How to adjust Ace side count for playing decisions
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zengrifter
Banned
Re: How to adjust Ace side count for playing decis
Richard Reid's advice from DBJ is to simply add the #Aces (x2 for a level-2) seen to the RC before converting to TC, when detirming insurance and and certain Ace sensitive hands. I would like to hear some coherrent methodology and reasoning on this myself! zg
Richard Reid's advice from DBJ is to simply add the #Aces (x2 for a level-2) seen to the RC before converting to TC, when detirming insurance and and certain Ace sensitive hands. I would like to hear some coherrent methodology and reasoning on this myself! zg
Rob McGarvey
Well-Known Member
Re: How to adjust Ace side count for playing decis
No. An Ace played is an Ace played. If you see it, it's a part of your betting count, and in this instance, a part of your modified playing count. It is treated something like a 2 for some playing decisions (+1). You can work out each play by using a BJ calculator like BeeJack2021.
No. An Ace played is an Ace played. If you see it, it's a part of your betting count, and in this instance, a part of your modified playing count. It is treated something like a 2 for some playing decisions (+1). You can work out each play by using a BJ calculator like BeeJack2021.
Adam N. Subtractum
Well-Known Member
21st Century Sidecounting...
Sidecounting has come a long way from the days of the antiquated excess/deficiency ace adjustment methods, with much easier mutations available to today's advantage player. The general concensus amongst most in the cardcounter community is that sidecounting is of little value when compared to the effort that is exerted in employing one. Furthermore, with the majority of blackjack in the world being multi-deck, where playing strategy is so much less important than betting, it would seem as though they might be right.
However, recent research, most notably that conducted by T-hopper (presented in his post "6D Bombshell: Playing Strategy is Key"), suggests that playing strategy can have much more of an impact in shoes than originally suspected. For example, in T-hopper's aforementioned post he reports that in a common 4.5/6 game, his T-H "Dollar-Weighted" basic strategy, and 2-7/T-A for betting, has a 30% higher ROI (return on investment) than KO betting w/ stock BS!!! I don't think many people realized the magnitude of this...we're talking about a dollar-weighted BS, that was the only improvment...no indices, and to top it off, this was with fair penetration! This alone should be enough to make doubters think again about the importance of playing strategy in shoe games, and about the use of sidecounts to further enhance that playing strategy.
Now we see there are substantial gains to be made from play, and we know an ace sidecount will increase our Playing Efficiency dramatically if we are using an Ace-reckoned count (PE improvments will be much less with an Ace-neutral count), so it seems obvious, even without getting into the numbers, the improvement will be noticable. The question is, is it worth the effort? Or as I've heard some counter's say, "What's the return per cell?" This is a relative question, and one only you can answer for yourself.
Now let's take a look at a few ways we can make sidecounting less of a burden. First and foremost, I believe the biggest flaw in old-school Ace sidecounts is that they were used with ace-neutral main counts, requiring conversion to an adjusted count EVERY single hand for betting purposes. Does this seem ridiculous to anyone else? Why would we want to make the ace adjustment 100% of the time, when we would have to do it less than 30% of the time (during PLAYING decisions) if we used an ace-reckoned count?? I don't have the exact numbers on-hand, but using Catch 22 we vary our strategy somewhere around 28% of the time (don't qoute me). Now doesn't that seem easier?, we've already cut the "load per cell" by 2/3.*
*I should note that some people may have difficulty sidecounting a card already included in the Running Count, effectively having to "count the same card twice".
Ok, now let's examine the actual adjustment procedure. First we'll start with the antiquated method:
-Antiquated Ace adjustment steps-
1. keep RC of Aces played
2. calculate decks remaining (decks in play - decks played)
3. calculate Aces remaining (total Aces - Aces played)
4. calculate excess/defic of Aces remaining (Aces remaining - 4*decks remaining)
5. Add excess to Running Count and convert to True Count
Simple huh? Its a wonder people used this method for so long. The first improvment that can be made was pointed out by Lance Humble in "The World's Greatest Blackjack Book", where he states that the player should start his Ace Running Count at decks played * 4 and count DOWN as the Aces are played. This method combines steps 1 & 3, as you see, because we no longer need to calculate Aces remaining...we are counting them down as they come out.
I should note the reason we have to use Aces remaining for our adjustment rather than using the number of Aces played, as we are doing with every other card in our RC. The reason that we can't just ADD in the number of Aces played to counteract its betting value of -1 in the RC, is that in doing so we are throwing our pivot off kilter. Take hi-lo for example, it is balanced with a pivot of zero, but if we take the Aces away we now have an unbalance of +4 per deck, and a pivot of 4 * decks in use. This was the mistake made by Richard Reid in early editions of his E-book "Dynamic Blackjack". The mistake has since been brought to his attention, and was corrected immmediately(a great feature of E-books).
Next you see in step 4 we have to calculate excess/deficiency. Now we don't have that problem (with an Ace-reckoned count), because we don't need to know the excess or deficiency of the Aces...we just need to know the amount remaining, so we can subtract that amount from our RC, and make playing strategy decisions with the higher PE of an Ace-nuetral system (without any adverse effects on the pivot).
Let's review the steps we've deemed necessary for our Ace adjustment:
-21st Century Sidecounting Steps-
1. Count down Aces played
2. Add Aces remaining to Running Count and convert to True Count
We've cut the steps form five to two, effectively increasing "return per cell" exponentially in my opinion.
On another note, additional adjustments can be made for certain plays where the Ace's ideal value is other than zero, such as doubling hard 10 & 11, and insurance. This will add to complexity, but since we've broken it (the sidecount) down so much, we've got some extra brain cells to throw around. These extra adjustments are not necessary, and will not dramatically effect your win rate.
A testament to the performance of this "new" method of Ace adjustment is found in some research done by Dr. Brett Harris. I don't have the study on-hand, but in a single deck comparo between Advanced Omega-II and Brh-II, where AO-II used a traditional sidecount and Brh-II simply subtracted 2 from the RC for every Ace seen (for playing decisions only), Brh-II outperformed AO-II. It should be noted that this very weak Ace adjustment performed with the Brh-II system has the pivot problem we discussed earlier. Brh-II is a +2 unbalanced system, so by subtracting one full rank (the Aces) from the RC, Brh-II is converted to a -2 pivot, a very much suboptimal point......but it STILL outperforms AO-II with the antiquated ace sidecount.
Another benefit of Ace sidecounts that I'll touch on is their use for betting purposes. In the system I developed and use, AnS-I (Ace variable Sidecount-I), I use the Ace sidecount to adjust the "variable pivot" that I employ for betting purposes. This allows me to have 100% accuracy of TC without ANY deck estimation whatsoever, as well as a slight increase in Betting Correlation. I haven't gotten to doing the numbers yet, but I believe it will prove to be the most powerful level one system (albeit with a sidecount) ever developed, with estimated BC of .977-.980, and PE of .65-.69 (depending on # of Ace adjustments used). From the little info I've heard of T-hopper's Advanced systems, I believe he is using a similar "variable pivot" scheme for betting, as well as similar ace adjustments for playing decisions.
There is another method, I believe developed by Pete Moss, that balances the Ace sidecount with another card, actually making it a "secondary" count. This is by my definition a multi-parameter system (technically an Ace sidecount makes for a multi-parameter system) because two seperate Running Counts must be kept, so I will not delve into the topic at this time. I believe (and Cacarulo has expressed the same thoughts) a properly implemented Ace sidecount system will outperform this hybrid anyway.
In conclusion, there is a lot to be gained from Ace sidecounting, even in today's deteriorating conditions, and it doesn't take a mind like Peter Griffin's to implement one. At the very least, attempt incorporating sidecounting into your pitch play, as even most beginners will not have a problem sidecounting less than 4-8 cards.
There are some finer points, such as the multitude of possible adjustments for playing strategy, as well as some minor points concerning betting, but I think I've pretty much got the point across.....the sidecount is far from dead.
ANS
Sidecounting has come a long way from the days of the antiquated excess/deficiency ace adjustment methods, with much easier mutations available to today's advantage player. The general concensus amongst most in the cardcounter community is that sidecounting is of little value when compared to the effort that is exerted in employing one. Furthermore, with the majority of blackjack in the world being multi-deck, where playing strategy is so much less important than betting, it would seem as though they might be right.
However, recent research, most notably that conducted by T-hopper (presented in his post "6D Bombshell: Playing Strategy is Key"), suggests that playing strategy can have much more of an impact in shoes than originally suspected. For example, in T-hopper's aforementioned post he reports that in a common 4.5/6 game, his T-H "Dollar-Weighted" basic strategy, and 2-7/T-A for betting, has a 30% higher ROI (return on investment) than KO betting w/ stock BS!!! I don't think many people realized the magnitude of this...we're talking about a dollar-weighted BS, that was the only improvment...no indices, and to top it off, this was with fair penetration! This alone should be enough to make doubters think again about the importance of playing strategy in shoe games, and about the use of sidecounts to further enhance that playing strategy.
Now we see there are substantial gains to be made from play, and we know an ace sidecount will increase our Playing Efficiency dramatically if we are using an Ace-reckoned count (PE improvments will be much less with an Ace-neutral count), so it seems obvious, even without getting into the numbers, the improvement will be noticable. The question is, is it worth the effort? Or as I've heard some counter's say, "What's the return per cell?" This is a relative question, and one only you can answer for yourself.
Now let's take a look at a few ways we can make sidecounting less of a burden. First and foremost, I believe the biggest flaw in old-school Ace sidecounts is that they were used with ace-neutral main counts, requiring conversion to an adjusted count EVERY single hand for betting purposes. Does this seem ridiculous to anyone else? Why would we want to make the ace adjustment 100% of the time, when we would have to do it less than 30% of the time (during PLAYING decisions) if we used an ace-reckoned count?? I don't have the exact numbers on-hand, but using Catch 22 we vary our strategy somewhere around 28% of the time (don't qoute me). Now doesn't that seem easier?, we've already cut the "load per cell" by 2/3.*
*I should note that some people may have difficulty sidecounting a card already included in the Running Count, effectively having to "count the same card twice".
Ok, now let's examine the actual adjustment procedure. First we'll start with the antiquated method:
-Antiquated Ace adjustment steps-
1. keep RC of Aces played
2. calculate decks remaining (decks in play - decks played)
3. calculate Aces remaining (total Aces - Aces played)
4. calculate excess/defic of Aces remaining (Aces remaining - 4*decks remaining)
5. Add excess to Running Count and convert to True Count
Simple huh? Its a wonder people used this method for so long. The first improvment that can be made was pointed out by Lance Humble in "The World's Greatest Blackjack Book", where he states that the player should start his Ace Running Count at decks played * 4 and count DOWN as the Aces are played. This method combines steps 1 & 3, as you see, because we no longer need to calculate Aces remaining...we are counting them down as they come out.
I should note the reason we have to use Aces remaining for our adjustment rather than using the number of Aces played, as we are doing with every other card in our RC. The reason that we can't just ADD in the number of Aces played to counteract its betting value of -1 in the RC, is that in doing so we are throwing our pivot off kilter. Take hi-lo for example, it is balanced with a pivot of zero, but if we take the Aces away we now have an unbalance of +4 per deck, and a pivot of 4 * decks in use. This was the mistake made by Richard Reid in early editions of his E-book "Dynamic Blackjack". The mistake has since been brought to his attention, and was corrected immmediately(a great feature of E-books).
Next you see in step 4 we have to calculate excess/deficiency. Now we don't have that problem (with an Ace-reckoned count), because we don't need to know the excess or deficiency of the Aces...we just need to know the amount remaining, so we can subtract that amount from our RC, and make playing strategy decisions with the higher PE of an Ace-nuetral system (without any adverse effects on the pivot).
Let's review the steps we've deemed necessary for our Ace adjustment:
-21st Century Sidecounting Steps-
1. Count down Aces played
2. Add Aces remaining to Running Count and convert to True Count
We've cut the steps form five to two, effectively increasing "return per cell" exponentially in my opinion.
On another note, additional adjustments can be made for certain plays where the Ace's ideal value is other than zero, such as doubling hard 10 & 11, and insurance. This will add to complexity, but since we've broken it (the sidecount) down so much, we've got some extra brain cells to throw around. These extra adjustments are not necessary, and will not dramatically effect your win rate.
A testament to the performance of this "new" method of Ace adjustment is found in some research done by Dr. Brett Harris. I don't have the study on-hand, but in a single deck comparo between Advanced Omega-II and Brh-II, where AO-II used a traditional sidecount and Brh-II simply subtracted 2 from the RC for every Ace seen (for playing decisions only), Brh-II outperformed AO-II. It should be noted that this very weak Ace adjustment performed with the Brh-II system has the pivot problem we discussed earlier. Brh-II is a +2 unbalanced system, so by subtracting one full rank (the Aces) from the RC, Brh-II is converted to a -2 pivot, a very much suboptimal point......but it STILL outperforms AO-II with the antiquated ace sidecount.
Another benefit of Ace sidecounts that I'll touch on is their use for betting purposes. In the system I developed and use, AnS-I (Ace variable Sidecount-I), I use the Ace sidecount to adjust the "variable pivot" that I employ for betting purposes. This allows me to have 100% accuracy of TC without ANY deck estimation whatsoever, as well as a slight increase in Betting Correlation. I haven't gotten to doing the numbers yet, but I believe it will prove to be the most powerful level one system (albeit with a sidecount) ever developed, with estimated BC of .977-.980, and PE of .65-.69 (depending on # of Ace adjustments used). From the little info I've heard of T-hopper's Advanced systems, I believe he is using a similar "variable pivot" scheme for betting, as well as similar ace adjustments for playing decisions.
There is another method, I believe developed by Pete Moss, that balances the Ace sidecount with another card, actually making it a "secondary" count. This is by my definition a multi-parameter system (technically an Ace sidecount makes for a multi-parameter system) because two seperate Running Counts must be kept, so I will not delve into the topic at this time. I believe (and Cacarulo has expressed the same thoughts) a properly implemented Ace sidecount system will outperform this hybrid anyway.
In conclusion, there is a lot to be gained from Ace sidecounting, even in today's deteriorating conditions, and it doesn't take a mind like Peter Griffin's to implement one. At the very least, attempt incorporating sidecounting into your pitch play, as even most beginners will not have a problem sidecounting less than 4-8 cards.
There are some finer points, such as the multitude of possible adjustments for playing strategy, as well as some minor points concerning betting, but I think I've pretty much got the point across.....the sidecount is far from dead.
ANS
zengrifter
Banned
Re: 21st Century Sidecounting... POM!
Adam gets my POM vote! zg
Adam gets my POM vote! zg
Rob McGarvey
Well-Known Member
I Believe.....
very much in the power of the Ace. And I also believe that anyone can figure out when a single or a double deck game is Ace rich or poor without going thru all of the calcs and division. We have to understand how to go thru the process at first, but after some serious practice, a player just "knows" Ace density. I wouldn't even call it intuition. It's like knowing you are awake when you are awake. A few months ago I spoke of the High Low MAX in one of my newsletters. Basically High Low with known Ace density.
I also believe your floating pivot point based on the A density is a very novel and deadly approach to using this information.
And I also believe that your post is not post of the month. It is at least post of the year, and you are poster of the year in my highest and most gracious opinion.
Thank you for sharing this very valuable information with me, and everyone else here. I think this info may open the eyes of the anti-ace density counters out there.
very much in the power of the Ace. And I also believe that anyone can figure out when a single or a double deck game is Ace rich or poor without going thru all of the calcs and division. We have to understand how to go thru the process at first, but after some serious practice, a player just "knows" Ace density. I wouldn't even call it intuition. It's like knowing you are awake when you are awake. A few months ago I spoke of the High Low MAX in one of my newsletters. Basically High Low with known Ace density.
I also believe your floating pivot point based on the A density is a very novel and deadly approach to using this information.
And I also believe that your post is not post of the month. It is at least post of the year, and you are poster of the year in my highest and most gracious opinion.
Thank you for sharing this very valuable information with me, and everyone else here. I think this info may open the eyes of the anti-ace density counters out there.
Adam N. Subtractum
Well-Known Member
Thanks zg!....
I value your opinion very highly, thanks for the kind words.
ANS
I value your opinion very highly, thanks for the kind words.
ANS
Sonny
Well-Known Member
Re: 21st Century Sidecounting...
So, instead of using an ace-neutral count and adding the ace sidecount for every betting decision, we should use an ace-reckoned count and subtract the ace sidecount for all playing decisions? So we are left with an unbalanced count for our PE? Interresting...
-Sonny-
So, instead of using an ace-neutral count and adding the ace sidecount for every betting decision, we should use an ace-reckoned count and subtract the ace sidecount for all playing decisions? So we are left with an unbalanced count for our PE? Interresting...
-Sonny-
zengrifter
Banned
Re: I Believe.....
"It's like knowing you are awake when you are awake. "
-----------------
... proclaimed the man, lost in his dream! zg
"It's like knowing you are awake when you are awake. "
-----------------
... proclaimed the man, lost in his dream! zg
zengrifter
Banned
Could the improved method ...
... be used to count 7s density (or 7s/8s as a block)? I'm trying to envision how that might work in application with the multiparam#s. zg
... be used to count 7s density (or 7s/8s as a block)? I'm trying to envision how that might work in application with the multiparam#s. zg
Adam N. Subtractum
Well-Known Member
There's nothin' new under the sun...
I believe that saying applies to our strategies as much as it does in almost every aspect of life. I thank you very much for the encouraging words Rob, but the ideas I proposed have been used by improvising card counters for many years. Pete Moss was using a TKO/Hi-Opt-I hybrid to make real money when I was still counting fives for quarters...and I don't mean greens, lol.
It's funny, I was just pondering on this thought recently, as I was reading over Thorp's BTD once again...he discovered backcounting, hole card play, sequencing, even a little risk-aversion. And one thing that particularly caught my attention was Thorp's use of "end play". As I was reading the section over once again, I remembered a recent post by Ted Forrester a.k.a alienated, in which he briefly discussed the exploitation of bordering (ST) segments, and I believe the follow-up post almost won POM on Green Chip. Though I didn't get much out of Ted's first post, I beleive the strategy is based on "end play", and am eagerly looking forward to any comments made by Ted on the subject. But anyway, the point was....oh yeah, old-school players rule. ;-)
ANS
I believe that saying applies to our strategies as much as it does in almost every aspect of life. I thank you very much for the encouraging words Rob, but the ideas I proposed have been used by improvising card counters for many years. Pete Moss was using a TKO/Hi-Opt-I hybrid to make real money when I was still counting fives for quarters...and I don't mean greens, lol.
It's funny, I was just pondering on this thought recently, as I was reading over Thorp's BTD once again...he discovered backcounting, hole card play, sequencing, even a little risk-aversion. And one thing that particularly caught my attention was Thorp's use of "end play". As I was reading the section over once again, I remembered a recent post by Ted Forrester a.k.a alienated, in which he briefly discussed the exploitation of bordering (ST) segments, and I believe the follow-up post almost won POM on Green Chip. Though I didn't get much out of Ted's first post, I beleive the strategy is based on "end play", and am eagerly looking forward to any comments made by Ted on the subject. But anyway, the point was....oh yeah, old-school players rule. ;-)
ANS
Adam N. Subtractum
Well-Known Member
Sonny, reread...this method does NOT affect pivot
Rob McGarvey
Well-Known Member
And so they should *LINK*
<P ALIGN="JUSTIFY">
Old school rocks daddy-o! grin Nothing new under the sun was recently discussed at BJ21. I started my last months newletter off with the relay about Donny S's comment in BJA where he states this. Then he goes on to cover risk aversive indices at new lengths, something I have become rather interested in, risk aversion for the online BJ player. (Had to go back and put a few periods in my rambling!) Thorp is as old school as they get, but this makes him the Austin Powers of the markets in 2003. Old school now has some amazing computer ability that they never had back in the day which empowers them even more. Ustons' #'s on some things is off by a hair (ie playing multi hands) but I am sure he would be all over this stuff if he didn't check out so soon.
So here we are, workin' our old school tunes with 2003 dance moves!
<P ALIGN="JUSTIFY">
From the newsletter: Last month at Stanford Wong's BJ21 site this was posted by OddBall: From page 300 of Blackjack Attack, Don Schlesinger says "There's nothing new under the sun, and, truth be told, it isn't very easy these days to find new areas of research concerning blackjack matters." Then he goes on to say "Reminds me of this old quote: "Everything that can be invented has been invented." Charles H. Duell, U.S. Commissioner of Patents, in 1899. It was noted that this was taken out of context, and that Don goes on to demonstrate the results of new research.
<P ALIGN="JUSTIFY">
John May then added: "Still rather odd. I would have thought that, even if you disqualify online blackjack altogether which is a continent of unexplored theoretical ground, you would still have plenty room for discovery in the almost infinite conceptual area of shuffle analysis, or perhaps the myriad new blackjack variants being presented. I'm currently engaged in about analysis of seven or eight new developments in blackjack which can conceivably yield significant practical returns. Finding new areas of research is not the problem. Finding time to do it all is my problem. Perhaps, if you replace "blackjack" with "traditional blackjack card counting" the sentence makes more sense." Finally, it was noted that this is a quote of Aristotle, and that Don was just setting getting ready to re-answer the age old question "When do I leave" and "What are risk aversive indices, and should I be using them."
<P ALIGN="JUSTIFY">
You are seeing what I was recently talking about at bjmath.com when I asked about risk aversion for onLine BJ........
<P ALIGN="JUSTIFY">
Old school rocks daddy-o! grin Nothing new under the sun was recently discussed at BJ21. I started my last months newletter off with the relay about Donny S's comment in BJA where he states this. Then he goes on to cover risk aversive indices at new lengths, something I have become rather interested in, risk aversion for the online BJ player. (Had to go back and put a few periods in my rambling!) Thorp is as old school as they get, but this makes him the Austin Powers of the markets in 2003. Old school now has some amazing computer ability that they never had back in the day which empowers them even more. Ustons' #'s on some things is off by a hair (ie playing multi hands) but I am sure he would be all over this stuff if he didn't check out so soon.
So here we are, workin' our old school tunes with 2003 dance moves!
From the newsletter: Last month at Stanford Wong's BJ21 site this was posted by OddBall: From page 300 of Blackjack Attack, Don Schlesinger says "There's nothing new under the sun, and, truth be told, it isn't very easy these days to find new areas of research concerning blackjack matters." Then he goes on to say "Reminds me of this old quote: "Everything that can be invented has been invented." Charles H. Duell, U.S. Commissioner of Patents, in 1899. It was noted that this was taken out of context, and that Don goes on to demonstrate the results of new research.
<P ALIGN="JUSTIFY">
John May then added: "Still rather odd. I would have thought that, even if you disqualify online blackjack altogether which is a continent of unexplored theoretical ground, you would still have plenty room for discovery in the almost infinite conceptual area of shuffle analysis, or perhaps the myriad new blackjack variants being presented. I'm currently engaged in about analysis of seven or eight new developments in blackjack which can conceivably yield significant practical returns. Finding new areas of research is not the problem. Finding time to do it all is my problem. Perhaps, if you replace "blackjack" with "traditional blackjack card counting" the sentence makes more sense." Finally, it was noted that this is a quote of Aristotle, and that Don was just setting getting ready to re-answer the age old question "When do I leave" and "What are risk aversive indices, and should I be using them."
<P ALIGN="JUSTIFY">
You are seeing what I was recently talking about at bjmath.com when I asked about risk aversion for onLine BJ........
zengrifter
Banned
Someone call the spam-remover, please!
Boundaries/end play: Part I
Sorry, I should have responded to your insightful remarks earlier. I've been a bit snowed under lately. You are absolutely right to draw a connection between boundary effects and end play. Conceptually they are identical. I pointed this out myself in one of my bj21 theory posts leading up to the segment boundary post you mention. John May has also pointed out similar things in the past. The differences are in application, especially the fact that the player has only imperfect knowledge about the location of the boundary when segment tracking. My boundary post focused on one specific scenario involving the player receiving 2 cards, the dealer 1, from the current segment, then the round being completed from the new segment. At the moment I am working on an almost complete treatment of boundary effects. For a no-holecard game I am trying to account for the following scenarios regarding segments A and B:
a) Both player and dealer receive no cards from A, all from B [0,0].
b) Player receives 1 card, dealer 0, from A, rest from B [1,0].
c) Player and dealer each receive 1 card from A [1,1].
d) Player receives 2 cards, dealer 1, from A [2,1].
e) Player receives all cards, dealer 1, from A [a,1].
f) Player receives all cards, dealer 2, from A [a,2].
g) Player and dealer both receive all cards from A [a,a].
A similar set of cases will be examined for holecard games.
Working out cases a) and g) is trivial. Case d) is the one I have already dealt with in my previous bj21 post. Although only one possibility, it is an especially important case because the player makes playing decisions based on knowledge of his/her first two cards and the dealer's upcard. Whether the true situation is [1,0], [1,1] or [2,1], the player's optimal way to play the hand will be the same, even though the previous betting decision was partly based on which of these cases was more likely to occur. I have also worked out cases b) and c). Note the applicability of case b) to the red-blue card scenario discussed in the past by John May. Cases e) and f) pose the greatest difficulties and will take more time. The main difficulties are caused by the fact that the player's hand is completed from a different segment to the dealer which raises questions about what strategy it is reasonable to assume. Since it is unlikely that the player will know exactly where the boundary is, it seems more reasonable to assume that his/her best guess is either the strategy based on [2,1] or [a,a]. Still, for completeness, it would be nice to determine the optimal strategies for [a,1] and [a,2]. Actually, [a,1] is of more importance than [a,2] because it has a greater frequency of occurrence (more on frequencies below).
Continued part II...
Sorry, I should have responded to your insightful remarks earlier. I've been a bit snowed under lately. You are absolutely right to draw a connection between boundary effects and end play. Conceptually they are identical. I pointed this out myself in one of my bj21 theory posts leading up to the segment boundary post you mention. John May has also pointed out similar things in the past. The differences are in application, especially the fact that the player has only imperfect knowledge about the location of the boundary when segment tracking. My boundary post focused on one specific scenario involving the player receiving 2 cards, the dealer 1, from the current segment, then the round being completed from the new segment. At the moment I am working on an almost complete treatment of boundary effects. For a no-holecard game I am trying to account for the following scenarios regarding segments A and B:
a) Both player and dealer receive no cards from A, all from B [0,0].
b) Player receives 1 card, dealer 0, from A, rest from B [1,0].
c) Player and dealer each receive 1 card from A [1,1].
d) Player receives 2 cards, dealer 1, from A [2,1].
e) Player receives all cards, dealer 1, from A [a,1].
f) Player receives all cards, dealer 2, from A [a,2].
g) Player and dealer both receive all cards from A [a,a].
A similar set of cases will be examined for holecard games.
Working out cases a) and g) is trivial. Case d) is the one I have already dealt with in my previous bj21 post. Although only one possibility, it is an especially important case because the player makes playing decisions based on knowledge of his/her first two cards and the dealer's upcard. Whether the true situation is [1,0], [1,1] or [2,1], the player's optimal way to play the hand will be the same, even though the previous betting decision was partly based on which of these cases was more likely to occur. I have also worked out cases b) and c). Note the applicability of case b) to the red-blue card scenario discussed in the past by John May. Cases e) and f) pose the greatest difficulties and will take more time. The main difficulties are caused by the fact that the player's hand is completed from a different segment to the dealer which raises questions about what strategy it is reasonable to assume. Since it is unlikely that the player will know exactly where the boundary is, it seems more reasonable to assume that his/her best guess is either the strategy based on [2,1] or [a,a]. Still, for completeness, it would be nice to determine the optimal strategies for [a,1] and [a,2]. Actually, [a,1] is of more importance than [a,2] because it has a greater frequency of occurrence (more on frequencies below).
Continued part II...
Boundaries/end play: Part II
Once I have worked out the various specific cases I can determine player expectations for different scenarios, assuming different levels of tracking precision. For instance, the player may merely be confident that the segment boundary will be crossed within the next 15 cards, or during the next round, etc. A weighted expectation can be calculated for any (A,B) based on the frequencies of the different types of boundary crossings that could occur within that range of cards and the player advantages associated with each of those distinct types of boundary crossings. Frequencies of crossing types can be influenced by the player's choice of betting box and the number of boxes open. For instance, if the player sits at box 1, the probability of [1,1] is all but eliminated, since the player's second card comes immediately after the dealer's first card. Similarly, if the player sits at box 7, the chance of [1,0] is all but eliminated.
The potential gains from exploiting segment boundaries are far from trivial, though I don't think I made this very clear in my bj21 post. Most people seemed to imagine that the concept was applicable only to an extremely narrow type of situation and/or would require rare genius to pull off. Neither perception is accurate. Potential gains are in the ballpark of sequencing, not straight counting, or even more conventional tracking. Nor is the frequency of boundary crossings negligible. With 3/4 deck tracked segments in a 5/6 game, there will be six crossings per shoe. At a full table a boundary is crossed every two to three rounds. As far as practicalities go, potential gains remain large even when tracking precision is quite low. This is because for some (A,B), most types of boundary crossings are advantageous, whereas for other (A,B), no types of boundary crossings are advantageous. Of course, less tracking precision results in smaller potential gains than would be possible with greater precision, just as greater accuracy in ace keying raises profitability. Finally, information regarding boundary effects is also useful from a cover perspective, since some of the most lucrative opportunities occur in rising counts, somewhat weakening the negative correlation between bets and count movements observable in a competent tracker's play.
I have already indicated at bj21 that my more complete treatment of boundary effects will probably not be posted, simply because the document will be too long, though I might post a condensed version. Nevertheless, I intend to make the completed work available free of charge to anyone who might be interested (all three of you...).
alienated
PS: Sorry if the above is difficult to follow. I'm rather busy at the moment and don't have time to explain things more simply. I'll try hard to write things clearly in the completed work.
Once I have worked out the various specific cases I can determine player expectations for different scenarios, assuming different levels of tracking precision. For instance, the player may merely be confident that the segment boundary will be crossed within the next 15 cards, or during the next round, etc. A weighted expectation can be calculated for any (A,B) based on the frequencies of the different types of boundary crossings that could occur within that range of cards and the player advantages associated with each of those distinct types of boundary crossings. Frequencies of crossing types can be influenced by the player's choice of betting box and the number of boxes open. For instance, if the player sits at box 1, the probability of [1,1] is all but eliminated, since the player's second card comes immediately after the dealer's first card. Similarly, if the player sits at box 7, the chance of [1,0] is all but eliminated.
The potential gains from exploiting segment boundaries are far from trivial, though I don't think I made this very clear in my bj21 post. Most people seemed to imagine that the concept was applicable only to an extremely narrow type of situation and/or would require rare genius to pull off. Neither perception is accurate. Potential gains are in the ballpark of sequencing, not straight counting, or even more conventional tracking. Nor is the frequency of boundary crossings negligible. With 3/4 deck tracked segments in a 5/6 game, there will be six crossings per shoe. At a full table a boundary is crossed every two to three rounds. As far as practicalities go, potential gains remain large even when tracking precision is quite low. This is because for some (A,B), most types of boundary crossings are advantageous, whereas for other (A,B), no types of boundary crossings are advantageous. Of course, less tracking precision results in smaller potential gains than would be possible with greater precision, just as greater accuracy in ace keying raises profitability. Finally, information regarding boundary effects is also useful from a cover perspective, since some of the most lucrative opportunities occur in rising counts, somewhat weakening the negative correlation between bets and count movements observable in a competent tracker's play.
I have already indicated at bj21 that my more complete treatment of boundary effects will probably not be posted, simply because the document will be too long, though I might post a condensed version. Nevertheless, I intend to make the completed work available free of charge to anyone who might be interested (all three of you...).
alienated
PS: Sorry if the above is difficult to follow. I'm rather busy at the moment and don't have time to explain things more simply. I'll try hard to write things clearly in the completed work.
Adam N. Subtractum
Well-Known Member
Pure genius Ted...
...unfortunately I am pressed for time at the moment, as well, and could only read through your posts once, but I think I follow you 100%, Ted. Looking forward to exploring into the subject. As for only us four being interested...hey, more for us. Thanks
ANS
...unfortunately I am pressed for time at the moment, as well, and could only read through your posts once, but I think I follow you 100%, Ted. Looking forward to exploring into the subject. As for only us four being interested...hey, more for us. Thanks
ANS