slightly delayed response to the lunatic fringe of tbj
I haven't posted for a couple of days - as I have been sick - and not up to either posting or even reading posts - but do want to throw my two cents in again - on several points
first: I previously posted on sample size needing to be based on what question you are really asking - and the difference between hypothesis testing and simply fishing through a data set for unusual hand sequences - or developing a basic strategy - this and some other comments on sample size evidently weren't clear or were misunderstood -
second - again - no one has posted anything which even comes close to being hard data which would indicate UB/Bet21 games/cards are biased - anecdotal 'bad beat' stories don't cut it -
so - here goes -
point one: I posted data on another thread tracking more than 4,900 player hands - this is hard data over a sizable sample size - usable for testing certain simple clear hypotheses - the reason I sampled this way was to determine three things 1. Am I being disadvantaged by receiving more stiffs than the other players?; 2. Am I being disadvantaged by receiving fewer blackjacks than the other players?; and 3. Are the hands being dealt the players in in the same proportions (bjs, stiffs, other hands) as expected through random chance? The sample size was indeed sufficient to answer these questions - and the answers affirmed that what we are seeing on UB/Bet21 conform to the expected probabilities - the small deviations from the known probabilities of the all player percentages and the difference between my hands and those of the other players are simply too small to be significant - if you aren't familiar with sampling size criteria and hypotheses testing and statistical significance - try surfing through Wolfram MathWorld or even Wikipedia for their articles on these topics - a sample of more than 4,900, with the results obtained, is plenty sufficient to establish that on these parameters, there is no reason to suspect non-random factors being involved. Feel free to conduct appropriate significance tests on the data I posted - there are several web sites where you can do this stuff on-line
point two: the 'concern' about dealer hands is bogus - tbj/ebj is a competition amongst the players, not between player and dealer - even if there are non-random factors affecting the dealer hands - it is irrelevant - as all players face the same dealer cards and all are affected equally - only non-random factors that affect the PLAYERS differentially, favoring one player over the others, or disadvantaging a particular player and not the others, are meaningful- as long as all players are affected equally - dealer cards are not a factor - the issue with seating assignments was VERY RELEVANT - as seating assignments affects betting position, and that does has a differential impact on players - and that can directly affect outcomes - that was a very serious issue as far as I am concerned - it also apparently has been resolved - my more recent seating assignments have seemed pretty random
point three: you can not apply the same probabilities to single discovered incidents of unusual card sequences that you would apply to a sample used for a hypothesis test. That was the gist of my posts/comments on sample size and hypotheses testing versus fishing expeditions - I will try to explain why - and why 'fishing' data is worthless -
we all know that the probability of getting a bj is 0.04751, right - so the odds of the dealer, or any player, getting 6 in a row are 0.000000242 (1 out of 4,132,231), very rare and a very unusual occurance - so, if you are playing one of the tables you have played on UB/Bet21, and you see such a rare event - you would rightfully be concerned, as to how fair the game is, right? - no, actually, wrong - because that 'expected probability' doesn't apply in that situation - the probabilities that do apply can be calculated as follows:
I have played about 1,200 tables on UB/Bet21 to date; figure that in the 61 tables I tracked for the data I posted, I tracked 4,932 hands for myself and the other players, with myself receiving 983 hands - so I played an average of 16.016 hands per table - apply that to 1,200 tables - and I have played about 19,219 hands - so have had 19,213 opportunities to see the dealer get a six or more hand sequence of bjs - so - the probabilitiy that I would - somewhere in those 19,213 opportunities see one or more such sequences is: 0.0046388675! not common - but not so rare at all - but - I am also watching not just the dealer, but my own cards and those of 6 other players - so there are actually 8 series of 19,213 hands that I am observing - so the probability that I will see at least one six-hand or more bj sequence amongst all the players and the dealer - are actually: 0.03650!!!! over 3% - so should I panic over observing an occurance that has a 3.6% probability of happening by random chance, for someone at one of my tables?? even worse for the meaningfullness of anecdotal bad beat 'data' - I am talking about only a single 'bad beat' scenario - there are obviously many hand sequences which are very improbable and would trigger off my paranoia - what if I am dealt 18 stiffs in a row? -that's a 0.000000457 probability - or the dealer shows a ten as an upcard 12 times in a row - that can't happen by random chance - can it? - that's only a 0.00000072 probability - but those sequences are actually more likely to occur than the sequence of six bjs in a row - so the probability that I will observe each of them AT LEAST ONCE in the hands I have played is higher than 3.5%!!! For 'fishing expeditions', where I am simply observing play - and 'seeing' these remote probabilties occur - the real probability I need to know is 'what is the probability that I will, in all the hands I have played, observe one or more of all the many possible various 'bad beat' sequences?' - not just the probability that I will observe a particular one - as I will identify and react to any that occur - well - I don't know how many such sequences there are - and couldn't even begin to calculate them - but there are very many that would qualify as 'bad beats' and be very long odds to happen - in a live tournament game at the Avi in Laughlin - I saw another player at my table get 5 bjs in the first seven hands - a 0.00000468893 probability - definitely an impossible bad beat - since it was the drunk-all-in-guy - and he won the two hands he didn't bj -
so lets, very very conservatively, say that there are 250 'bad beat' sequences we would detect, as experienced players - then the probability that I would see at least one of these sequences ocur in the 19,213 opportunities for each of seven players and the dealer on UB/Bet21, using the probability for six bjs in a row as the base, is: 0.9999079 - virtually certain to see at least one - and a 0.4293503 probability that I will see TEN or more of them occur!!! Those are the relevant probabilities for your observations - when you are scanning a large data set for any of very many possible long odds sequences - which is exactly what you are doing - you are certain to find several, or even many - by random chance - that's how it works - finding such sequences means NOTHING - if you didn't observe such sequences happening - THAT would be unusual - and a matter for real concern - because they are expected to happen - by chance - and you would then be observing a serious deviation from random results if you didn't see any - they would have to be rigging the game to avoid them happening!
if you want to establish that these low probability sequences have any relevance or suggest in any way they are not simply expected artifacts of random chance - you need to track over massive numbers of tables - and show they fall into a non-random pattern and/or relate them to regular, non-random, external events, - such as : ' whenever my account balance goes over $1,000 at the next table the dealer gets six bjs in a row, and this has happened three times' - now that would be worth suspicion, and further testing as a hypothesis - but highly improbable bad beat anecdotes are simply interesting stories and provide no reason to suspect non-randomness.