Following are the results.
Casino Bar Third Card Distribution
Card  Casino Bar  Casino on Air 

A  48  52 
2  54  45 
3  71  45 
4  42  58 
5  46  45 
6  39  43 
7  33  32 
8  36  37 
9  24  24 
10  20  12 
J  13  19 
Q  20  12 
K  15  16 
Total  461  440 
I wish to note that I have never played at Casino on Air since they left Starnet, so I can not corroborate the Casino on Air results.
Casino Bar Response
Shortly after I posted my study I received a letter from the Casino Bar attorneys who denied my allegations, saying in part "Your report is tendentious and is of a slanderous nature. We can hardly comprehend how you could possibly reach these incorrect and misleading conclusions." In the interests of fairness I temporarily removed my report to give Casino Bar time to investigate my findings. During this waiting period, I posted at the request of the Casino Bar attorneys our exchanges.On June 23 I received a report from the Casino Bar attorneys by Yair Tauman, PhD, Hebrew University, a leading professor of game theory in the economics department at Stony Brook State University of New York. Here is his report in its entirety.
(1)
I agree with
calculated probabilities of Mr. Shackleford. I also agree that experimental
results reported by Mr. Shackleford are extremely unlikely under the hypothesis
of a fair dealer, but at the same time his data is very unlikely to be
generated under his own hypothesis as I will explain in paragraph (5) here
below.
(2)
I myself ran
experiments on Casino Bar?s site and I derived very different results. I played
1313 hands until I obtained 400 relevant situations (where the player had total
of 1621 and the dealer had a total of 1216). The results I arrived at are
showing in the following table:
Dealer?s
card total 
Total* 
Busts
on 3^{rd}card* 
Theoretical
expected # of busts 
Busts
on 3^{rd}higher card 
12 
82 
31 
25.23 
43 
13 
82 
26 
31.54 
38 
14 
81 
36 
37.38 
44 
15 
83 
48 
44.7 
54 
16 
72 
45 
44.3 
45 
Total 
400 
186 
183.15 
224 
* Out of the
400 relevant situations
The table
certainly indicates that the results match a fair dealer and are very unlikely
to be generated by a "cheating" dealer.
(3)
I ran (with the
help of a colleague from MIT in
(4)
The average
return of Mr. Shackleford was 95.7% on his 1245 hands. This outcome is still
statistically possible (with a sample of 10 rounds each of 1245 hands), provided that Mr. Shackleford is an experienced player and
that he played his hands perfectly. However,
(5)
The data provided
by Mr. Shackleford is a little puzzling if we take his hypothesis about the
"cheating" dealer seriously. We can use the same method of analysis he used but
in a different way. If Casino Bar really were cheating as described by Mr.
Shackleford, then one can calculate the chances of busting. With a total of 12
it is (4/13)?, because it would have to be that there was a bust on both
of the next two cards (with the "second chance" method). We can draw a similar
table to that of Mr. Shackleford
Dealer?s
card Total 
Total obtained by Mr.
Shackleford 
Probabilities
under the 2^{nd}chance method 
Expected
# of busts 
Actual # of Busts 
12 
84 
(4/13)?=0.0947 
7.95 
11 
13 
61 
(5/13)?=0.1479 
9.02 
13 
14 
67 
(6/13)?=0.213 
14.27 
18 
15 
61 
(7/13)?=0.2899 
17.68 
21 
16 
59 
(8/13)?=0.3787 
22.34 
26 
Total 
332 

71.26 
89 
The variance
of the new distribution is 84 * 0.0947 (10.0947) + 61 * 0.1479 (10.1479) +
???.= 52.26, giving a standard deviation of 7.25. Now
the observed total was 89, which is (8971.26) / 7.25
= 2.44 standard deviations higher than the expectation. This happens with a
probability significantly less than one in a hundred. This shows that the data
provided by Mr. Shackleford does not match his own predictions and that his
hypothesis of a "second chance" method has no basis.
Summary
My own
experiments show that the dealer of Casino Bar Black Jack game is fair. Out of
400 relevant situations the dealer busted on the 3^{rd} card slightly
more than he was expected to. The average return documented by Casino Bar is
about 97.6%, which is very reasonable for an average player. Finally, the
hypothesis of Mr. Shackleford that Casino Bar is cheating by the "second
chance" method should be rejected by his own data, with a significant level of
less than 1%.
My Response
I was very pleased to read Mr. Tauman's opening statements in point 1 agreeing with my calculated probabilities and that my results were "extremely unlikely under the hypothesis of a fair dealer."
In point 2 Mr. Tauman reports that he received a fair game. This I do not dispute. My allegation is that when I played on May 27, 2002, I did not get a fair game. Furthermore three other independent testers shortly after that date also evidently did not get fair games either. Casino Bar has never directly alleged that my data is incorrect and they have my log files at their disposal.
In point 3 Mr. Tauman says the expected results given the manner of dealing suggested by the code is a return of 93.8%, which is much less than the 97.6% actual return reported by Casino Bar. The 93.8% sounds reasonable to me and I do not claim that Casino Bar is dealing unfairly all the time.
In point 4 it is noted my own return was 95.7%, which I agree is possible in a fair game assuming proper basic strategy, which I do follow (sometimes with composition dependent exceptions). I would also argue this return is closer to the 93.8% assuming the dealer is dealing seconds than the 99.8% assuming a fair game under Casino Bar rules, which are quite good. In a sample of 1245 hands the actual return will vary from the expected return by as much as 6.4 percentage points 95% of the time, so my actual return proves nor disproves anything.
In point 5 Mr. Tauman is correct that my results do not mesh well with the method of dealing seconds I describe above. If I test my results against the hypothesis that the code is accurate my results are indeed 2.44 standard deviations above expectations, for a probability of 0.73% of being this high or greater. I would like to emphasize that my goal was not to prove that the code is accurate, rather to disprove a fair game.
Retest Option
The Dispute Continues
Following is a letter I received from the Casino Bar attorneys on June 28, 2002:
Dear Sirs,
Re: COA World Entertainment Limited
Further to Prof. Yair Tauman's report, a leading Professor of Game Theory, PhD, at Tel Aviv University, we would like to draw your attention to the following:
Professor Yair Tauman is a renowned expert in the field of mathematics and statistics, with expertise in Game Theory and Probabilities. Prof. Tauman served as an associate editor of the 'International Journal of Game Theory' and the 'Games and Economic Behavior' publication. His teaching career spans over famous institutions in the US such as Stanford, Ohio State, SUNY at Stony Brook, Kellogg School of Business at Northwestern University and in the two largest universities in Israel, Tel Aviv and Jerusalem.
Prof. Tauman's finding prove, without dispute, that the Black Jack game played in Casino Bar is fair, leaving your conclusions with no basis and thereby untrue.
We reject the way your last report has been phrased and published. Pursuant to Prof. Tuaman's report, we expected to receive, to the very least, an apology. Accordingly, we are advised to instruct you to immediately rescind publications in this regard and post a fully pledged apology with respect to your reckless and defamatory implications as noted above, to be circulated via the same media that served your report.
Our client never turned to you to conduct a test of Casino Bar's Black Jack game, and still maintains that whether you perform a retest or otherwise is at your sole discretion.
In addition, we were instructed to assess COA's losses and damages resulting from your original posting and once these are crystallized, we would advice as to further measures to be taken against yourself and all parties involved in this matter. It is also to note, in this regard, that the losses and damages incurred by COA have intensified due to your inclusion of Casinoonair.com in your original report, in spite of the fact that you have clearly stated that you have not played at Casino on Air.
Nothing contained herein will be deemed to constitute a waiver of any of COA's rights or remedies, all of which are specifically reserved.
Best regards,
Gideon Levit, Adv.
Abramovich, Yosef, Hakim
Following is my response sent by my attorney
Dear Mr. Levit:
As you know, I am an intellectual property attorney and appear on behalf of Michael Shackleford.
I am attaching Mr. Shackleford's response to your June 28 letter. I am in complete agreement with Mr. Shackleford's response on legal grounds.
Just because Mr. Tauman got a fair game during his tests does not mean Mr. Shackleford got a fair game on May 27, 2002, which is what Mr. Shackleford's report states. Casino Bar has access to the log files of Mr. Shackleford's play and has never denied Mr. Shackleford's hands that even your expert stated was "extremely unlikely" in a fair game. Further, it is also noted that destruction of the log files would have legal consequences, of which I am sure you are aware. Also, two of Mr. Shackleford's colleagues referenced in his report have irrefutably videotaped and taken screen shots of their results.
Since truth is a complete defense to defamation, you still have not pointed out which part of Mr. Shackleford's report is false. Please do so. If you cannot do so, Mr. Shackleford owes you no apology or retraction. Further it is noted that pursuing legal action would only cause great negative publicity for your client, because it would likely be a widely publicized case, and the irrefutable evidence discussed above would likely be introduced at trial and hence more widely publicized.
Sincerely,
{name removed online per attorney's request}, Esq.
(Mr. Shackleford's letter follows)
Dear Sirs:
In response to your last letter I am declining to make an apology on my web site or any significant changes. Following are my comments about the specific points of your letter.
As I said online I respect Professor Yair Tauman and his report. His credentials are not in dispute.
I do not claim on my site that Casino Bar always plays unfairly at blackjack. Rather I claim that I personally did not get a fair game on May 27. Even Mr. Tauman said "I agree with calculated probabilities of Mr. Shackleford. I also agree that experimental results reported by Mr. Shackleford are extremely unlikely under the hypothesis of a fair dealer." So your own expert is agreeing with me. Just because he got a fair game doesn't prove I didn't.
Regarding Casino on Air I am only reprinting data I got from another person who believes in honest Internet gaming. I do not claim to have personally played there. However I believe his results corroborate my own findings since Casino on Air is a sister casino to Casino Bar.
It does not matter that I wasn't asked to do the study. You or anyone advertising on my site open themselves to greater scrutiny. When I received several complaints from my readers about carrying Casino Bar ads I felt obligated to test the game myself.
You may tally up the damages as you see fit. Since I only am reporting truthfully what happened to me at Casino Bar I see no reason to feel accountable. It will be up to you to seek damages through the U.S. courts, in which I feel your chances of success are also "extremely unlikely.". Regards,
Michael Shackleford
June 29, 2002
First Retest
Casino Bar Retest 1 Results
Dealer 2card Total  Bust on Third Card  

Yes  No  Total  
12  8  10  18 
13  13  21  34 
14  10  11  21 
15  11  8  19 
16  9  5  14 
total  51  55  106 
Retest 1 Expected Busts
Dealer 2card Total  Sample Total  Probability of Bust  Expected Busts 

12  18  30.77%  5.54 
13  34  38.46%  13.08 
14  21  46.15%  9.69 
15  19  53.85%  10.23 
16  14  61.54%  8.62 
total  106  47.15 
Second Retest
To confirm the Custom Strategy Cards retest I tested Casino Bar again on December 13, 2002. However I speculated that the system may have been programmed to give me a fair game. So I played from a friend's home on his account, which I funded. My test was the same as my first and second tests, the frequency of the dealer busting on the third card when the player had a total of 16 to 21 and the dealer was in danger of busing on the 3rd card. Following are my results.
Casino Bar Retest Results
Dealer 2card Total  Bust on Third Card  

Yes  No  Total  
12  6  25  31 
13  5  27  32 
14  10  26  36 
15  14  19  33 
16  8  20  28 
total  43  117  160 
Retest Expected Busts
Dealer 2card Total  Sample Total  Probability of Bust  Expected Busts 

12  31  30.77%  9.54 
13  32  38.46%  12.31 
14  36  46.15%  16.62 
15  33  53.85%  17.77 
16  28  61.54%  17.23 
total  160  73.46 
This time I videotaped my play, should my results ever be contested in court.