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Playtech Live Blackjack – A short study of card distributions
Posted by THEPOGG on Oct 31, 2012
Recently, at thread on the Wizard of Vegas site that made some worrying suggestions about the fairness of Playtech’s Live Dealer Blackjack game (http://wizardofvegas.com/forum/gambling/blackjack/11643-online-games-using-playtechs-latvian-casino/) was brought to our attention. The opening poster in the thread asserts that they recorded a dramatic shortage of Aces over a 10 shoe random sample. Two important issues arise here; firstly, for those that aren’t familiar with Blackjack, Aces strongly favour the player and are the single most important card when card counting, often being counted separately due to their significance and secondly the deficit of Aces the poster claims to have seen would be statistically impossible within the given sample size if the shoes played contained the correct number of Aces randomly dispersed over the shoe. If these claims turned out to be true, this would put the player at a far greater disadvantage than they should be and unquestionably constitutes cheating.
As many of our top rated casinos use Playtech software, we chose to conduct our own investigation.
For this study we chose to play the same 10 shoe sample as the original poster in the Wizard of Vegas thread, however instead of simply looking at the number of Aces we received, we chose to look at the distribution of all the card ranks over the sample size – removing Aces is not the only way to bias a deck in favour of the casino, removing any ten value card or adding low value cards could achieve the same effect.
As supporting evidence for this study we also chose to video the playing sessions, so that you can check our numbers for yourself. As all online live blackjack has a very very slow rate of play, we’ve had to break this up over three session. We’ve tried to keep the shoes grouped together as much as possible so that you can see that we’ve not picked and chosen which shoes to show you so shoe 1 and 2 are found in the Live Blackjack 1 video, shoes 3-6 are found in the Live Blackjack 2 video and shoes 7-10 are found in the Live Blackjack 3 video. As one of our reviewers compiled these videos for us and it’s very important that they retain their anonymity, we have taken every precaution we could to remove any information that might identify the actual tables in question.
Below you’ll find all three videos and a spreadsheet of the individual and combined shoe results. Now in any suit of cards there are 13 ranks and each of those ranks is represented evenly within a complete deck of cards. So the over our sample size of 2043 cards seen, each rank of cards should have appeared on average 1/13 of 2043 times or 157.15 times. Looking at our results the lowest occurring rank was the 2s which only appeared 146 and the most frequently occurring rank was the 3 which appeared 168 times. It should be fairly evident even to those with no mathematical background that even our two extreme results are far from an unlikely distance from the expected result, but for the sake of completeness we’ll complete the mathematical tests on this distribution. It should also be noted that we received 156 Aces which is very very close to the predicted 157.15.
To do this we use a Chi Squared calculator, which can be found at http://www.physics.csbsju.edu/cgi-bin/stats/chi-square_form.sh?k=13. The Chi Squared calculation basically calculates how closely the actual results fit the expected Normal distribution. In this instance we’ve already set the calculator to use 13 variables – one for each rank of card. So we enter in the x boxes how many of each rank we received and in the E boxes we put the number we expected to receive (2043 /13 = 157.15). To learn more about the Chi Squared distribution see http://en.wikipedia.org/wiki/Chi-squared_distribution. This gives us the results;
chi-square = 3.72
degrees of freedom = 12
probability = 0.988
To break this down, a probability value of 0.05 or less (on a scale of 0-1) is considered a mathematically significant deviation from the expect result. If a full 10 shoes had been seen – i.e. every card – the probability would reach 1 if all the cards that should have been present were present. In our sample we have a probability of 0.988 telling us that with 2043 cards seen the distribution of cards is extremely likely to matches that which we would expect to see (i.e 157.15 of each rank). This is only an approximation of how well the data matches the Normal distribution, there are more accurate ways of calculating this, but give the high probability we’ve received already we don’t feel the need to take this any further.
So why does the Wizard of Vegas thread show such dramatically different results? Well there are many possible explanations some of which I’ve detailed below;
The poster could have wrongly identified the shuffle point (penetration). If they were only seeing 2 decks dealt out of 8 the number of Aces they received is perfectly normal. This seems unlikely though as shown in the videos the standard shuffle point appears to be around the 4 deck mark.
Human error in recording the number of Aces seen .
Human error in recording the number of shoes played. Looking at the number of cards seen invalidates the need to know the number of shoes played. Going by the number of shoes played makes the assumption that you are seeing the same number of cards in every shoe and hence should see the same number of Aces. If you look at our lowest cards seen in a shoe we should only have seen (188/13) 14.5 Aces, whereas our highest shoe (226/13) should have shown 17.4 Aces, so as you can see unless your estimate of the penetration is accurate and consistent from one shoe to the next the results could deviate substantially from the expected result making this an inherently error prone system.
Or perhaps there is a problem, only we’ve not seen it due to game selection; there are several versions of live dealer blackjack and we only used the single seat/multi-seat tables, timing – perhaps this only happens at certain times or under certain conditions, or perhaps Playtech having seen this issue discussed on a high profile gambling forum stopped the practice of shorting the deck before we took our sample.
From a personal perspective I find the last possibility unlikely. Playtech are probably the highest profile online casino software provider in the market at the moment and work with many of the biggest names in offline as well as online gaming. If they were to get caught intentionally cheating – and make no mistake about it, the degree of shorting discussed in the original Wizard of Vegas message board post could not be achieved accidentally – many of their biggest clients would likely want to distance themselves from the company as quickly as possible to protect themselves from the reputational fall out. It simply doesn’t seem worth their while to risk that sort of loss of custom and reputation simply to offer their clients a couple of extra percent on their live game returns.
Of course none of this actually proves anything other than the distribution of cards over this particular sample were normal. Shorting the deck does not have to be a process that is applied to every shoe of play and could easily enough be used selectively on different shifts, by certain members of staff or even against certain players/bet sizes. However the indication from the original post was that the investigation that turned up the lower than expected number of Aces was conducted after several player complaints regarding abnormal results. It therefore seems likely that either this would have to be a widespread practice or that the investigation just happened to take place during a period where the shoes were coincidentally being shorted and if that were the case as we took three different samples we’d increased the chances of encountering one of these periods, which didn’t happen. For my money I think you’re probably getting exactly what it says on the tin when you play Playtech’s Live Dealer Blackjack.
I’d like to thank aka23 from Beating Bonuses and Michael Shackleford The Wizard of Odds for consulting on this study.
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