# Online Blackjack Analysis:

#### cbrodley

##### Dormant account
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.

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.

You think BJ online is single deck game? I am sure 90% is 8decks or more, shuffled each time....

You think BJ online is single deck game? I am sure 90% is 8decks or more, shuffled each time....

Not at all. But the number of decks and a random shuffle makes no difference to a deck of cards nor to the odds; there are still 52 cards in 4 suits and the odds of drawing a particular card remain the same if all decks are standard.

CGB

Not at all. But the number of decks and a random shuffle makes no difference to a deck of cards nor to the odds; there are still 52 cards in 4 suits and the odds of drawing a particular card remain the same if all decks are standard.

Actually the number of decks is very important, and matters a lot. The more decks, the more the casino wins. So modelling an 8 deck game on a single deck is a bad move.

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.

A more typical game would be 49%/42%/8% Try this:

And you experienced a 1 in 100 event.

How many people play blackjack at The Bellagio each day? A lot more than 100.

So that kind of result will happen to someone there nearly every day (usually more than once).

Would you complain?

No.

So why complain when something pretty normal happens online?

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 .

I won't disagree with that. But as that statement fails to define 'sufficiently skewed', it means nothing.

And what that comes down to is 'yes, 139 hands is much too small a sample', if you are talking about some reputable casino software, such as cryptologic/rtg/microgaming/playtech/wagerworks/etc.

But if you are talking about an unknown casino with novel software, then it could well be sufficient to create a presumption that the casino is bad. Not proof. But enough to say 'run away, there are 15,000 other online casinos to play at'.

But you haven't stated, so the value of your statistic is not that high at the moment.

'Online blackjack' covers a multitude of sins.

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 ?

To clarify:

In 139 hands, the dealer was dealt two cards adding to 17-21 (inclusive of bj) 51 times?

And of those 51 hands, he won 32 hands, pushed 8, and lost 11?

And why are you saying there should be 2 bjs for player and dealer? 139 hands / 21 is ~ 7, not 2.

The dealer got the expected number, you got less, about a 4% chance (1 in 25 trials), but this doesn't really take us further than we were above - your losing more hands than expected and you getting fewer blackjacks than expected are heavily correlated, so this statistic doesn't reveal anything worthwhile.

As for your 0.00000671 statistic, you seem to be working on the assumption that if the dealer has 17-21 from 2 cards, then he has only a 50/50 chance of winning.

This is completely incorrect.

Given that the dealer was dealt 17-21, he is not going to bust. You, as the player OTOH, are highly likely to bust, because with a hand of 17-21 there are the following combinations

TJQK - 7
TJQK - 8
TJQK - 9
TJQK - TJQK
9-8
9-9
9-A
8-A
7-A
6-A
TJKQ-A

and their reverses

All of those hands would have an upcard of 7-T + A. All of which leave the player hitting hands up to and including 16 - which spells a very high chance of busting, i.e. losing before the cards are even turned over.

And the most likely dealer hand of all is 20. Clearly a dealer hand of 20 is a HEAVY favourite.

So it's just nonsense to say that the dealer winning 32 out of 51 with two first cards of 17-21 is unusual. In fact, it sounds about right to me.

The player's result is actually the subpar one - with a 17-21 hand, the player should win the majority of hands - once again, he has a strong chance of having 20 (very strong), as well as blackjack. That you only won half is once again about a 3% event - nothing strange considering we already know you experienced a 1% loss on your session.

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

You're fishing.

Your post gets worse as it goes on.

So what if the dealer got 12 7s?

7s are not even a good card. There are so many things you could measure, they're not all going to come up exactly on distribution. Cherry picking statistics that are not even meaningful and saying it proves cheating is no use to anybody.

FWIW, the odds of the dealer drawing a 7 will not be 1 in 13. Why? Because the cards in the dealer's hand influence the remainder of the deck - if one of his cards is 2-5 then he WILL be hitting, whereas if he has a 7, then if he as a JQKT or A, he's going to stand - if dealer has a 7 in his hand, there are 5 out of 13 ranks that will force him to stand. Obviously the 2-5 + another card hand (dealer MUST hit) compared with 7 + another card (high chance dealer has 17 or 18 = STAND), means the deck will be richer in 7s than you're assuming, and the conditional probability that a card dealt when a player/dealer HITS is a 7, is a lot more than 1/13.

So your finding that the dealer got lots of 7s and the player lots of 8s and 10s is hardly a surprise, given that the player/dealer is more likely to be hitting when he HASN'T got one of these cards in his hand, and accordingly they will occur more frequently in drawn cards than your naive model assumes.

If you want to model this, write a blackjack simulator, tell it to perform 139 hands a hundred thousand times, and then look at some of the losing results.

The distribution of those results (i.e. the distributions conditional on the player losing fairly badly (something that will happen on a regular basis)) would display similar 'unlikely' results to those you are claiming to suggest show that something is awry for this result.

Thank you Lawnet for such a detailed response. I'm not at all sure what fishing is but I was genuinely looking for comment.

Can I make it clear that nobody was accused of cheating; I was seeking to understand. There is too much in your response for me to understand off the top of my head so I'll go away and study it and come back to you later if I may.

Thanks again

CGB

Thank you Lawnet for such a detailed response. I'm not at all sure what fishing is but I was genuinely looking for comment.

If you want to conduct a statistical test, you need to establish what it is you attempt to prove or disprove before you do so.

Finding patterns/anomalies in data AFTER you've done the play is simply fishing. You can find 'patterns' in anything.

Good post cbrodley .

When you were saying the software knows all your bets etc I can understand what you mean. But given the industry has been going over ten years and BJ has a 0.5% advantage for the casino, don't you think this may have been exposed by now? Also as many players don't play correctly the real take is more like 1.5%. Rather than focusing on cheating players a casino could make a lot more money by attracting a lot of players to turn over a lot of money. So for all the successful casinos cheating would not really increase their profits.

You also said that in a B&M casino you have the reassurance of seeing the dealer at work. But be assured if a skilled dealer was dealing off the bottom of the deck you would never be able to see it. It may be counter intuitive but it's a lot easier to cheat at a B&M casino than online. If you have magician training then it would be easy to falsify and cheat with decks. Also the player has no hand history or audit trail to look at.

IMO the major software providers are safer for players than B&M casinos.

However as thelawnet said not all software is safe so you are correct to be vigilant.

Thank you Diamond Geezer. Let me accept all that you, thelawnet and casinojack have said with one exception.

I said in response to casinojack that multiple decks did no affect the odds since 13/52 is precisely the same as 1300/5200. Multiple decks and cut card make it difficult for card counters but should not affect the odds. If they do I should like to know how and why. In fact multiple decks and continuous shuffling should keep the odds very stable because discards have a very minimal impact.

My scepticism, (paranoia ?) remains. It is correct to say that my experience was a 1% experience and will happen everyday to somebody but the recurrence of 1% experiences to the same person is of concern. You only have to read these boards for confirmation that this concern is fairly widespread. I'm tired of the Dealer playing 5-J-6 and the programmer being so lazy they seem always to be the same cards !

Enough for now. I would thank you guys for your responses but I don't know how to find the Thank you button.

Cheers

CGB

Thank you Diamond Geezer. Let me accept all that you, thelawnet and casinojack have said with one exception.

I said in response to casinojack that multiple decks did no affect the odds since 13/52 is precisely the same as 1300/5200. Multiple decks and cut card make it difficult for card counters but should not affect the odds. If they do I should like to know how and why. In fact multiple decks and continuous shuffling should keep the odds very stable because discards have a very minimal impact.

For an infinite deck, then given that you have a ten, the chance of an ace (for blackjack) is 1/13. For a single deck, the chance is 4/51 - more than 1/13.

So for a single deck, you are more likely to get bj, which pays 1.5. The more likely you are to get bj, the more you will win.

That's one way that single deck is different. There are others.

Thanks thelawnet, that was quick, you must be awake 24/7.

Actually that much I had figured. The exact odds are 0.0196078 to 0.0192307 or 4.7 occurrences in 100,000 ! That I should live that long.

This sort of emphasises my point. From what you and casinojack were saying made me think I was missing something major. Such miniscule shifts in the odds (even accumulated) do not account for much that is reported on this board and yet they are represented as if they explained things.

The truth of the matter is that they don't. They would make a difference to the casino margin at the end of the month but the difference in odds for an individual player would go unnoticed. Something that happens once every 25,000 attempts would not even register, and nor should it.

Cheers

CGB

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