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  #11  
Old April 11th, 2010, 10:30 PM
k_c k_c is offline
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Originally Posted by DMMx3 View Post
I am pretty comfortable with statistics and do not think there is anything blatantly inaccurate about my findings or the methods used to collect the data.

I tested from the beginning because I could not believe that the casino as it seemed would offer a fair game. In fact, I never saw a card that I didn't track. (I guess I'm the Will Rogers of card tracking...or something.)

I tested a hypothesis based on the overall RC of all cards seen. I ran 10000 trials of the same number of cards (in the same number of shoes), and got a p value of ~.02 for obtaining a net RC of my result, or lower.

Also, I tracked all cards, not just my hands and the dealers (I am guessing that is what you were getting at with the 2175 hand assumption?) Sometimes I played the dealer heads up, other times it was a fuller table of 5 or more players. I don't have a count for the number of hands I (or the dealer and I) played, but that doesn't seem relevant anyway.

Do I need more trials? Well to be ~2% confident, no. But I would like to increase the confidence, and thus, as I stated, I plan to continue tracking.

Feel free to PM me if you would like to see all of the data. I have it in a pretty simple excel file.

Data Summary:

Cards tracked: 9789
Shoes tracked: 45
Overall RC: -94

A while back I was running sims in order to find a way to do analysis to compare different counting systems using basic total dependent strategy and variable bet spreads.

Anyway I somewhat surprisingly found average pre-round running count to be negative in every sim. This was just an effort to begin using combinatorial analysis in conjunction with simulation, so there isn't a lot of data because each composition is computed for EV using basic strategy prior to each round and when I did them I had a very old slow computer. Sims were heads up, player vs dealer.

I found some old spreadsheets with some results.

2 decks, 1000 shoes, 13018 rounds
Average HiLo RC = -0.28, Average HiLo TC = -0.23

6 decks, 164 shoes, 7516 rounds
Average HiLo RC = -0.28, Average HiLo TC = -0.16

Anyway I think average (HiLo) RC will always be less than 0 in the long run because a lot of hands end with being busted, and there are a lot of pat, undrawn to hands consisting of mainly high cards.

I made an open source Excel Spreadsheet to display data. It comes with a sample data file that you import into an empty spreadsheet template by running a macro called ImportData. (You run the macro and browse to simFile.txt.) There are some macros you can run once data is imported and I made an effort to allow for adding and switching counts as well as changing spreads. If you want to download, the link is at the bottom of the page. I'm sure it'll show average running counts are negative.

The sample data is for single deck. I have a spreadsheet on my old computer that I think is displaying the sample data. It is 500 shoes, 3037 rounds. Average HiLo RC = -0.11, Average HiLo Tc = -0.12.

My email through my website isn't working right now and my web host's customer service is very poor so the email address listed in the download won't work.

Anyway, this may be what you're seeing in your results.
  #12  
Old April 12th, 2010, 10:04 AM
DMMx3 DMMx3 is offline
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Quote:
Originally Posted by k_c View Post
A while back I was running sims in order to find a way to do analysis to compare different counting systems using basic total dependent strategy and variable bet spreads.

Anyway I somewhat surprisingly found average pre-round running count to be negative in every sim. This was just an effort to begin using combinatorial analysis in conjunction with simulation, so there isn't a lot of data because each composition is computed for EV using basic strategy prior to each round and when I did them I had a very old slow computer. Sims were heads up, player vs dealer.

I found some old spreadsheets with some results.

2 decks, 1000 shoes, 13018 rounds
Average HiLo RC = -0.28, Average HiLo TC = -0.23

6 decks, 164 shoes, 7516 rounds
Average HiLo RC = -0.28, Average HiLo TC = -0.16

Anyway I think average (HiLo) RC will always be less than 0 in the long run because a lot of hands end with being busted, and there are a lot of pat, undrawn to hands consisting of mainly high cards.

I made an open source Excel Spreadsheet to display data. It comes with a sample data file that you import into an empty spreadsheet template by running a macro called ImportData. (You run the macro and browse to simFile.txt.) There are some macros you can run once data is imported and I made an effort to allow for adding and switching counts as well as changing spreads. If you want to download, the link is at the bottom of the page. I'm sure it'll show average running counts are negative.

The sample data is for single deck. I have a spreadsheet on my old computer that I think is displaying the sample data. It is 500 shoes, 3037 rounds. Average HiLo RC = -0.11, Average HiLo Tc = -0.12.

My email through my website isn't working right now and my web host's customer service is very poor so the email address listed in the download won't work.

Anyway, this may be what you're seeing in your results.
This is interesting, and I am pretty sure one of my Blackjack books gets into something like this, though I can't remember any of the specifics. I'll have to see if I can find it.

But, I think you are saying that you found more high cards than low cards, in the cards exposed, correct? In my sample I found more low cards than high cards.

I'm still tracking data, and have about 90 shoes of data at this point. Using R (stat programming language), it seems the confidence that the shoe is "fair" is now 2.9%.

For now I'm playing the game under the assumption that there are some cards removed, and adjusting my estimated advantage based on that. So, if the deck is unfair, I'm playing closer to accurate, and if it is legit, I am playing sort of conservative and hurting my WR (tho helping my ROR.)

Thanks for the post -- if I can find the book that talks about the effect you seem to have witnessed, I'll post more about it.
  #13  
Old April 12th, 2010, 10:32 AM
k_c k_c is offline
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Quote:
Originally Posted by DMMx3 View Post
This is interesting, and I am pretty sure one of my Blackjack books gets into something like this, though I can't remember any of the specifics. I'll have to see if I can find it.

But, I think you are saying that you found more high cards than low cards, in the cards exposed, correct? In my sample I found more low cards than high cards.

I'm still tracking data, and have about 90 shoes of data at this point. Using R (stat programming language), it seems the confidence that the shoe is "fair" is now 2.9%.

For now I'm playing the game under the assumption that there are some cards removed, and adjusting my estimated advantage based on that. So, if the deck is unfair, I'm playing closer to accurate, and if it is legit, I am playing sort of conservative and hurting my WR (tho helping my ROR.)

Thanks for the post -- if I can find the book that talks about the effect you seem to have witnessed, I'll post more about it.
What I'm saying is that running count measured just before a round begins (when player must determine bet size) is on average negative in a game of blackjack, meaning in the case of HiLo, more tens and aces have been dealt than 2 though 6 at the beginning of each round. It would be intuitive to think that if cards are randomly dealt then on average running count should equal 0 in the long run, but this doesn't seem to be the case when a condition of the dealing process is cards are being dealt according to blackjack rules and player using basic strategy when measured at the beginning of a round.

Btw I assign negative tags to negative cards and positive tags to positive cards. By doing that running count can be figured by what remains in the shoe rather than worrying about what has been removed from it.
  #14  
Old April 12th, 2010, 02:48 PM
DMMx3 DMMx3 is offline
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KC -

Yes, I get what you are saying and think that I have read about this effect before. This makes my findings somewhat more unusual.
  #15  
Old April 12th, 2010, 08:42 PM
Nynefingers Nynefingers is offline
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KC, I suspect that at least part of what you found might be attributed to the cut card effect. As you know, when the count is negative, you tend to be more likely to get an extra round. Have you tried the same sims with a fixed number of rounds rather than a cut card?
  #16  
Old April 14th, 2010, 09:04 PM
k_c k_c is offline
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Quote:
Originally Posted by Nynefingers View Post
KC, I suspect that at least part of what you found might be attributed to the cut card effect. As you know, when the count is negative, you tend to be more likely to get an extra round. Have you tried the same sims with a fixed number of rounds rather than a cut card?
The last change I made to my spreadsheet template was to determine the minimum number of rounds played for all rounds in the sim and then to compute EV assuming number of rounds were fixed at this minimum. This wasn't as yet in the spreadsheet template I offered for download.

My results were (for single deck 500 shoes) s17, DOA, 1 split all pairs, 1 card to split aces, NDAS, NS, full peek

calculated full shoe EV using TD basic strategy: -.0147%
EV for all rounds (determined by cut card - 60% pen): -.08%
EV for rounds without cut card: -.08%
EV for rounds with cut card: -.08%

EV for 5 fixed rounds (5 was the min for any shoe): -.03%

So EV for 5 fixed rounds was much closer to the calculated EV than the EV where the shuffle point was determined by a cut card.

Although the data sample is small, all EVs are computed values.

When I get some time, I will add the average running count for 5 fixed rounds to see how it compares with the average running count for all rounds using a cut card.
  #17  
Old April 15th, 2010, 11:52 AM
k_c k_c is offline
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Quote:
Originally Posted by DMMx3 View Post
I am pretty comfortable with statistics and do not think there is anything blatantly inaccurate about my findings or the methods used to collect the data.

I tested from the beginning because I could not believe that the casino as it seemed would offer a fair game. In fact, I never saw a card that I didn't track. (I guess I'm the Will Rogers of card tracking...or something.)

I tested a hypothesis based on the overall RC of all cards seen. I ran 10000 trials of the same number of cards (in the same number of shoes), and got a p value of ~.02 for obtaining a net RC of my result, or lower.

Also, I tracked all cards, not just my hands and the dealers (I am guessing that is what you were getting at with the 2175 hand assumption?) Sometimes I played the dealer heads up, other times it was a fuller table of 5 or more players. I don't have a count for the number of hands I (or the dealer and I) played, but that doesn't seem relevant anyway.

Do I need more trials? Well to be ~2% confident, no. But I would like to increase the confidence, and thus, as I stated, I plan to continue tracking.

Feel free to PM me if you would like to see all of the data. I have it in a pretty simple excel file.

Data Summary:

Cards tracked: 9789
Shoes tracked: 45
Overall RC: -94
This might address your concern more directly. I have been working to be able to analyze probabilities mathematically relative to any given counting system. Below data assumes you have seen x number of cards and lists the probabilities of all possible HiLo running counts after x cards have been dealt from a single deck. This is just an example and the same could be done for any (reasonable) number of decks or another counting system and any number of cards dealt.

This seems simple enough, but there always seems to be complications.

Above style probabilities would apply when making playing decisions and assume no other specific knowledge other than the referenced counting system's count. (Hand's composition is completely ignored.)

However for betting, count is only meaningful at the start of each round and that is what my other posts in this thread tried to tangentially address.

I guess what I'm trying to say is that it may make at least some difference at which points you are recording data.

Also, rather than using a counting system, maybe you might consider just recording number of each rank that is dealt as a check. For example, all twos could be replaced by fives and using HiLo as a check wouldn't pick that up.

Hope this helps.

Code:
cards = 0
RC = 0    prob = 1

cards = 1
RC = -1    prob = 0.384615
RC = 0    prob = 0.230769
RC = 1    prob = 0.384615

cards = 2
RC = -2    prob = 0.143288
RC = -1    prob = 0.180995
RC = 0    prob = 0.351433
RC = 1    prob = 0.180995
RC = 2    prob = 0.143288

cards = 3
RC = -3    prob = 0.0515837
RC = -2    prob = 0.103167
RC = -1    prob = 0.231674
RC = 0    prob = 0.227149
RC = 1    prob = 0.231674
RC = 2    prob = 0.103167
RC = 3    prob = 0.0515837

cards = 4
RC = -4    prob = 0.0178964
RC = -3    prob = 0.050531
RC = -2    prob = 0.130538
RC = -1    prob = 0.184689
RC = 0    prob = 0.23269
RC = 1    prob = 0.184689
RC = 2    prob = 0.130538
RC = 3    prob = 0.050531
RC = 4    prob = 0.0178964

cards = 5
RC = -5    prob = 0.00596546
RC = -4    prob = 0.0223705
RC = -3    prob = 0.0662342
RC = -2    prob = 0.121356
RC = -1    prob = 0.18365
RC = 0    prob = 0.200846
RC = 1    prob = 0.18365
RC = 2    prob = 0.121356
RC = 3    prob = 0.0662342
RC = 4    prob = 0.0223705
RC = 5    prob = 0.00596546

cards = 10
RC = -10    prob = 1.16786e-005
RC = -9    prob = 0.000127403
RC = -8    prob = 0.000737876
RC = -7    prob = 0.00298907
RC = -6    prob = 0.00919385
RC = -5    prob = 0.0227287
RC = -4    prob = 0.0462951
RC = -3    prob = 0.07939
RC = -2    prob = 0.115749
RC = -1    prob = 0.144822
RC = 0    prob = 0.155911
RC = 1    prob = 0.144822
RC = 2    prob = 0.115749
RC = 3    prob = 0.07939
RC = 4    prob = 0.0462951
RC = 5    prob = 0.0227287
RC = 6    prob = 0.00919385
RC = 7    prob = 0.00298907
RC = 8    prob = 0.000737876
RC = 9    prob = 0.000127403
RC = 10    prob = 1.16786e-005

Last edited by k_c; April 15th, 2010 at 12:48 PM.
  #18  
Old April 15th, 2010, 09:39 PM
DMMx3 DMMx3 is offline
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Quote:
Originally Posted by k_c View Post
Also, rather than using a counting system, maybe you might consider just recording number of each rank that is dealt as a check. For example, all twos could be replaced by fives and using HiLo as a check wouldn't pick that up.

I did record the specific ranks. I used the RC as a means of testing a simpler hypothesis. Here is the data (in case you were interested):

2: 742
3: 775
4: 778
5: 763
6: 746
7: 767
8: 751
9: 757
X: 2964
A: 746

I have more data on my home computer (approx 2x as many trials), but this is all I have retrievable from work, via files in email. This is the same data that shows the RC at -94 (or 94).
  #19  
Old April 15th, 2010, 10:26 PM
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SleightOfHand SleightOfHand is offline
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Quote:
Originally Posted by DMMx3 View Post
I did record the specific ranks. I used the RC as a means of testing a simpler hypothesis. Here is the data (in case you were interested):

2: 742
3: 775
4: 778
5: 763
6: 746
7: 767
8: 751
9: 757
X: 2964
A: 746

I have more data on my home computer (approx 2x as many trials), but this is all I have retrievable from work, via files in email. This is the same data that shows the RC at -94 (or 94).
idk what the standard deviation is like, but it appears to look somewhat ok. Sure, the X and A are occuring less frequently, but the 6 and 2 has a similar frequency as well, which a cheating casino wouldn't do. Not sure how much the cut card effect would change this as well.
  #20  
Old April 16th, 2010, 12:20 AM
Nynefingers Nynefingers is offline
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If you have the data from all of the hands, you should do what k_c mentioned and find the minimum number of hands dealt in any shoe. Then analyze your data by only looking at that number of rounds from each shoe rather than looking at data all the way to the cut card and see if your count is more neutral. The cut card effect means that on shoes where the count is negative after some number of rounds have been played, you are more likely to get an extra round because in order for the count to go negative, you've had more large cards come out, which means you have used fewer cards. This means that if the count is negative (excess small cards remaining), you are more likely to get an extra round dealt. Check and see if that doesn't explain your extra 94 small cards.
 

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