What are the odds of getting an 8 card 20?

Note: The bulk of this post was already posted by myself on another thread.

And what are the odds of the dealer drawing 7 card 17-21 more than 5 times in a 50 hand sequence? I have observed this occurence 6 times now in single week alone playing at Bet21.com

Is there something wrong with the RNG at Bet21.com?

Folks, the question has been raised, and the only way to answer it is this - someone needs to independently collect the data in large enough amounts required to do the analysis properly and determine whether the RNG is delivering properly.

And no, I am not volunteering for the data analysis job.

I would posit that since Dave and Joe (among others) are taking the stance that nothing is wrong with the cards, then they should also be happy to see an independently published analysis to --empirically-- allay any fear that there is a problem. Maybe they can arrange for it to be done? Maybe not....

Now for the gasoline.

As you may know, I have even gone so far as to play the cash tables at Bet21.com. I suggest that the logs of the cash tables, since I am told they use the same RNG engine, would provide more than enough data should someone with connections (Dave? Joe?) at UB get access for the purpose of such an analysis based on a list of standard, most often used discrete points for verfiable and significant results, and make the results public. There are likely 10s of millions of hands logged.

So, NOW, lets go off on THAT tangent.....

One of the first items I personally would like to see included are the probabilities/percentage of dealer hands made from 6, 7, or even 8 cards. Yes, 8 cards. Perhaps even 9? LOL, can't believe I suggested that....though it is mathematically possible....hence it must happen....in some corner of the universe....

I have never seen a dealer make either an 8 or 9 card hand in live play in all these years. I have never had one myself.

Within just months I have seen dealers make hands with 8 cards over 10 times playing at Bet21.com - and 6 or 7 cards is common enough that it is a common topic of conversation among the cash players. Mind you, I don't rule out that it is likely "short term" sampling of data, but I just made my own 8 card 20 for the first time ever tonite on those same tables.....and it was spooky......only at UB.....

I know that there was scatalogical relevance when I got those 8 cards -- but what is the statistical relevance of a single instance?

Again, until a truly detailed analysis is done, we are all playing on good faith expectations. If you play at Bet21.com, you are taking that leap of faith OF YOUR OWN FREE WILL just like at any other casino.

In meantime, my advice to everyone is to get your ass up from in front of your computer and go interact with live humans at a bricks-n-mortar casino more often. Play some single deck where these statistical variations are less volatile and don't impact an Elimination other than to eliminate a few chips from either the dealer's tray or your own stack.....

Kaminari

 

tiny

Kaminari

I'd love to answer your question but when I asked a month or 2 ago what the odds of a 5 card charlie were nobody was able to answer.

This does lead on to a question of my own which I hope will lead one way or another to answer to your question.

When I was working on a small probability calculator a few months back I looked at up to 8 card hands and recognized that the odds of them occurring was very, very small. So when pondering your question I thought I'd play around with some numbers and came up with some results that surprised me and makes me wonder whether they were correct in anyway.

Here's what I did: I assumed the probability of a 7 card charlie was about 1% so I wanted to calculate the probability of it happening in a 50 hand sequence. The answer I came up with was 30.6% which just seems odd to me, I don't know why. I calculated it this way - (0.01 x 0.99^49) x 50. Is the equation anyway near correct?

Cheers

Reachy

 

8 decks

The chances are OK to draw 8 cards to 20 from an 8 deck shoe. Most of the time you would see the dealer do it tho. Playing single deck games has the dealer drawing 6 cards from time to time, so if you have 8 decks it doest seem unthinkable to grab 8 cards. But, if you saw it happening time and time again it would fit the odd dealing cycles spoken of here.

You just never know about things in life, I was going on a camping trip today and a freak snowstorm shut the roads down at 4000feet for Murphy's sake.

 

Thanks for the attempt

Reachy,

Lets not use an assumption.

Since I am not a formally trained professional statistician I was hoping someone would confidently lead me to an equation to use. I have however verified that a dealer 5 card "charlie" appears approximately 1.2 percent of the time on 6 deckers, and that dealer 7 card make appears approximately .01 percent, whereas dealer 8 card make would be .00045 percent.

According to the table below, you would need to play approximately 210,000 hands (2,128,834,249/10128) to expect to observe dealer make an 8 card hand once, thus the number of times I have seen it (10) you would expect me to have played well over 2 million hands during the three month period of occurence. I don't think I've spent THAT much time playing. And my memory isn't THAT selective either.

This leads me to the suspicion that the odds of seeing what I have observed are beyond astronomical since I don't think I have played anywhere near 200,000 hands in the past 5 years.

Can someone come up with an equation using the data supplied that predicts the probability of dealer make on 7 cards 5 times within a 50 hand sequence even one time? As I have said, I have observed this 6 times in a single week of play on the Bet21.com cash tables.

How about back-to-back 7 card make? 3 in a row...?

I am sorry, but I think something is either wrong with my math, or wrong with the RNG on Bet21.com cash tables. I know what I have seen, so I hope my math is just bad.

K

>>>>>>>>>>>>>>>>>>>>>>>>>>
Below is from a table found on Wizard of Odds listing the probabilities of dealer make hands for 6 Deck s17 DS RSA from the following number of cards (heads up play). I made slight format edits to accomodate the cut-&-paste, but changed none of the statistical info. The URL is: http://wizardofodds.com/askthewizard/blackjack-faq.html

Dealer Hand Probabilities
Event Observations/ Probability

Dealer blackjack 97940000 0.0474278361
Player blackjack, no dealer blackjack 87823688 0.0425289716
2 cards 406164309 0.1966866886
3 cards 453039024 0.2193859565
4 cards 151522915 0.0733755767
5 cards 26606271 0.012884193
6 cards 2903511 0.0014060368
7 cards 205782 0.0000996508
8 cards 9253 0.0000044808
9 cards 268 0.0000001298
10 cards 3 0.0000000015
Total Hands Observed 2065032016

Player Hand Probabilities
Event/Observations /Probability

Player blackjack 97936983 0.0460049828
2 cards 1193785045 0.560769372
3 cards 325677353 0.152983894
4 cards 120180207 0.0564535295
5 cards 19891981 0.0093440722
6 cards 2248456 0.0010561912
7 cards 181767 0.0000853834
8 cards 10128 0.0000047575
9 cards 376 0.0000001766
10 cards 10 0.0000000047
11 cards 1 0.0000000005
Total Hands Observed 2128834249

 

Gotta agree with Kam here..

I have played a little reg BJ but watched the high rollers more often.(its amazing how many HR shoot 200 a hand for hours and they recieve not one bonus dollar,comp point,hotel,meal,etc....talk about foolish....these guys hitting like that in a real game would earn high comps in any casino, but they play a bad game for nothing...what do they say about a fool and his money?? ;-)

I saw far too many 3 in a row dealers BJ to ever consider this game for more than penny stakes.

I have noticed a difference between reg and tournament dealers...regular game will more often deal stiffs but its easy to hit those up for a total of 19 with dealers ten showing....yes of course its dealer 20 but it feels good to better the stiffs..lol

Ive played tons of 8deck shoes....saw 7 once....never saw 8.

Never saw 8 in a row dealer BJ or 21 either ...but I have on Bet21...

And Id bet money on the number of times a dealer shows at least 2 aces up in the first 8 hands of any tournament game but especially sit and go.

Just start noting how often you are offered "Insurance?" during the first 8...

This is off the charts and enough alone to make the deal suspect.

 

Frequency of hands

Something doesn't look right for the dealer made hands chart from the wizzardofodds. The sum of the probabilities adds up to .5039. If you add the dealer BJ's then it gets up to .5513. Now if you add the probability the dealer will bust .2857 to this you only get .8387 for all possibilities instead of 1.0000.

However there should be a shorter way, other than playing billions of hands, that yields the exact answers. In Peter Griffin's book "The Theory of Blackjack" he gives a simple basic program that will calculate the dealer probabilities. The program goes through all possible drawing sequences. If the program is modified to keep track of each sequence to a dealer standing number or bust there are only 54433 separate sequences in an 8 deck game where the dealer stands on soft 17. For dealer hitting soft 17 there are 70561 sequences.

For example getting to a total of 17 can occur as follows:

10 + 7 has a probability of (128/416)*(32/415) = 0.023726

Another sequence would be 7 + 10 with the same probability.

And yet another sequence to hard 17 would be:

A + A + A + A + A + A + A + 5 + A + A + A + A + A with a probability of 3.7432 E-16 thats 3.7432 times 10 to the minus 16.

A sequence for busting could be 10 + 6 + 8; and another sequence of the 70561 ways is 10 + 6 + 9

Another modified program will have to be written to keep track of the number of ways (and the sums of the corresponding probabilities) for made hands of 5 cards, 6 cards, 7 cards etc.


................................BlueLight

 

Dealer Charlies

Just ran the calculations for various Dealer card Charlies (made hands) for different decks and different dealer soft standing totals. H17S17 = dealer stands on soft 17. H17S18 = dealer stands on soft 18 (hits soft 17)


..........................................1 DECK...................................
........................H17S17..................................H17S18.........

Bust............. .2835854025........................... .2874850247
2 Card.......... .3484162896........................... .3363499246
3 Card.......... .2705279035........................... .2729411765
4 Card.......... .0832911626........................... .0875636408
5 Card.......... .0130162834........................... .0142910498
6 Card.......... .0011097598........................... .0013007036
7 Card.......... .0000519453........................... .0000667259
8 Card.......... .0000012417........................... .0000017385
9 Card.......... .0000000115........................... .0000000157
10 Card......... 1.84616E-11........................... 1.84616E-11
11 Card.................0.............................................0.......


............................................8 DECK...................................
.......................H17S17....................................H17S18.........

Bust............ .2818390975............................ .2856747739
2 Card......... .3490268767............................ .3371640408
3 Card......... .2667866561............................ .2686778328
4 Card......... .0856459545............................ .0900431243
5 Card......... .0149434519............................ .0163878115
6 Card......... .0016352961............................ .0018969524
7 Card......... .0001170223............................ .0001473846
8 Card......... .0000054796............................ .0000077947
9 Card......... .0000001624............................ .0000002784
10 Card....... .0000000028............................ .0000000065
11 Card........ 2.22929E-11............................ 9.35161E-11
12 Card........ 4.90990E-14............................ 7.60949E-13
13 Card...............0..................................... 2.63806E-15
14 Card...............0..............................................0.......

These numbers should be exact since every possible sequence was evaluated.
As a check the busts were calculated separately; then the columns were added to see if the totals came out to 1.0000000000 or close to it.


..................................BlueLight

 

Complete Charts from Wizard of Odds

Some of the info did not carry through the original cut and paste. The charts below now add up to 1.0000000 as you rightly point out they should.

Player Hand Probabilities

Event /Observations /Probability
Player busts 276659980 0.1299584409
Player surrenders 92261962 0.0433391947
Player blackjack 97936983 0.0460049828
2 cards 1193785045 0.560769372
3 cards 325677353 0.152983894
4 cards 120180207 0.0564535295
5 cards 19891981 0.0093440722
6 cards 2248456 0.0010561912
7 cards 181767 0.0000853834
8 cards 10128 0.0000047575
9 cards 376 0.0000001766
10 cards 10 0.0000000047
11 cards 1 0.0000000005
Total 2128834249 1


Dealer Hand Probabilities
Event /Observations /Probability
Player busts first 276659980 0.1339737001
Player surrenders 92261962 0.0446782235
Dealer busts 469895050 0.2275485544
Dealer blackjack 97940000 0.0474278361
Player blackjack, no dealer blackjack 87823688 0.0425289716
2 cards 406164309 0.1966866886
3 cards 453039024 0.2193859565
4 cards 151522915 0.0733755767
5 cards 26606271 0.012884193
6 cards 2903511 0.0014060368
7 cards 205782 0.0000996508
8 cards 9253 0.0000044808
9 cards 268 0.0000001298
10 cards 3 0.0000000015
Total 2065032016 1

 

gnats jade stalk

I'm surprised that the numbers are so small for 7 and 8 card charlies. Since 99.87% of my blackjack playing is online I guess I must be used to seeing them!

I can answer 1 of your questions Kam. Here are the probabilities for sequential charlies:

5 CC

1=1.494%
2=0.0223%
3=0.0003%

6 CC

1=0.1635%
2=0.000267%
3=4.37072^-7%

I probably don't need to go on do I? For a 7 or 8 CC the odds of sequential episodes occurring will be infinitesimally small. Doesn't mean it won't happen though...



Cheers

Reachy

 

1 deck

I think the numbers, looking at from the wiz and BL, are right at about 1.3/1000 to draw 6 cards no bust. I saw the dealer do it twice last trip from a single deck dealt at least 50% pen. But Im confused to the logic when its compared to the 8 deck with same rules as it says 1.9/1000 for 8 decks. Ignoring the 'hard' math it would seem with all the small cards in multiples of 8:1 and small cards out numbering 10s by 2.25:1 there is a much better chance of smalls clustering- hence a better chance of getting a line of cards under face value of 5. But, the math works out to 1.3 vs 1.9. Interesting at least. In this case, Kam is investigating at bet21, if you see 8 card runs time after time that isnt right. For 6 card draws at about 2 of 1000 hands its not unthinkable to see the 5 and 6 card draws tho, from time to time because you could get lucky and sit at right times.

BTW, the math tables for the players cards are not accurate IMO, people at tables playing in real life, not a computer using infinite deck, wont keep hitting. The very thought/emotion of busting separates them from the math model.

 

More example of why this site needs to assure the good paying customers of a fair and random deal...

What are the odds?

 

What ARE the odds?

Guys,

What makes these extreme events even more puzzling is the claim that the cards are a 6 deck shoe shuffled after every hand -- or aproximately 40 cards, depending on who you hear tell it.

What are the odds of Rando's example given even a 40 card shuffle sequencing?

This behavior of extreme swings to both small and large cards at both ends of the spectrum makes me speculate that we are more likely playing with an "infinite deck" that gets shuffled after EACH CARD, just a random generator spitting out cards.....

Caveat Emptor

Kaminari

 

do agree with your concern ken. although i am not of great mathematical inteligence as yourself and many others on this site, there does seem to be something fishy with bet21. i have decided to play down the monies that i have left in my account and do not intend to continue to support bet21 with future play. i hope that i am wrong and it can be proved in the future that bet21 is legitimate in their presenting of their games, as well as their overall operations.

 

quantum

4 sequential BJs = 0.000426883%

Approximately

Cheers

Reachy

PS. Like your lunar background.

 

Yet Another Sighting!!!!

Saw another 8 card dealer make tonite.....

 

Kam,

Press screen shot when you see those....that way if Bet 21 ever does decide to do the right thing then they can track suspect hands and explain how it is normal and random.

 

Probability of 8 card Charlie

I have played BJ off and on since 1978. I think I have seen only "one" 8 card Charlie. In a 6 deck game where the dealer hits soft 17 the probability of an 8 card charlie is .000007356814 for any given hand. That's one chance in 136,054.
If you were to play a hundred hand session of BJ then the chance of at least one 8 card charlie is one in 1361 sessions.
Something must be wrong with the RNG for that site. Maybe low cards come out in a clumps at certain times.

............................BlueLight

 

When I was dealing, I dealt one 8 card and two 6 card 21's in one 20 minute rotation on a double deck table, so while it isn't likely, it does happen. Dealt other 6-8 card but not close together like that.