cbrodley
Dormant account
- Joined
- Sep 29, 2009
- Location
- Victoria, Australia.
This is an analysis of 139 hands of Blackjack online for comment.
Expected results: Dealer wins 48% (67): Player 44% (61) and 8% (11) Push.
Actual results: Dealer wins 59% (82): Player 33% (46) and 8% (11) Push.
Chi Squared Test of results is 0.022. Player retires hurt.
Notice: The total number of wins (128) is exactly compliant with the expected result but sadly they were mal-distributed.
A chi squared test is simply a test of reasonableness. Generally speaking anything above 0.05 is thought to be reasonable. Anything below 0.05 is questionable; an indication, but only an indication, that there may be other factors at work. The level of significance of 0.05 is arbitrary but generally accepted. It does not prove anything. These results will occur 22 times in every 139,000 hands played or once in every 6,320 hands. The standard responses to this situation are:
a. 139 hands is much too small a sample, you need millions of hands.
or
b. You hit a bad patch and are a lousy loser or a very bad player.
Neither of which is true. Eliot Jacobson said in a post on 17th November 2007
All one needs is a chi-squared or other statistic that is sufficiently skewed to make flawed software, cheating or malice more likely the cause than any other reasonable cause .
The first four cards out of the shoe in a single-handed game are the most important because they determine how the player will respond. (In on-line BJ they might also determine how the Dealer will respond too but that is an unworthy thought and should be ignored.) They are also important because no matter how bad the player he or she has absolutely no influence on the outcome.
Two Card Totals 17-21:
The chances of drawing a two card total between 17 and 21 are a shade below 1:3 so in 139 hands(2x139) there should be 93 such totals evenly divided between Player and Dealer or 46 each. A blackjack will occur once in every 21 hands or 2 BJ each. A push will occur 8% of the time so that there should be 8 pushes. One can easily formulate an expected result; moreover, since the Player cannot bust the wins should be 50:50 after allowing for Pushes.
Expected results: Each get 46 hands, win 19 hands , with 2 Blackjacks and there are 8 pushes.
Actual Results: Dealer gets 51, wins 32 with 7 Blackjacks and push 8 Chi Test result 0.00000671.
Player gets 42, wins 20 with 2 Blackjacks and push 8 Chi Test result 0.95.
A statistician, looking at these results, would say the Players result is normal but whats the Dealer on ? Which is a very good question.
Mind you a Dealer will get this result 7 times in 1 million sessions of 139 hands or once in 20 million hands but why does it happen on my stag ?
Drawn cards from 7-17:
If there is any part of online Blackjack that arouses suspicion it is those cards that are drawn. In a b&m casino you have the comfort of watching; in an online casino the system has to know your bet, the dealers cards and your cards. You dont have to be paranoid to be wary so how did it go.
Well it is a little strange. The Dealer drew 67 cards and managed to draw twelve 7s; the Player drew 89 cards and managed to draw twelve 8s and eleven 10s. The chi squared test results for these distributions are:
Dealer: 0.029.
Player: 0.467
Total: 0.66
Clearly, the Dealer is on something. A result of 0.029 is an indication, nothing more, that something is amiss but every result for the dealer is amiss. The Players and the Total results are normal.
On 30th December 2007 Nashvegas wrote:
I am only concerned with actual totals or skewed results that favor the house but are within the wiggle room of expectation thus allowing the software to be declared statistically fair even though it may be statistically and consistently skewed.
That I think is an excellent point. You can skew things and remain within the bounds of reasonability but if they all skewed in the same direction the overall result is horrific. In the result above the Dealers drawn cards are very suspect but if you were simply to evaluate the total of drawn cards then nothing would appear to be amiss.
In all the posts that I have read members are talking about streaks, losing runs, bet size and the arguments are endless. One thing we all know is that there are 52 cards in a deck made up of four suits with 13 cards numbered from 2 to Ace. Removing or adding cards is not allowed, it alters the odds. If we paid more attention to the cards that are dealt and to whom they are dealt, and at what count they are drawn I think we would learn a great deal.
For a first post I think that is more than enough.
Happy hunting.
CGB.
Expected results: Dealer wins 48% (67): Player 44% (61) and 8% (11) Push.
Actual results: Dealer wins 59% (82): Player 33% (46) and 8% (11) Push.
Chi Squared Test of results is 0.022. Player retires hurt.
Notice: The total number of wins (128) is exactly compliant with the expected result but sadly they were mal-distributed.
A chi squared test is simply a test of reasonableness. Generally speaking anything above 0.05 is thought to be reasonable. Anything below 0.05 is questionable; an indication, but only an indication, that there may be other factors at work. The level of significance of 0.05 is arbitrary but generally accepted. It does not prove anything. These results will occur 22 times in every 139,000 hands played or once in every 6,320 hands. The standard responses to this situation are:
a. 139 hands is much too small a sample, you need millions of hands.
or
b. You hit a bad patch and are a lousy loser or a very bad player.
Neither of which is true. Eliot Jacobson said in a post on 17th November 2007
All one needs is a chi-squared or other statistic that is sufficiently skewed to make flawed software, cheating or malice more likely the cause than any other reasonable cause .
The first four cards out of the shoe in a single-handed game are the most important because they determine how the player will respond. (In on-line BJ they might also determine how the Dealer will respond too but that is an unworthy thought and should be ignored.) They are also important because no matter how bad the player he or she has absolutely no influence on the outcome.
Two Card Totals 17-21:
The chances of drawing a two card total between 17 and 21 are a shade below 1:3 so in 139 hands(2x139) there should be 93 such totals evenly divided between Player and Dealer or 46 each. A blackjack will occur once in every 21 hands or 2 BJ each. A push will occur 8% of the time so that there should be 8 pushes. One can easily formulate an expected result; moreover, since the Player cannot bust the wins should be 50:50 after allowing for Pushes.
Expected results: Each get 46 hands, win 19 hands , with 2 Blackjacks and there are 8 pushes.
Actual Results: Dealer gets 51, wins 32 with 7 Blackjacks and push 8 Chi Test result 0.00000671.
Player gets 42, wins 20 with 2 Blackjacks and push 8 Chi Test result 0.95.
A statistician, looking at these results, would say the Players result is normal but whats the Dealer on ? Which is a very good question.
Mind you a Dealer will get this result 7 times in 1 million sessions of 139 hands or once in 20 million hands but why does it happen on my stag ?
Drawn cards from 7-17:
If there is any part of online Blackjack that arouses suspicion it is those cards that are drawn. In a b&m casino you have the comfort of watching; in an online casino the system has to know your bet, the dealers cards and your cards. You dont have to be paranoid to be wary so how did it go.
Well it is a little strange. The Dealer drew 67 cards and managed to draw twelve 7s; the Player drew 89 cards and managed to draw twelve 8s and eleven 10s. The chi squared test results for these distributions are:
Dealer: 0.029.
Player: 0.467
Total: 0.66
Clearly, the Dealer is on something. A result of 0.029 is an indication, nothing more, that something is amiss but every result for the dealer is amiss. The Players and the Total results are normal.
On 30th December 2007 Nashvegas wrote:
I am only concerned with actual totals or skewed results that favor the house but are within the wiggle room of expectation thus allowing the software to be declared statistically fair even though it may be statistically and consistently skewed.
That I think is an excellent point. You can skew things and remain within the bounds of reasonability but if they all skewed in the same direction the overall result is horrific. In the result above the Dealers drawn cards are very suspect but if you were simply to evaluate the total of drawn cards then nothing would appear to be amiss.
In all the posts that I have read members are talking about streaks, losing runs, bet size and the arguments are endless. One thing we all know is that there are 52 cards in a deck made up of four suits with 13 cards numbered from 2 to Ace. Removing or adding cards is not allowed, it alters the odds. If we paid more attention to the cards that are dealt and to whom they are dealt, and at what count they are drawn I think we would learn a great deal.
For a first post I think that is more than enough.
Happy hunting.
CGB.