# Blackjack probability question for BJ players

##### Webmaster
I am not as good at figuring out math when it comes to blackjack so I ask that those who are great at it help me.

I played blackjack at a place I felt was fishy because the dealer kept having 20 or blackjack dealt so I decided I would come back again later and start to track the play.

In session 1 I played 230 hands I counted each time both of us were dealt 20 or BJ. In 230 hands the dealer had 16 blackjacks, I had 4. The dealer dealt himself 29 20's, I was dealt 20 14 times. I emailed and asked for the logs and got them very quickly.

In session 2 I played exactly 200 hands. The dealer had 14 blackjacks, I had 2. The dealer was dealt 20 32 times, I was dealt 20 11 times. I have emailed the casino and asked for logs to this session repeatedly and have yet to have a response.

Obviously the results are very screwed up. Do I have enough hands to make this mathematically useful? Do I need more hands? What are the probabilites of the above results? Thank you in advance.

I should include that in the 2 sessions combined of 430 hands I lost 25 units. The number of busts seemed normal and my number of double and splits wins seemed normal.

The probability of getting 6 or fewer BJ's in 430 hands is between 0.00011 (1 deck) and 0.00014 (8 decks). The probability of getting 30 or more BJ's in 430 hands is between 0.024 (8 decks) and 0.029 (1 deck).

When you talk about dealing 20s, do you mean just the first two cards?

Yes I only counted the first 2 cards. I counted A9 or two 10 value cards. I already assume the dealer will get more 20's since he will draw more often thus making that kind of useless info.

GrandMaster said:
The probability of getting 6 or fewer BJ's in 430 hands is between 0.00011 (1 deck) and 0.00014 (8 decks). The probability of getting 30 or more BJ's in 430 hands is between 0.024 (8 decks) and 0.029 (1 deck).

Would you agree that, given 36 BJ's, the odds of the player getting 6 or fewer is about 1 in 28,700?

It's not like the total number of BJ's is that far off.

Obviously losing 25 units in 430 hands ain't no big deal. Wish that was all I lost yesterday.

The probability of being dealt 25 or fewer 20's in 430 hands is between 0.00036 (8 decks) and 0.00078 (1 deck). The probability of being dealt 61 or more 20's in 430 hands is between 0.00041 (1 deck) and 0.00082 (8 decks).

If you count BJ's and 20's together, it gets worse. The probability of being dealt 31 or fewer BJ's or 20's in 430 hands is between 0.00000024 (8 decks) and 0.00000048 (1 deck). We are talking about probabilities between 1 in 4 million and 1 in 2 million. The probability of being dealt 91 or more BJ's or 20's in 430 hands is between 0.00047 (1 deck) and 0.00082 (8 decks).

The results are indeed very suspicious. Would you share with us what software it was, or at least PM me if you don't want to make it public?

A BJ occurs about once in every 21 hands.

I pm'd the casino where this game took place to Grandmaster. For now I do not wish to start trouble, especially because they are a sportsbook and I have NFL futures on who will win Superbowl, one team I bet has a great chance as a 35-1 underdog so I dont want to start public trouble.

Should I email them this thread and ask them to explain how my 2 tracked sessions were possible? Should I go back and get more hands (betting \$1 a hand now) to make it more mathmatically useful? I have beaten this game in the past, and I have played many many hours before busting in the past too. The last few sessions just seemed impossible which is why I decided to track it.

let me guess. is it an one of those EFS carribean processing casinos? such as betonusa.com or silverstarcasino?

I pm'd the casino where this game took place to Grandmaster. For now I do not wish to start trouble, especially because they are a sportsbook and I have NFL futures on who will win Superbowl, one team I bet has a great chance as a 35-1 underdog so I dont want to start public trouble.

Should I email them this thread and ask them to explain how my 2 tracked sessions were possible? Should I go back and get more hands (betting \$1 a hand now) to make it more mathmatically useful? I have beaten this game in the past, and I have played many many hours before busting in the past too. The last few sessions just seemed impossible which is why I decided to track it.

I sure as hell wouldn't go back for more of the same. I'd hav't to think that Jersey's guess is a pretty solid one. Have a good one.

Should I email them this thread and ask them to explain how my 2 tracked sessions were possible? Should I go back and get more hands (betting \$1 a hand now) to make it more mathmatically useful? I have beaten this game in the past, and I have played many many hours before busting in the past too. The last few sessions just seemed impossible which is why I decided to track it.

Well I wouldn't worry about it all that much - I guess overall I wouldn't go so far as to classify it as "very suspicious". After all, the total number of BJ's and 20's aren't that far off. And, overall, being down 25 units is nothing. And you say you've played in the past with nothing apparently crazy.

I'm not sure what the point of combining these 2 probabilities is either. I mean if I'm dealt the same 2 cards twice in a row against the same dealer up card, the odds are billions to one but so what. I think this should be analyzed as 2 separate events. So I get 1 in 6800 (8D) for the player BJ's and 1 in 810 for the 20's. Or even 1 in 2800 for 20's, your worst number.

Maybe it's just what questions you ask. What if one just asked what are the chances of 36 BJ's or 86 20-totals in 860 hands? Like 1 in 20 or so for each, right?

I'd still get the logs for these 2 sessions and ones in the future if you decide to play more.

GM - I'm getting higher chances of player 20 than you - what prob are you using? (I'm using .01134 for A,9 & .08911 for 10,10 for 6D from a table.)

As a side-question, what would you find to be the most overall fair indicator for a fair game? I guess I always think it's units up or down over hands played in the absence of first 2 cards vs dealer upcard.

I have had a massive win and a couple of smaller ones. I am still waiting on the other logs. Like I said everything else was normal, or maybe it was even in my favor more then normal. I will look into this when i get the logs for session two. This is why I didnt put the places name in the post. The loss is not all that staggering, just the number of BJ's and 20's for the dealer were impossible. I had a lot of lucky hits into his 20's too to help with some of them. I have to think something is off for there to be such odd outcomes on different days. I will wait a few days and try again and see what happens.

I guess if the loss is in the expected range it does not really matter what gets dealt to determine fair.

As a side-question, what would you find to be the most overall fair indicator for a fair game? I guess I always think it's units up or down over hands played in the absence of first 2 cards vs dealer upcard.

Units up or down is my vote

I played with my winnings off the game last night and had a very normal game. In exactly 100 hands I had 5 BJ's, he had 4. We were dealt 20 exactly the same number of times and just as before the splits, doubles and busts were normal and I lost .5 units which is about exactly what it should have been.

On another math impossibility note I was dealt BJ in spanish 21 at 32red today 4 times in a row. At least the impossible was in my favor. I love that game and its too bad more dont offer it, I guess not enough house edge.

I don't know why. but I continue to have very very bad results playing MG's BJ.

Just finished a session of 32 hands.

lost 22 hands
win 7 hands
push 3 hands.

I lost the last 16 hands in a row until my bankroll went to zero, no push in between. about -2.4 SD. Not very bad indeed compared to my previous result.

And yesterday in 80 hands down 30 units. -3.0 SD Max lossing streak is 10 no push in between.

Last edited:
ftg said:
I don't know why. but I continue to have very very bad results playing MG's BJ.

Just finished a session of 32 hands.

lost 22 hands
win 7 hands
push 3 hands.

I lost the last 16 hands in a row until my bankroll went to zero, no push in between. about -2.4 SD. Not very bad indeed compared to my previous result.

And yesterday in 80 hands down 30 units. -2.5 SD Max lossing streak is 10 no push in between.

That sort of streak's very common at MG casinos - presumably it's not really random but as with other on-line casino software it's almost impossible to prove. At MG at least you seem to get comparable winning streaks and it evens out in the long run. Best to autoplay to the lowest possible stake and leave it to play in the background to avoid unnecessary stress What they want is for you to play a negative progression or chase losses in which case the streakiness will usually make very short work of your deposit.

On another math impossibility note I was dealt BJ in spanish 21 at 32red today 4 times in a row. At least the impossible was in my favor. I love that game and its too bad more dont offer it, I guess not enough house edge.

Even more remarkable in that one gets BJ maybe once every 23.5 to 24 hands in Span 21. It is alot nicer when the impossibility is on your side.

I like to play Span 21 in B&M casinos due to the lower house edge and the fun of extra pay-offs. Last trip I had 2 7 of spades vs a dealer 7 for the possible \$5000 super-bonus. It was fun til the 5 of spades came out.

What is the HA of Span 21 where you play?

Clayman said:
GM - I'm getting higher chances of player 20 than you - what prob are you using? (I'm using .01134 for A,9 & .08911 for 10,10 for 6D from a table.)

I agree with you on the probability of A,9, but I get 0.09399 for the probability of getting two 10 value cards.

I did the Aztec Riches sign up bonus \$100 for \$100. Did 50 cents autoplay BJ in bonus account. Busted before it even got close to the 20x WR. Did the real account and same thing happened!

I am kinda scare of MG BJ now!

GrandMaster said:
I agree with you on the probability of A,9, but I get 0.09399 for the probability of getting two 10 value cards.

Thanks - the table was for playable hands so it did not include player hands vs dealer BJ.

DrNo888 said:
I did the Aztec Riches sign up bonus \$100 for \$100. Did 50 cents autoplay BJ in bonus account. Busted before it even got close to the 20x WR. Did the real account and same thing happened!

Seems a bit unusual you could lose 2 200-unit bankrolls consecutively in 3600+ hands or less in each account of wagering. I'd think your risk of ruin would be less than 1% in each case. Way less with fewer hands.

Did you change the auto-play table appropriately?

How many hands did you actually play on each account?

On another math impossibility note I was dealt BJ in spanish 21 at 32red today 4 times in a row. At least the impossible was in my favor. I love that game and its too bad more dont offer it, I guess not enough house edge.
The house edge of Spanish 21 depends on the exact set of rules, with unfavourable rules (H17 and no redouble) it is 0.76%, with better rules it is about 0.4%, comparable to a 4 deck BJ game. I am sure that fewer people know correct Spanish 21 strategy than correct BJ strategy, and Spanish 21 is less vulnerable to counting, so Spanish 21 is actually a better game for the casino.

It doesn't surprise me at all that Clayman plays Spanish 21 in land based casinos. It has the lowest house edge of any game in Atlantic City, with the single exception of craps w/5 times odds. (5x odds craps has a much greater bankroll requirement than Spanish 21)

Here is the link to Michael Shackleford's article on Spanish 21:

There were two mistakes in the original Casinio Player article.

1) Casino Player printed 2 basic strategy charts. One chart was for "dealer STANDS on Soft 17", the other chart was for "dealer HITS on soft 17". Well, in the final published article they accidently switched the two charts. I ended up playing the HITS on 17 chart even though I was playing the Atlantic City game. It cost me a few \$\$\$, and I wan't at all happy about it. It took months before I saw the correction.

2) Shackleford stated the house edge as 0.34%, which he later corrected to be 0.40%. (Dealer stands on soft 17). I'd like to know the reason for his error.

Michael Shackleford (otherwise known as the Wizard of Odds) has all the correct basic strategy info listed on his website:

Better yet, his website compares the house edge of almost every major gambling game around!! And he introduces a new concept called the "element of risk":

The only game that has a lower house edge is Las Vegas single-deck bj!

The "element of risk"(average loss divided by total money bet) of Atlantic City's Spanish 21 is only 0.30% (despite a house edge of 0.40%)

However conventional AC bj has an element of risk of 0.38% (depite a house edge of 0.43%)

This means there is a significant advantage to playing Spanish 21 as opposed to playing conventional bj.

Better yet, at almost every casino in AC, the dealers CONSTANTLY make the mistake of paying bonuses on SPLIT hands. For example splitting 8's and being dealt 6,7,8 on one of the split hands. Dealers almost always pay 3:2 despite the hand being split. Sometimes the dealers have to get pit approval, but I rarely been denied bonus payments on these hands. THIS definately lowers the house edge even further.

Oh, and not to mention all the mistakes dealers make in the players favor, that they don't make on conventional bj. IE. when you get a total of 10 or 11, dealing you another card automatically without letting you double. Then if you get a good hand, you ask the pit to let you double, and if you get a lousy hand you keep hitting.

Some casinos comp better than others, so if you do a lot of shopping around, you'll usually find a casino whose comps are lucrative enough to not only overcome the house edge, but to give the player a tiny advantage. Better yet are promos where a player can get double or triple comps on certain days.

Only once in the past 3 years of playing did I get a "super bonus oppotunity". I had two 7 of diamonds vs. the dealers 7 of spades. When I hit my hand, I received an 8 of diamonds. I was really pissed.

In 5 years of watching the game being played I never saw anyone win the super bonus. But once at Trump Plaza, I saw an Asian guy get the opportunity for the Super bonus, and since I was standing right there I told him NOT to split his 2 7 of spades, since he could win \$1000. He heard every word I said, but wouldn't listen to me. Right after he split, the 3'rd 7 of spades came out of the shoe. He didn't even realize just what he had given up.

Hi Dave
Yes, I think the "elelment of risk" is even a better guide than HA.

Not 100% sure but I think it's right to pay on a 678 after splitting - in fact all bonus 21 hands except the Super-bonus which is not allowed after splitting. The bonus 21 hands are only not allowed after doubling, I believe.

Speaking of playing with the wrong BS, I could tell from across the table one guy was using the H17, no re-doubles card for the S17 game. When I told him, he kept using it anyway saying "it's better than nothing".

The dealers do make alot of mistakes and pass you by very quickly. For me, especially on 17 vs Ace when you want to surrender and the famous 3-or-more-card 17 vs Ace that one should hit. No one ever likes that play

I guess you can't blame the dealer too much for dealing it like BJ since most players seem to play it like BJ.

Sadly, with the 6-5 BJ payoff for single-deck BJ, it no longer is the best game - really about the worst now.

As far as that poor Asian guy who may have heard but apparently didn't understand, that really, really hurts. No one should have allowed that to happen. In my case the dealer had to get the pit boss who had to phone upstairs and wait for the "eye in the sky" to take pictures. Only then would he deal the last card. It took 6-8 minutes. Kind of hard to split after that!

Courtesy of Grandmaster: (so you know it's right!)
Odds of getting the opportunity of 2 suited 7's vs dealer 7 are about 1 in 8360.
Odds of achieving 3 suited 7's vs dealer 7 are about 1 in 550,000.
Odds of getting 3rd suited 7 after you have the first 2 average about 1 in 66, a little less if dealer's 7 is suited and a little more if it is non-suited.

Don't you love how they pay you 200-1 max for something that happens once in 550,000 tries. If I ever bet \$5000/hand, I bet this is the hand I'd get dealt.

Clayman said:
Hi Dave
As far as that poor Asian guy who may have heard but apparently didn't understand, that really, really hurts. No one should have allowed that to happen. In my case the dealer had to get the pit boss who had to phone upstairs and wait for the "eye in the sky" to take pictures. Only then would he deal the last card. It took 6-8 minutes. Kind of hard to split after that!

Why do they need to take picture? Just to prevent the dealer from colluding with you or in case you do a sleight of hand?

I wonder what the asian guy's face looked like! Or he didn't know there was a bonus to be had even after the event?

sw2003 said:
Why do they need to take picture? Just to prevent the dealer from colluding with you or in case you do a sleight of hand?

I guess - they just said "No one touch the table" and that this was their policy (Casino Niagara). Even going so far as to say, had the dealer not followed this policy, there could have been a problem with being paid.

So for 6 minutes, I had time to figure out in my head I had a 1 in 66 chance of just how I was going to spend \$5000 tax-free dollars!

I don't know about his face but it wasn't pretty when someone hit a \$50,000 progressive with only one coin bet!

Question Online blackjack
Replies
9
Views
2K
Replies
50
Views
4K
Replies
213
Views
14K
Replies
1
Views
3K
Replies
8
Views
3K