Specific Interests of 2-deck[+ indexes correlating]

#1
Hello - 1st time post here. Hopefully I'm posting this in the right category, as I feel it could be classified as mathematics also. And thanks to anyone able to promptly point me in the right direction, as I appreciate the time of others.

Lately I've been playing specifically 2-deck pitch in LV, with about 65%-75% penetration(depending on the dealer, sometimes they cut it light or deeper). Rules are as follows: [Dealer Hit soft 17], [double any 2 cards], [split up to 4 times], [aces able to be re-split], [double after split], [no surrender]. Have been playing 2-deck basic strategy using a Hi-Lo count, and under ideal conditions, playing the dealer alone. Haven't sensed heat yet, using a 1:4 spread mostly.

My specifics come into question now; I just finished Beat the Dealer and Blackbelt in Blackjack : Playing 21 as a Martial Art. I know Thorp has indexes listed in Beat the Dealer, but are his specifically correlating to single-deck or are those the best mathematical indexes for any # of decks? I ask because most of his references are old-school, as most people describe his book to be, referencing to 1-deck.

Having a RC and TC going can only get you so far; I've been running into a few situations to where I'm assuming I'm playing it wrongly[all references are 2-deck games]; like a +8 RC with 1 deck remaining, and I have 16 against a dealer 7. I feel I'm suppose to be staying here, and Thorp's charts confirm an index of >10 merits a stand. With an RC of +8 and 52 cards left, you're looking at [8/52 or ~15]. Earlier today I hit there, feeling awkward because I knew the RC was huge and the penetration was getting good. 10 came off and I busted, confirming my miss-play. Also the RC was -9 at 1 point, and I had a 14 against a dealer 2 with under a deck left, and I didn't hit that. Again, I felt weird thinking I was probably making the wrong play. Thorp's chart shows a 14 against dealer 2 you hit an index < -05, which in my case an index of ~ -18. Basically, I want to memorize the perfect, correct, indexes for this specific set of rules but I don't know if Thorp's are 1-deck specific or if there is a 2-deck specific set of indexes some-1 can reference me to.

In Arnold Snyder's Blackbelt in Blackjack : Playing 21 as a Martial Art, he references in the back of the book to having specific reports for 1/2/4/6/8 decks. If I ordered his 2-deck report, it might have the information I need but I can't confirm. I don't mind ordering it if that's the case but specifically I wanted to have the proper information for when I play tomorrow. I don't want to lose small edges like I did earlier today, hitting 16 against 17 on a high RC, etc.

My math is sharp, my memory is good, and this past week I've been wanting to learn anything and everything I can; I just feel like I can add another .5% advantage if I have access to the perfect indexes for this game setup. And as far as the week has gone, I've had 4 winning sessions, 2 losing after today. Today's loss was pretty bad; over 2 hours and ~ 9-11 double-downs, I lost all but 1[very improbable I know .. fluctuation isn't always fun I guess]. This was even after I tried to neutralize the night by Wong'ing out twice to go piss and get a new shuffle when I got back on early -5 to -8 counts.

Hopefully any1 who managed to read this all can point me in the right direction; I just want to fine-tune my indexes from home so I don't make subtle mistakes costing me small edges and money when I play tomorrow. Thanks for any help and references that are prompt.
 
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jack.jackson

Well-Known Member
#2
IcyM said:
Hello - 1st time post here. Hopefully I'm posting this in the right category, as I feel it could be classified as mathematics also. And thanks to anyone able to promptly point me in the right direction, as I appreciate the time of others.

Lately I've been playing specifically 2-deck pitch in LV, with about 65%-75% penetration(depending on the dealer, sometimes they cut it light or deeper). Rules are as follows: [Dealer Hit soft 17], [double any 2 cards], [split up to 4 times], [aces able to be re-split], [double after split], [no surrender]. Have been playing 2-deck basic strategy using a Hi-Lo count, and under ideal conditions, playing the dealer alone. Haven't sensed heat yet, using a 1:4 spread mostly.

My specifics come into question now; I just finished Beat the Dealer and Blackbelt in Blackjack : Playing 21 as a Martial Art. I know Thorp has indexes listed in Beat the Dealer, but are his specifically correlating to single-deck or are those the best mathematical indexes for any # of decks? I ask because most of his references are old-school, as most people describe his book to be, referencing to 1-deck.

Having a RC and TC going can only get you so far; I've been running into a few situations to where I'm assuming I'm playing it wrongly[all references are 2-deck games]; like a +8 RC with 1 deck remaining, and I have 16 against a dealer 7. I feel I'm suppose to be staying here, and Thorp's charts confirm an index of >10 merits a stand. With an RC of +8 and 52 cards left, you're looking at [8/52 or ~15]. Earlier today I hit there, feeling awkward because I knew the RC was huge and the penetration was getting good. 10 came off and I busted, confirming my miss-play. Also the RC was -9 at 1 point, and I had a 14 against a dealer 2 with under a deck left, and I didn't hit that. Again, I felt weird thinking I was probably making the wrong play. Thorp's chart shows a 14 against dealer 2 you hit an index < -05, which in my case an index of ~ -18. Basically, I want to memorize the perfect, correct, indexes for this specific set of rules but I don't know if Thorp's are 1-deck specific or if there is a 2-deck specific set of indexes some-1 can reference me to.

In Arnold Snyder's Blackbelt in Blackjack : Playing 21 as a Martial Art, he references in the back of the book to having specific reports for 1/2/4/6/8 decks. If I ordered his 2-deck report, it might have the information I need but I can't confirm. I don't mind ordering it if that's the case but specifically I wanted to have the proper information for when I play tomorrow. I don't want to lose small edges like I did earlier today, hitting 16 against 17 on a high RC, etc.

My math is sharp, my memory is good, and this past week I've been wanting to learn anything and everything I can; I just feel like I can add another .5% advantage if I have access to the perfect indexes for this game setup. And as far as the week has gone, I've had 4 winning sessions, 2 losing after today. Today's loss was pretty bad; over 2 hours and ~ 9-11 double-downs, I lost all but 1[very improbable I know .. fluctuation isn't always fun I guess]. This was even after I tried to neutralize the night by Wong'ing out twice to go piss and get a new shuffle when I got back on early -5 to -8 counts.

Hopefully any1 who managed to read this all can point me in the right direction; I just want to fine-tune my indexes from home so I don't make subtle mistakes costing me small edges and money when I play tomorrow. Thanks for any help and references that are prompt.
More than likely Thorps indexes were generated for single deck only. And as a side note, the indexes for H17 v S17 and DAS vs Ndas would make a noticeable difference as well for single deck. CVdata can do all this for you, btw.

Now before commenting on Thorps counts and the accuracy thereof, i wanted to make sure your calculating your TCs correctly. Unless your dividing by 1/2 decks this is not right.

With an RC of +8 and 52 cards left, you're looking at [8/52 or ~15].
Are you dividing by 1/2 decks? And if so, are you using the correct indexes for such? Please explain.
 
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#3
IcyM said:
Having a RC and TC going can only get you so far; I've been running into a few situations to where I'm assuming I'm playing it wrongly[all references are 2-deck games]; like a +8 RC with 1 deck remaining, and I have 16 against a dealer 7. I feel I'm suppose to be staying here, and Thorp's charts confirm an index of >10 merits a stand. With an RC of +8 and 52 cards left, you're looking at [8/52 or ~15]. Earlier today I hit there, feeling awkward because I knew the RC was huge and the penetration was getting good. 10 came off and I busted, confirming my miss-play.
You are not calculating the TC correctly. You divide the RC by the # of remaining decks. RC +8 with 1 deck remaining TC = 8/1 = 8. [AND 8/52 is not ~15. It is 1/7.5 = 0.133]

IcyM said:
Also the RC was -9 at 1 point, and I had a 14 against a dealer 2 with under a deck left, and I didn't hit that. Again, I felt weird thinking I was probably making the wrong play. Thorp's chart shows a 14 against dealer 2 you hit an index < -05, which in my case an index of ~ -18. B
TC at RC -9 with less than a deck left is less than -9 which is less than the index of -5. You should have hit. Your problem is in calculating the proper TC to compare to the indices. -9/(3/4 of a deck) = -9*4/3 = -12. Invert the fraction and multiply to get the result of dividing by a fraction.

Again TC = RC/(# of decks remaining). I hope that helps.
 
#4
I was under the impression, in a 2-deck game, if 1 deck was played with a RC +9, the TC would also be +9 but the index value would be 9/52 or ~ 18. Whereas if its early in the deck and u have a +4 count fast, the TC would be more like +2 but the index value would still be ~ +4. (4/96ish). If this information is wrong then I've miss-read but I think this is how he listed his index values.
 

bigplayer

Well-Known Member
#5
IcyM said:
I was under the impression, in a 2-deck game, if 1 deck was played with a RC +9, the TC would also be +9 but the index value would be 9/52 or ~ 18. Whereas if its early in the deck and u have a +4 count fast, the TC would be more like +2 but the index value would still be ~ +4. (4/96ish). If this information is wrong then I've miss-read but I think this is how he listed his index values.
Why would you ever have that impression? The TC is the same TC for both betting and index play. If the Index is +10 and your TC is +9 you play basic strategy for that decision.

What kind of math are you using...9/52 does not remotely equal approximately 18 and 4/96 is not remotely 4. 936/52 would be 18.
 

PierceNation

Well-Known Member
#6
IcyM said:
Hello - 1st time post here.
Welcome :)

Earlier today I hit there, feeling awkward because I knew the RC was huge and the penetration was getting good. 10 came off and I busted, confirming my miss-play
One hand is not enough to confirm a miss-play. Several times ive pulled a 2 whilst doubling an 11 vs dealer 6, was that wrong? nope.

I think its important to point out that indexes are reassessed all the time, using thorps indexes may not be optimal. Its also important to point out that some indexes are far more important in terms of EV and use than others.

16 vs 7 is probably one of the least important. The count has to be sky high for you to stand on that hand, and even then its a protective stand, you won't win a 16 v 7 in the long run, no matter what the TC is (With a RC of 8 and one deck left, you have a TC of 8, not enough for a stand anyway..you made the right choice)

If I were you I would look up the 'illustrious 18' indices from blackjackattack (or just search the net). Im a great believer in knowing as many indices as possible, but it will help you understand the importance of some indexes over others, and how to use that knowledge to your advantage.

On a slightly seperate note, using HiLo, especially in a pitch game, will not give you the fantastic Playing Effiency that you are looking for.

For this reason I would suggest (when you feel completely comfortable with your current system) moving onto the Zen count. It is vastly superior in PE to HiLo. HiLo is too weak for Double deckers.

Hope that helps

Pierce
 
#7
bigplayer said:
Why would you ever have that impression? The TC is the same TC for both betting and index play. If the Index is +10 and your TC is +9 you play basic strategy for that decision.

What kind of math are you using...9/52 does not remotely equal approximately 18 and 4/96 is not remotely 4. 936/52 would be 18.


Because when I read, it seemed there was a difference in a TC and Thorp's index values; TC is based on deck's remaining[RC/deck's remaining], usually an integer of 1-8, but obviously not uncommon to have to use .25 or .5 value values also to account for 1/4 or 1/2 decks. Whereas it sounded that Thorp's index value's are based on unseen card's remaining[RC/unseen cards] - completely different from unseen deck/s remaining because you're dividing the RC by a larger number and multiplying by 100(to get it's percent value, which Thorp describes the final number as being the high low index). When everyone is sitting here saying you can't do math for ****, I'm just using those references; RC +9/52 = .17307(I said 18 because 9/50 seemed mentally easier to = 18). Multiply this by 100, as Thorp has described in his book(to change to percent multiply by 100), to get the final result of high low index number.

Reference page 96 of Beat the Dealer if you feel there is little validity to what I describe. My only issue is miss-information is the worst of results I could ask for, so please keep that in mind.
 
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#8
PierceNation said:
Welcome :)



One hand is not enough to confirm a miss-play. Several times ive pulled a 2 whilst doubling an 11 vs dealer 6, was that wrong? nope.

I think its important to point out that indexes are reassessed all the time, using thorps indexes may not be optimal. Its also important to point out that some indexes are far more important in terms of EV and use than others.

16 vs 7 is probably one of the least important. The count has to be sky high for you to stand on that hand, and even then its a protective stand, you won't win a 16 v 7 in the long run, no matter what the TC is (With a RC of 8 and one deck left, you have a TC of 8, not enough for a stand anyway..you made the right choice)

If I were you I would look up the 'illustrious 18' indices from blackjackattack (or just search the net). Im a great believer in knowing as many indices as possible, but it will help you understand the importance of some indexes over others, and how to use that knowledge to your advantage.

On a slightly seperate note, using HiLo, especially in a pitch game, will not give you the fantastic Playing Effiency that you are looking for.

For this reason I would suggest (when you feel completely comfortable with your current system) moving onto the Zen count. It is vastly superior in PE to HiLo. HiLo is too weak for Double deckers.

Hope that helps

Pierce

Thanks for the advice; I'll search those indices after this reply.

Yeah I know Hi-Lo is a low-level count, and was considering improving to a level 2 like you suggested such as Zen. I've just been using the Hi-Lo truthfully because it is convenient for the game I play. Playing headsup vs a dealer is sometimes tough to keep a count because they try to talk more if you're playing at odd-hours since it might be slower or some dealers might deal fast if they want to try to clear you out, more-so if they 1) thought u were counting and 2) cared u were counting. Ideally I will learn a higher-strength system soon, but for now I'd rather try to keep things as natural as I can regardless.

I just want to learn the indices because yesterday I lost 3 unit bet instead of winning it by not hitting 14 vs dealer 2 when the count was very negative. I just feel if I make even 2-3 of those errors over a 3 hour session or so I'm really going to take a negative advantage, even if it's considered a small error.

I just don't see much discussion of 2-deck, or their listed index values. Hopefully I'll find what I need over the next day or so :) Thanks again.
 
#9
IcyM said:
Because when I read, it seemed there was a difference in a TC and Thorp's index values; TC is based on deck's remaining[RC/deck's remaining], usually an integer of 1-8, but obviously not uncommon to have to use .25 or .5 value values also to account for 1/4 or 1/2 decks. Whereas it sounded that Thorp's index value's are based on unseen card's remaining[RC/unseen cards] - completely different from unseen deck/s remaining because you're dividing the RC by a larger number and multiplying by 100(to get it's percent value, which Thorp describes the final number as being the high low index). When everyone is sitting here saying you can't do math for ****, I'm just using those references; RC +9/52 = .17307(I said 18 because 9/50 seemed mentally easier to = 18). Multiply this by 100, as Thorp has described in his book(to change to percent multiply by 100), to get the final result of high low index number.

Reference page 96 of Beat the Dealer if you feel there is little validity to what I describe. My only issue is miss-information is the worst of results I could ask for, so please keep that in mind.
Compare Thorp's indices to normal HILO indices. They would have to be vastly different to make this correct (a factor of about 2). It sounds like he was talking about half deck TC not full deck TC. If this is correct the indices are about double the normal 1 deck TC indices.
 
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#10
IcyM said:
I just want to learn the indices because yesterday I lost 3 unit bet instead of winning it by not hitting 14 vs dealer 2 when the count was very negative. I just feel if I make even 2-3 of those errors over a 3 hour session or so I'm really going to take a negative advantage, even if it's considered a small error.
You do know -18 is less than -5 right.
 

FLASH1296

Well-Known Member
#11
" … specific reports for 1/2/4/6/8 decks. If I ordered his 2-deck report, it might have the information "

The 2-deck report is long out of print.

Let me know if you find a copy.
 

FLASH1296

Well-Known Member
#12
" … specific reports for 1/2/4/6/8 decks. If I ordered his 2-deck report, it might have the information "

to get a copy go to:

(Dead link: http://www.gamblersbookclub.com/Category/86-Blackjack_books)

♠ Snyder, Arnold, Beat the 1, 2, 4, 6, and 8-Deck Game, Cardoza Publishing, 2005.
These books provide frequency distributions for blackjack games and guides for using them to analyze the profit available and flux inherent in different approaches to the games. They have helped players analyze not only card-counting approaches, but a number of original advanced techniques that they would otherwise not be able to analyze without writing their own computer simulation programs. If you don’t know what a frequency distribution is and why they’re important, read Blackbelt in Blackjack first.

Revised and updated in March 2005. The 2005 editions are available now through Cardoza Publishing, at 1-800-577-WINS
or: Cardoza Publishing, P.O. Box 1500, Cooper Station, New York, NY, 10276.

Also available at Gamblers Book Store in Las Vegas.
 
#13
tthree said:
You do know -18 is less than -5 right.
:) "Draw if your index is less than or equal to." When my value was -18 by the references I'm using, the -5 on the chart means I draw there, not stand, which confirmed my miss-play :\ That's why I feel these minor errors will be costly; and I'm not sure what the standard indices are for other more normal charts. I was hoping when Wong's book arrives it will have index tables that I can reference more easily. Still waiting 5 days to get it though.

FLASH1296 said:
" … specific reports for 1/2/4/6/8 decks. If I ordered his 2-deck report, it might have the information "

to get a copy go to:

(Dead link: http://www.gamblersbookclub.com/Category/86-Blackjack_books)

♠ Snyder, Arnold, Beat the 1, 2, 4, 6, and 8-Deck Game, Cardoza Publishing, 2005.
These books provide frequency distributions for blackjack games and guides for using them to analyze the profit available and flux inherent in different approaches to the games. They have helped players analyze not only card-counting approaches, but a number of original advanced techniques that they would otherwise not be able to analyze without writing their own computer simulation programs. If you don’t know what a frequency distribution is and why they’re important, read Blackbelt in Blackjack first.

Revised and updated in March 2005. The 2005 editions are available now through Cardoza Publishing, at 1-800-577-WINS
or: Cardoza Publishing, P.O. Box 1500, Cooper Station, New York, NY, 10276.

Also available at Gamblers Book Store in Las Vegas.
Thank you for the information! :) Have you personally ever looked over any of them(as in, they are very helpful and informative?) If so I can check out the gambler's book store if that is still around.
 

PierceNation

Well-Known Member
#14
IcyM said:
Playing headsup vs a dealer is sometimes tough to keep a count
Thats fair enough, stick with HiLo for now then, The power of a level 2 count would be lost if you were inaccurate.

I just want to learn the indices because yesterday I lost 3 unit bet instead of winning it by not hitting 14 vs dealer 2 when the count was very negative.
1. Its very important to realise that you didnt lose that particular hand because of the count, the index, or anything else other than devation (luck for want of a better word). You can make 10 errors in a row and still win them all, thats the nature of the game. A particular indice does not guarantee a win or loss on that hand, it just increases the expectation of that hand. This may mean you will win 52 out of 100 hands instead of 50 on that particular matchup.

Some errors will cost you more than others. Misplaying 15 vs 10 will cost you a good chunk of your EV, whereas hitting 16 vs 7 when it is not suggested will be relatively small. due to the infrequency of:
1. The high count that requires a stand.
2. Actually dealt that hand at said high count.

Once youv'e checked out the Ill18 you will see which ones are imperative to maintaining your EV.

I understand that there is a minimal amount to research the double deck game, this is mainly because the pitch games nowadays are usually so bad it is more advantegeous to play 6 deckers with far better rules and penetration.
 
#15
PierceNation said:
Thats fair enough, stick with HiLo for now then, The power of a level 2 count would be lost if you were inaccurate.



1. Its very important to realise that you didnt lose that particular hand because of the count, the index, or anything else other than devation (luck for want of a better word). You can make 10 errors in a row and still win them all, thats the nature of the game. A particular indice does not guarantee a win or loss on that hand, it just increases the expectation of that hand. This may mean you will win 52 out of 100 hands instead of 50 on that particular matchup.

Some errors will cost you more than others. Misplaying 15 vs 10 will cost you a good chunk of your EV, whereas hitting 16 vs 7 when it is not suggested will be relatively small. due to the infrequency of:
1. The high count that requires a stand.
2. Actually dealt that hand at said high count.

Once youv'e checked out the Ill18 you will see which ones are imperative to maintaining your EV.

I understand that there is a minimal amount to research the double deck game, this is mainly because the pitch games nowadays are usually so bad it is more advantegeous to play 6 deckers with far better rules and penetration.

I'm fully aware of the point about variance in luck and its fluctuation vs expected value. I would rather play the hand perfectly and lose it then play it wrong and win it. Luck is short-based and I could play sub-par in comparison to index values and win hugely, and then play super-par in comparison to index values and lose hugely. Over the long-run though, I need to recognize my bad plays if I want to keep small advantages.

I'm gonna go pick up some more books today and see if I feel adding a stronger count is plausible.

In reference to the 2-deckers, some of their rules(H17 + no surrender) are dis-advantageous I would agree. I referenced my scenario(the game I play and its rules) to the chart in Snyder's book BLACKBELT IN BLACKJACK; playing in the game is suppose to give the player a consistent advantage to generate profit, as anything above 50 in his book is considered very good(I think these rules gave a total of ~65). It's to be noted that this games set of rules give -.4% to the player using basic strategy; I feel it is beatable and profitable if 100+ hours of play were considered using 1:4, even a 1:2 if you bet your advantages of .5% or higher. I wouldn't be surprised if Wong'ing out 2-4 times over your whole session on high negative counts would put you at 0% disadvantage either. Maybe my assumptions are off but it seems like a profitable path in direct correlation to a 6-deck shoe with similar/better rules(S17 + surrender). Granted, if you have a team vs a 6-deck you can have your gorilla come in on +20 counts and surely crush it faster, but coming from a person who wanted to develop skills just to play by myself, the 2-decker seems like the best idea to generate advantages.
 

FLASH1296

Well-Known Member
#16
Your understanding of the mathematics of the game needs a boost.

Just because you matt have played a hand "incorrectly", your actual

projected e.v. was probably on the order of 1.0% of you bet.

So .. you lost a few cents or maybe even a buck. ~(@)_(@)~

At such a poor T.C. you were obviously betting minimally.
 
#17
on wongs book

Think his indicies are for 4 deck?
Which is multi deck; like double deck, you can use those.
He tells you how to calculate TC and use indicies.
He has s17 & h17 iindicies.
Being a little off on indicies does not matter, dont get obsessed

It also has the halves count, the strongest count without a side count. It's very similar to hi lo with nearly same indicies. It's the natural step up.

You probably need to spread your play around.
 

PierceNation

Well-Known Member
#18
IcyM said:
I'm fully aware of the point about variance in luck and its fluctuation vs expected value. I would rather play the hand perfectly and lose it then play it wrong and win it. Luck is short-based and I could play sub-par in comparison to index values and win hugely, and then play super-par in comparison to index values and lose hugely. Over the long-run though, I need to recognize my bad plays if I want to keep small advantages.

I'm gonna go pick up some more books today and see if I feel adding a stronger count is plausible.

In reference to the 2-deckers, some of their rules(H17 + no surrender) are dis-advantageous I would agree. I referenced my scenario(the game I play and its rules) to the chart in Snyder's book BLACKBELT IN BLACKJACK; playing in the game is suppose to give the player a consistent advantage to generate profit, as anything above 50 in his book is considered very good(I think these rules gave a total of ~65). It's to be noted that this games set of rules give -.4% to the player using basic strategy; I feel it is beatable and profitable if 100+ hours of play were considered using 1:4, even a 1:2 if you bet your advantages of .5% or higher. I wouldn't be surprised if Wong'ing out 2-4 times over your whole session on high negative counts would put you at 0% disadvantage either. Maybe my assumptions are off but it seems like a profitable path in direct correlation to a 6-deck shoe with similar/better rules(S17 + surrender). Granted, if you have a team vs a 6-deck you can have your gorilla come in on +20 counts and surely crush it faster, but coming from a person who wanted to develop skills just to play by myself, the 2-decker seems like the best idea to generate advantages.
In all fairness the rules you listed were fairly good for a double-decker, and with a score of 65 on the SPI, it makes a good play. However the SPI is a rough estimate, and I am unsure how well a 1-4 spread will do for you, I would SIM it against the 6 deck option to see which comes out on top.

Regarding the indices, I wouldn't personally rely on Thorps book, its a great piece of blackjack history but not really relevant to the game today. You would do much better with a more up-to-date set of indexes for HiLO, or Zen if you decide to upgrade. If you are interested in playing as perfectly as possible for the two deck game, then the indices will be slightly different to the 4D and 6D versions.

Wongs book will be your best bet for accurate TC based indices.

If you choose to upgrade to Zen, do not use the true edge method in BiB, use the TC adjustment indices, which can be obtained if you look in the right places.

Pierce
 

k_c

Well-Known Member
#20
The first thing that needs clarification is the way Thorp defined his HiLo indexes (aka indices.) His indexes are defined as TC per card * 100 instead of TC per deck. In order to convert from TC per card to TC per deck just multiply by 52/100.

The second thing that could use clarification is the method of arriving at an index. It appears to me that the positive indexes in Beat the Dealer are derived by simply removing low cards (2-6) from a full single deck until this causes a change in strategy. The negative indexes are derived by simply removing high cards (T-A) from a full single deck until this causes a change in strategy. However, in a real blackjack game it is not likely that cards are dealt in this way. His indexes may be right for the condition of no 7,8,9,T,A (+) or no 2,3,4,5,6,7,8,9 (-) removed but are not necessarily right for a greater majority of deck compositions. The function of an index is to gain the most overall EV for possible compositions but there is no guarantee it will be right for all compositions.
 
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