Effect of count on dealer probs

From www.bjmath.com

Posted by MathProf on 3 Oct 1998, 2:50 pm
In a thread below, I made a statement that the probability of the Dealer breaking would increase with moderate increases in the Count, although would eventually decrease. I had in mind comments that Griffin had made about Dealer breaking as a function of 10s density. Don disagreed with that, and SW added some clarifying comments in support of Don's position. So to further clarify the situation, I prepared some brief calculations. The tables below show final Dealer probabilities. The calculations are with exact methods. The first tables studies the effect of tens density. What I did here was to start with a single deck, and then add (or subtract) a 10 at each level to increase the proportion. The initial pack is a Single Deck minus 6 tens (for 46 cards) and the final pack is Single Deck + 20 tens, and contains 72 cards. Normal composition is noted with a *. As you can see from the table, the Bust probability increases until the density gets to the 42% level before starting to decrease, as Griffin had suggested.

% 10s Bust Under 17 18 19 20 21 BJ Sum 21.7 26.96 0.00 14.54 15.48 14.91 15.16 9.08 3.86 100.00 23.4 27.37 0.00 14.35 15.21 14.70 15.51 8.80 4.07 100.00 25.0 27.72 0.00 14.17 14.94 14.49 15.89 8.53 4.26 100.00 26.5 28.03 0.00 13.99 14.69 14.28 16.32 8.27 4.42
100.00 28.0 28.31 0.00 13.80 14.44 14.07 16.78 8.02 4.57 100.00 29.4 28.54 0.00 13.62 14.20 13.87 17.27 7.79 4.71 100.00 * 30.8 28.75 0.00 13.44 13.97 13.68 17.78 7.56 4.83 100.00 32.1 28.92 0.00 13.27 13.75 13.48 18.31 7.34 4.93 100.00 33.3 29.07 0.00 13.09 13.53 13.29 18.86 7.13 5.03 100.00 34.5 29.19 0.00 12.92 13.32 13.11 19.42 6.92 5.12 100.00 35.7 29.29 0.00 12.75 13.11 12.93 19.99 6.73 5.19 100.00 36.8 29.37 0.00 12.59 12.91 12.75 20.57 6.54 5.26 100.00 37.9 29.43 0.00 12.42 12.72 12.57 21.16 6.36 5.32 100.00 39.0 29.48 0.00 12.26 12.53 12.40 21.76 6.19 5.38 100.00 40.0 29.51 0.00 12.10 12.35 12.24 22.36 6.02 5.42 100.00 41.0 29.52 0.00 11.95
12.17 12.07 22.96 5.86 5.46 100.00 41.9 29.52 0.00 11.80 12.00 11.91 23.57 5.70 5.50 100.00 42.9 29.51 0.00 11.65 11.83 11.76 24.17 5.55 5.53 100.00 43.8 29.49 0.00 11.50 11.67 11.61 24.77 5.41 5.56 100.00 44.6 29.45 0.00 11.36 11.51 11.46 25.38 5.27 5.58 100.00 45.5 29.41 0.00 11.22 11.35 11.31 25.98 5.14 5.59 100.00 46.3 29.36 0.00 11.08 11.20 11.17 26.57 5.01 5.61 100.00 47.1 29.30 0.00 10.95 11.05 11.03 27.17 4.89 5.62 100.00 47.8 29.23 0.00 10.81 10.91 10.89 27.76 4.77 5.63 100.00 48.6 29.16 0.00 10.68 10.77 10.76 28.35 4.65 5.63 100.00 49.3 29.08 0.00 10.56 10.63 10.63 28.93 4.54 5.63 100.00 50.0 29.00 0.00 10.43 10.50 10.50 29.51 4.43 5.63
100.00

Then I went to study the effects of the HiLo Count. Here I started with a 10 deck Pack. At each level I added 4 10s and a Ace, and removed a low card. This produces a "typical" or representative pack with a prescribed HiLo True Count. That True Count is given in the first column of the table below. The table below shows that there is a different pattern for HiLo. The maximum value of dealer breaking is attained at approximately normal deck composition. In particular, Don and SW were correct (and yes, I was incorrect) in stating that there was less total dealer breaking in positive HiLo Shoes.

HiLo Bust Under 17 18 19 20 21 BJ Sum -10.0 27.85 0.00 14.53 15.55 14.60 15.79 9.01 2.67 100.00 -9.0 28.00 0.00 14.40 15.40 14.50 15.98 8.87 2.85 100.00 -8.0 28.13 0.00 14.27 15.25 14.40

16.19 8.73 3.04 100.00 -7.0 28.24 0.00 14.14 15.11 14.29 16.40 8.58 3.23 100.00 -6.0 28.34 0.00 14.02 14.96 14.19 16.62 8.43 3.43 100.00 -5.0 28.43 0.00 13.90 14.82 14.08 16.86 8.28 3.63 100.00 -4.0 28.49 0.00 13.78 14.68 13.98 17.10 8.13 3.84 100.00 -3.0 28.54 0.00 13.67 14.54 13.87 17.35 7.97 4.06 100.00 -2.0 28.56 0.00 13.56 14.40 13.77 17.62 7.81 4.28 100.00 -1.0 28.57 0.00 13.45 14.27 13.66 17.90 7.65 4.51 100.00 0.0 28.56 0.00 13.34 14.13 13.56 18.18 7.48 4.74 100.00 1.0 28.53 0.00 13.23 14.00 13.46 18.48 7.32 4.98 100.00 2.0 28.48 0.00 13.13 13.87 13.36 18.79 7.15 5.23 100.00 3.0 28.41 0.00 13.03 13.74 13.25 19.11 6.98 5.48 100.00 4.0
28.31 0.00 12.93 13.62 13.16 19.45 6.80 5.74 100.00 5.0 28.19 0.00 12.83 13.50 13.06 19.79 6.63 6.00 100.00 6.0 28.05 0.00 12.73 13.38 12.96 20.15 6.45 6.27 100.00 7.0 27.89 0.00 12.64 13.26 12.87 20.52 6.28 6.55 100.00 8.0 27.70 0.00 12.55 13.15 12.77 20.90 6.10 6.83 100.00 9.0 27.49 0.00 12.46 13.04 12.68 21.29 5.92 7.12 100.00 10.0 27.25 0.00 12.37 12.93 12.60 21.70 5.74 7.41 100.00

PS: Both tables were done using S17.

--------------------------------------------------------------------------------

Responses
Re: Effect of Count on Dealer Probs. - Don Schlesinger -- 3 Oct 1998, 5:44 pm

I found that article on www.bjmath.com

I dont understand something.
4 tens and an Ace minus a low card in a ten pack simulation should give a +0.6Hi-Lo true point count per level not +1 as the article suggests.

Did I miss something? I would really apprecieate any feedback on this.
Is this article correct or not?

--------------------------------------------------------------------------------

... that what MathProf did was add four 10s, and one Ace, and also deduct one low card for each rank that has a positive tag. Ie. He removed one 2, one 3, one 4, one 5, and one 6. This produces a perfectly average 10-deck shoe with TC = +1.

Best,
ETF

Ok now I got it.

What does this different pattern means anyway?

Should I asume that a counting system that counts aces as zero has a better expectation per true point count that Hi-Lo?

Means, does not follow.

The first test just added 10s.

The second test added tens/Aces and removed low cards.

If a test where 4 tens were added and 4 low cards were removed leaving Aces, was done, and it showed a higher prob of dealer breaking, then and only then, would it show that an Ace neutral count is a better indicator of dealer busting. (Pardon my grammar.)

It is true that Ace Neutral counts generally have a higher playing efficiency. I may be biased, but I think the higher betting efficiency of the hi-lo outweighs the former, since it's the $$$s I'm after!

I think that the first test is the same with adding tens and subracting low cards.

It simply uses a single pack for simplysitis sake.

I really dont understand why a third test should be done with a ten pack card.

It makes sence for the dealer to bust more often when aces are missing.

Ace is a good card for the dealer.It saves him from 6s and 16s.It is good for the player only because it gives the blackjack bonus and some doubles.

I calculated a +0.15 expectation/true point count in favor of an ace neutral counting system.

The only problem is that I dont know that for sure.... my math suxs!!!!And I dont even have a computer to help me

Pavlos said,
> I think that the first test is the same with adding tens and subracting low cards.
>It simply uses a single pack for simplysitis sake.

From your original post:

>>Posted by MathProf on 3 Oct 1998, 2:50 pm
>>...
>> The first tables studies the effect of tens density. What I did here was to start with a single deck, and then add (or subtract) a 10 at each level to increase the proportion. The initial pack is a Single Deck minus 6 tens (for 46 cards) and the final pack is Single Deck + 20 tens, and contains 72 cards.
>>...

The last line makes me sure that he was only adding or subtracting tens in the first test.

>I really dont understand why a third test should be done with a ten pack card.

Just to use the 'Scientific Method.' Using all the same variables except one such as leaving the Aces and remove the 9s instead.

>It makes sence for the dealer to bust more often when aces are missing.
>Ace is a good card for the dealer.It saves him from 6s and 16s.It is good for the player only because it gives the blackjack bonus and some doubles.
>I calculated a +0.15 expectation/true point count in favor of an ace neutral counting system.
>The only problem is that I dont know that for sure.... my math suxs!!!!And I dont even have a computer to help me

Absolutely! Very good analysis. I agree with everything except your math doesn't seem to sux. I haven't done the math but your answer seems to be on the order of being correct, good job!

If the test was done as described above the increase in Playing Efficiency is +0.18. I saw it on qfit, check it out link is below.

When you compare Counting Systems you should look at the overall effects of removal, not only the EORs on dealer probs.
In your post you said that the ace was only good for the players because of the BJ-bonus and the successful doubles.You should have dropped the "only" since these are very important points.
Besides, It helps also the player to bust less often who after all has to draw before the dealer.
All this explains why ace-neutral systems without sidecount are rather inefficient.

Francis Salmon

Dear Salmon.

Again a deep thank you for the surrender indices you gave me.I own you that.

However I think that you have missed my point.I agree that an ace rich deck is good for the player.No further comments on this.

However as a post that I put on bjmath.com I was wondering wheather the extra chance of dealer busting makes up for the missed blackjacks and doubles.That should reflect on the overal expectation per true point count that a system gives.

Please before dissagring consider the below not so uncommon senario.

A counter plays 2 hands on the table.The chance of having 2 blackjacks at the same time is rather minimal.
The counter risks 2 bets (equal I asume) using Hi-Lo.
He risks 2 bets and has a high chance for a single blackjack.
Thats a high risk for an expectation that ranges from negative to +2.5
Most often it might be +0.5

Now consider the same counter using an ace neutral count.
He is not chasing after the welcome occasional blackjack.
He bets his money when the dealer has maximun chance to bust according to MathProf statistics.
Thats a +2 expectation.Not great but not bad.He also enjoys a better winning rate of doubles compared to Hi-Lo given the fact that the chance to be dealt an ace on 11 is reduced.

Shouldnt all that make up for the missed blackjacks and doubles?
Thats my final point.

I dont compare counting systems.
I compare the expectation a counting systems gives per true point count.
The +0.15 expectation per true point count that I calculated with my pour math in conjuction withe +.10 a surrender table gives to a card counter gives total +0.25/true point count.

That a huge increase mind you.Would you give up all that for an extra blackjack or two?I think not.

A counter plays 2 hands on the table.The chance of having 2 blackjacks at the same time is rather minimal.
The counter risks 2 bets (equal I asume) using Hi-Lo.
He risks 2 bets and has a high chance for a single blackjack.
Thats a high risk for an expectation that ranges from negative to +2.5.Most often it might be +0.5.

I don't quite understand your point here.By the way, two BJs at once occur often.Sometimes I even have 3 simultaneous BJs and in one case this was even met by a dealer-bj.
Outcomes for 2 simultaneous hands can range from -12 to +12 assuming sp2 and das.

I dont compare counting systems.
I compare the expectation a counting systems gives per true point count.
The +0.15 expectation per true point count that I calculated with my pour math in conjuction withe +.10 a surrender table gives to a card counter gives total +0.25/true point count.
That a huge increase mind you.Would you give up all that for an extra blackjack or two?I think not.

What do mean with your +0.15% expectation. Actually the expectation per true count for average rules is about 0.5%,with surrender its even more.The fact that the EOR for an ace is higher than the one for a ten proves that what you're saying is wrong.
The only valid argument for an ace-neutral count is the increased playing efficiency but this is negligible in shoe games.

Francis Salmon

My whole argument can be summarized in the "about +0.5%" you mentioned.

As you also pointed out for a surrender table the expectation per true point count is +0.6% per true point count.(and more the higher the count)

My pour math indicated me an additional +0.15% expectation per true point count for a counter that uses a ace neutral system.

Thats a total of 0.75% advatage per true point count!!!

A counter thats uses such a system is very close to a +2% advatage over the house.

Using MathProf statistcs I have proven to myself that the additional dealer busting makes up for any lost blackjack bonus.

I wasnt able to calculate the expectation value of soft total doubles since it involes 3+card combinations (the soft total and the dealer upcard the card you receive on a double plus the additional cards the dealer is going to get)

It is there that I need your help or anybodys help for that matter.

Thank you for your time.

> Using MathProf statistcs I have proven to myself that the
> additional dealer busting makes up for any lost blackjack bonus.

What "lost bonus" do you mean? An ace-neutral system will keep a side count of aces so that the betting decisions are based on an ace-reckoned count. The only time the ace-neutral player uses the "ace-less" count is for playing decisions. From what I can tell, an ace-neutral system with an ace side count will recognize the same advantages as an ace-reckoned system.

-Sonny-

Pavlos thinks that an ace-neutral count is better than hilo even without side-count.Unfortunately,I was unable to took him out of that idea.

Francis Salmon

Dear Salmon.

You got it right that I think an ace neutral count gives a better expectation per true point count than hi-lo.Even without side count.

My poor math was this.

Let A be chance of dealer busting with a 10 only system and B the chance for Hi-Lo.

Assume that player and dealer has the same chance of blackjack at any given count.( I think thats accurate)

Let C be the chance of blackjack for 10 only system and C* for Hi-Lo.

Now G=(A-B)x U x 2 Gives the increased expectation for the 10 only system.
F=(C*-C)x 1.5 Gives the reduced expectation because of lower Blackjack chance.

U=1-P where P=corresponds of how often a player playing basic strategy busts before the dealer.

Well you are all well aware that basic strategy calls for stand on almost all bust hands when the dealer has a bust hand as well.
You are also aware that when the dealer has 7-A he has the minimun chance to bust and it is only on this hands a player has to take chances of busting.

So whats the value for P?

I gave blindly a 0.25 value for P => U=0.75
As you can see for the +3 True count you get a positive result when you do the G-F calculation.

Then I did a more careful study and decided that it is more fair to give a 0.15 value for P => U=.085

So much the better.That way I predicted a +0.45% at +3 true point count.

There you got the 0.15 positive expectation per true point count for the 10 only system.