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#21
April 16th, 2010, 10:00 AM
 London Colin Senior Member Join Date: Aug 2009 Posts: 378

Quote:
 Originally Posted by Nynefingers 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.
I confess I'm slightly confused, but surely the cut-card effect can have no bearing on the overall RC, which is the metric that I understand was taken?

If you start averaging by round, or by shoe, in some way, then perhaps you will see its impact. But if you just count the total number of cards seen of each denomination (or track the running count, which is the same thing, except that you cannot distinguish between cards with the same tag, or get any information about cards with a tag of 0), then I don't think it shoud have any effect.
#22
April 16th, 2010, 01:52 PM
 k_c Executive Member Join Date: May 2007 Posts: 624

Quote:
 Originally Posted by London Colin I confess I'm slightly confused, but surely the cut-card effect can have no bearing on the overall RC, which is the metric that I understand was taken? If you start averaging by round, or by shoe, in some way, then perhaps you will see its impact. But if you just count the total number of cards seen of each denomination (or track the running count, which is the same thing, except that you cannot distinguish between cards with the same tag, or get any information about cards with a tag of 0), then I don't think it shoud have any effect.
I think if you were to simply burn a random number of cards and then checked the long run probabilities of the remaining cards then I think they would be what is intuitively expected. Average HiLo running count would be 0. Average probability of ranks ace through 9 remaining would 1/13. Average probability of tens remainiong would be 4/13.

However, dealing a game of blackjack is not quite the same as simply burning a random number of cards. Dealer must draw according to a fixed set of rules. If he busts with a ten then the hand is over but that is one less ten available for the next round. If he has 2 tens he is pat and that is 2 less tens available for the next round. If he has blackjack he flips it over and that is one less ten and one less ace available for the next round. A player that plays basic strategy is similarly playing a fixed strategy that might have an effect on probabilities.

I believe the sum effect of this difference makes the average pre-round (HiLo) running count less than zero. Every sim I have run seems to confirm this, at least for the case of playing to a cut card.

To me the best explanation is an example. I added a couple of things to my Excel spreadsheet project. It now displays average computed EV both playing to a cut card and playing a fixed number of rounds. It also now displays average running count both playing with a cut card and playing a fixed number of rounds.

After download run ImportData macro and browse to simFile.txt to import data.
After data is entered run the MiscInfo macro and click 'Show cut card info'. You will see that average HiLo running count for a fixed number of rounds is -0.03 and using a cut card average HiLo running count is -0.16. I believe cut card effect tends to be greater the fewer the number of starting decks.

This time the included data is for 6 decks, s17, double any 2 cards, split aces once, split 2-10 3 times (up to 4 split hands,) 1 card to split aces, no double after split, no surrender, full peek, blackjack pays 3 to 2 using total dependent basic strategy. It was a sim of 100 shoes to 70% penetration. It looks to me like that about matches the condition DMMx3 was looking at.
#23
April 16th, 2010, 02:43 PM
 London Colin Senior Member Join Date: Aug 2009 Posts: 378

Quote:
 Originally Posted by k_c I think if you were to simply burn a random number of cards and then checked the long run probabilities of the remaining cards then I think they would be what is intuitively expected. Average HiLo running count would be 0. Average probability of ranks ace through 9 remaining would 1/13. Average probability of tens remainiong would be 4/13. However, dealing a game of blackjack is not quite the same as simply burning a random number of cards. Dealer must draw according to a fixed set of rules. If he busts with a ten then the hand is over but that is one less ten available for the next round. If he has 2 tens he is pat and that is 2 less tens available for the next round. If he has blackjack he flips it over and that is one less ten and one less ace available for the next round. A player that plays basic strategy is similarly playing a fixed strategy that might have an effect on probabilities. I believe the sum effect of this difference makes the average pre-round (HiLo) running count less than zero. Every sim I have run seems to confirm this, at least for the case of playing to a cut card.
There is a distinction to be drawn between the average pre-round running count, and the simple overall grand-total running count (or more usefully, the frequency of each card denomination).

My point above was that the cut-card effect specifically ought not to have an impact on the latter.

Even your points about the impact of dealer drawing rules and player Basic Strategy surely only apply to the final round of each shoe, as far as their impact on the overall frequency of each denomination is concerned.

I look at it this way -

If you place a cut card at some random point in a deck, you are going to see all the cards up to that point, regardless of the rules of blackjack. The rules will only affect how those cards get distributed among the various hands, and hence the number of rounds played and the average count at the start of each round.

The final round, however, (regardless of whether a cut card is being used) will impart a fraction of its skewed frequencies to the grand total. But I imagine it would take very frequent shuffling and/or a very big sample size to give a measurable effect.
#24
April 16th, 2010, 06:46 PM
 k_c Executive Member Join Date: May 2007 Posts: 624

Quote:
 Originally Posted by London Colin There is a distinction to be drawn between the average pre-round running count, and the simple overall grand-total running count (or more usefully, the frequency of each card denomination). My point above was that the cut-card effect specifically ought not to have an impact on the latter. Even your points about the impact of dealer drawing rules and player Basic Strategy surely only apply to the final round of each shoe, as far as their impact on the overall frequency of each denomination is concerned. I look at it this way - If you place a cut card at some random point in a deck, you are going to see all the cards up to that point, regardless of the rules of blackjack. The rules will only affect how those cards get distributed among the various hands, and hence the number of rounds played and the average count at the start of each round.
That sounds like about what I'm trying to say.

Quote:
 Originally Posted by London Colin The final round, however, (regardless of whether a cut card is being used) will impart a fraction of its skewed frequencies to the grand total. But I imagine it would take very frequent shuffling and/or a very big sample size to give a measurable effect.
All I can say is that in every sim that I've run, none of which use an overwhelming number of shoes/rounds because I'm using exact calculations to determine actual EV for a simmed shoe in them, the average pre-round RC (using HiLo, but seems similar with other counts) is always negative. For the most part this was measured using a cut card. This includes the fact that for a freshly shuffled shoe (HiLo) running count always = 0, so there is at least one data point that leans the average toward 0 after evry shuffle. If this average was actually = 0 in the long run, I think one would expect to see some positve and some negative results in smaller samples, but the average is ALWAYS < 0

I just recently added testing the RC for a fixed number of rounds but it appears that for this, the average is closer to 0. Maybe a larger sample would show that this average is indeed 0 and maybe it's just closer to 0.

The actual calculated EV for a fixed number of rounds so far has turned out to be more than the actual calculated EV when playing to a cut card. In general I think it is accepted that this is true. My sims just show this in a different way. The main purpose of my sims is to use calculated EV. For every round composition is recorded and EV calculated without regard to any count. After that any count can be referenced so things like average running count are just a byproduct.

Now when it comes to pure statistics I will defer to just about anyone. I found it interesting that DMMx3 seems to have an approach to make sense out of numerous small samples rather than one overwhelmingly large sample, which unfortunately tends to bring out vampires to jump on his neck.
#25
April 16th, 2010, 07:42 PM
 London Colin Senior Member Join Date: Aug 2009 Posts: 378

Quote:
 Originally Posted by k_c All I can say is that in every sim that I've run, none of which use an overwhelming number of shoes/rounds because I'm using exact calculations to determine actual EV for a simmed shoe in them, the average pre-round RC (using HiLo, but seems similar with other counts) is always negative. For the most part this was measured using a cut card. This includes the fact that for a freshly shuffled shoe (HiLo) running count always = 0, so there is at least one data point that leans the average toward 0 after evry shuffle. If this average was actually = 0 in the long run, I think one would expect to see some positve and some negative results in smaller samples, but the average is ALWAYS < 0
I think we are still talking at cross purposes. All my assertions have been in relation to the grand total RC, whereas you are dealing with the pre-round average. I'm not trying to cast doubt on your results or your logic. I just don't think it relates to what the OP has been saying.

Quote:
 Originally Posted by k_c Now when it comes to pure statistics I will defer to just about anyone. I found it interesting that DMMx3 seems to have an approach to make sense out of numerous small samples rather than one overwhelmingly large sample, which unfortunately tends to bring out vampires to jump on his neck.
I may have misunderstood, but I thought that all DMMx3 was saying was that after seeing 9789 cards, over the course of 45 shoes, the grand total RC for the cards seen was +94. And then later, that this count came from the following distribution -

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

That's why I've been saying that the only possible (but entirely negligible) impact of the game of blackjack on these results, as compared to simply dealing out the cards one after another, would have to stem from the final round in each of the 45 shoes.

I reserve the right to defer to more people than you do, but the above distribution does not look particularly unusual to me. (If every denomination were to hit its expected number, the figures would be 3012 for the tens, and 753 for the non-tens.)
#26
April 16th, 2010, 08:46 PM
 k_c Executive Member Join Date: May 2007 Posts: 624

Quote:
 Originally Posted by London Colin I think we are still talking at cross purposes. All my assertions have been in relation to the grand total RC, whereas you are dealing with the pre-round average. I'm not trying to cast doubt on your results or your logic. I just don't think it relates to what the OP has been saying. I may have misunderstood, but I thought that all DMMx3 was saying was that after seeing 9789 cards, over the course of 45 shoes, the grand total RC for the cards seen was +94. And then later, that this count came from the following distribution - 2: 742 3: 775 4: 778 5: 763 6: 746 7: 767 8: 751 9: 757 X: 2964 A: 746 That's why I've been saying that the only possible (but entirely negligible) impact of the game of blackjack on these results, as compared to simply dealing out the cards one after another, would have to stem from the final round in each of the 45 shoes. I reserve the right to defer to more people than you do, but the above distribution does not look particularly unusual to me. (If every denomination were to hit its expected number, the figures would be 3012 for the tens, and 753 for the non-tens.)
I agree with that. It didn't seem that unusual to me either.

I guess in order to contrast his results with mine then he would need to have recorded RC data prior to each round.
#27
April 17th, 2010, 01:01 AM
 DMMx3 Member Join Date: Jan 2010 Posts: 72

Quote:
 Originally Posted by k_c I agree with that. It didn't seem that unusual to me either. I guess in order to contrast his results with mine then he would need to have recorded RC data prior to each round.
Looking at the Ten count in the data I provided, the average number of each rank of tens is 741, which is lower than all the other ranks. This sort of struck me as odd.

Still tracking though, and am now at a p value of .041.

One possibility that I have sort of discounted (for no reason other than simplification) is that not every shoe necessarily contains the same cards. There could be half fair shoes and half unfair shoes. Or any other distribution. And they could be unfair in different ways. Or maybe they are unintentionally unfair. Perhaps a couple tens got lost somewhere. (Though the cards are extremely large so this seems unlikely....)

Or maybe it is completely fair and my results thus far have just been a bit unusual. Or perhaps it can all be explained away with the cut card effect. I'll have to think more on that. Unfortunately I don't have round by round data so I'd have to start tracking that sort of thing from scratch.
#28
April 17th, 2010, 03:19 PM
 k_c Executive Member Join Date: May 2007 Posts: 624

Quote:
 Originally Posted by DMMx3 Looking at the Ten count in the data I provided, the average number of each rank of tens is 741, which is lower than all the other ranks. This sort of struck me as odd. Still tracking though, and am now at a p value of .041. One possibility that I have sort of discounted (for no reason other than simplification) is that not every shoe necessarily contains the same cards. There could be half fair shoes and half unfair shoes. Or any other distribution. And they could be unfair in different ways. Or maybe they are unintentionally unfair. Perhaps a couple tens got lost somewhere. (Though the cards are extremely large so this seems unlikely....) Or maybe it is completely fair and my results thus far have just been a bit unusual. Or perhaps it can all be explained away with the cut card effect. I'll have to think more on that. Unfortunately I don't have round by round data so I'd have to start tracking that sort of thing from scratch.
After thinking about it I think you are better off not changing. I was fixated on pre-round composition because that's the point player needs to determine bet size. Just look at what has been dealt at the shuffle point.

fwiw I ran a 6 deck 1,000,000 shoe sim to a pen of 218 cards using comp dependent basic strategy keeping track of how many of each rank had been cumulatively played at shoe's shuffle. I recorded intermediate results after 50, 100, 1,000, 100,000, and 1,000,000 shoes. The expected parameter for non-tens = 1/13 * (cards dealt) and for tens = 4/13 * (cards dealt). RC is accumulated running count. RC should probably tend to be small when compared to total cards dealt, I would guess. Since this is all post last round maybe a cut card may not affect RC at all.

Code:
```•initSimulatedDealing(6,1,218,0,1000000,1)
shoes =   50
1  852  expected =  848.308
2  848  expected =  848.308
3  808  expected =  848.308
4  847  expected =  848.308
5  839  expected =  848.308
6  863  expected =  848.308
7  838  expected =  848.308
8  856  expected =  848.308
9  872  expected =  848.308
10  3405  expected =  3393.23
RC =  52
shoes =   100
1  1692  expected =  1696.77
2  1690  expected =  1696.77
3  1649  expected =  1696.77
4  1713  expected =  1696.77
5  1695  expected =  1696.77
6  1712  expected =  1696.77
7  1700  expected =  1696.77
8  1688  expected =  1696.77
9  1719  expected =  1696.77
10  6800  expected =  6787.08
RC =  85
shoes =   1000
1  16986  expected =  16947.2
2  16954  expected =  16947.2
3  16922  expected =  16947.2
4  16913  expected =  16947.2
5  16966  expected =  16947.2
6  16970  expected =  16947.2
7  16809  expected =  16947.2
8  17090  expected =  16947.2
9  17029  expected =  16947.2
10  67674  expected =  67788.6
RC =  20
shoes =   100000
1  1.69518e+06  expected =  1.69495e+06
2  1.69649e+06  expected =  1.69495e+06
3  1.69533e+06  expected =  1.69495e+06
4  1.69329e+06  expected =  1.69495e+06
5  1.69468e+06  expected =  1.69495e+06
6  1.69461e+06  expected =  1.69495e+06
7  1.69497e+06  expected =  1.69495e+06
8  1.69492e+06  expected =  1.69495e+06
9  1.69421e+06  expected =  1.69495e+06
10  6.78067e+06  expected =  6.7798e+06
RC =  1469
shoes =   1e+06
1  1.69461e+07  expected =  1.69491e+07
2  1.69511e+07  expected =  1.69491e+07
3  1.6949e+07  expected =  1.69491e+07
4  1.69501e+07  expected =  1.69491e+07
5  1.69483e+07  expected =  1.69491e+07
6  1.69476e+07  expected =  1.69491e+07
7  1.69507e+07  expected =  1.69491e+07
8  1.69541e+07  expected =  1.69491e+07
9  1.69491e+07  expected =  1.69491e+07
10  6.77925e+07  expected =  6.77965e+07
RC =  -5969

Number of decks:   6
Cards dealt to cause shuffle:   218
Total shoes:   1e+06
Total rounds:   4.03466e+07
Total hands:   4.12249e+07
Player blackjacks:   1.91142e+06
Dealer blackjacks:   1.91375e+06
Total result:   -244360```

Last edited by k_c; April 17th, 2010 at 03:50 PM.
#29
April 18th, 2010, 12:39 AM
 Nynefingers Senior Member Join Date: Oct 2009 Posts: 355

Thanks, k_c, that's quite interesting.
#30
May 22nd, 2010, 09:36 AM
 KimLee Member Join Date: Apr 2010 Posts: 70

Quote:
 Originally Posted by London Colin after seeing 9789 cards, ... the grand total RC for the cards seen was +94.
Not unusual; the standard deviation of RC is Sqrt(10/13*9789) = 87.

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