indices

indices

Where does everyone out there get their indices? It seems that there are discrepancies between different sources, which unnerves me a little. I get my hi-lo indices from PBJ by Wong, but I have heard of many other sources, such as Casino Verite. The reason I ask this question is that I have been using an index of 0 for 12 v 6 in a 6D, S17 game, yet there are others who are using values closer to -1. Which is correct? Which source should I trust? How much of a difference does it make?

--Thanks, Homer J.

indices question - addition

Can I add to this please Homer.

Will indices (e.g. Wong's S17 6 Deck Hi-lo) vary between games, such as ENHC vs what Homer plays, and how much will that variation if it exists matter?

Cheers Homer,

BB.

One problem is that there is sometimes . . .

no correct answer - Risk nas to be weighed with optimal results and sometimes those two do not work togather.

BUT - that does not answer your question. Personally I'd go with the simulations. It's VERY easy to do 1 billion hand sims now and most books were written when 100,000 was a pretty good number.

Not saying SW was/is wrong but there are many fuzzy areas even with KO and Red7 (my two fav's for simming)

indices

I have indices from Wong's PB and SBA, 500 mil hands, sig 4. They are within 30 cents of each other on billion hand sims with a 4 deck game, 1 cut off, and a bet spread yielding a win rate in the area of 85 dollars/one hundred hands. Repeated sims yield the same results.

A straight forward answer

Most people get their indices directly from the book that they learned their count from. As Pikachu said, if an index number is only slightly off it makes very little difference. There are two reasons for your discrepencies; one is the difference betweena normal set and a risk-averse set. RA indices are designed so that you will not have to wager as much money on plays that are very close to 50/50, so that your variance will be greatly lowered. Number two is that a different set of rules will create slightly different indices sometimes. H17 and S17 and DAS will create differetn indeices...always trust a sim that was run on the exact game you expect to play, and if you are not able to run a sim, always trust the numbers you get from a book or other trustable sourse and know that slight differences are ok, and will cost you an unnopticeable difference over time.

Shotkaller

6D, S17 indices can be found elsewhere!

Homer

PBJ indices are for the four deck variety and there are some differences. The 12 vs. 6 is -1 for the six deck game. If you don't own Blackjack Attack, there is an article entitled "Illustrious 18 Revisited" by Cacarulo at BJMath.com which will give you six deck indices for the catch 22. In the Green Chip archives, the same author has an articles evaluating the gain of using exact indices, i.e, 3.9, vs. floored and rounded indices and for all practical purposes, the realistic gain from using these exact indices might be .3 to .4 percent over floored indices.

Risk Adverse, or RA indices may add around 3 % to overall gain. Changing the 10 vs. T indice, as an example, from 4 to a RA of 7 allows one to get most of the EV gain from that play with a great reduction in variance. In general, employing RA indices allows one to use a greater spread which more than makes up for lost EV.

If I'm not mistaken, the BJSchool on this site makes use of RA indices where applicable and BJ Attack II provides these as well.

Personally, I use the RA indices from these sources and the catch 22 indices from the above mentioned article, although I can't seem to knock some of the exact indices out of my head and will use them dependent upon conditions (card eating effects, nearing the end of a shoe issues, ploppy clearing, etc.)

Hope This Helps
Telescopic

Cost of playing wrong

The indices from most books are based on simulations which is not the best technique to get a precise result. A better method is combinatorial analysis and the results should be rounded to one decimal place and not to integers.
As I said on other occasions hitting any negative running count with 12 vs. 6 in a shoe game is definetely wrong. The correct index is -1.3.If you hit at the beginning of a six deck shoe (RC=-1,TC=-0.2) you get an error of 1.4%. In case of a $25 bet this means 35 cents at every occurrence.Up to you to decide whether this is insignificant.

Francis Salmon

Why are Sims not the best technique ??? (nt)

Error margin

It's a well known fact that sims have a persistent error margin even after millions of trials. That's why it's not an adequate tool to deal with close shots. Why allow for an error when you can calculate it correctly with probability theory.

Francis Salmon

Truncating vs Flooring

Both indices are correct. Wong index is truncated (0) while the other is floored (-1). What's the difference you may ask? In a truncated system a TC of 0 means any count between (-1,+1). Since the exact index is -1.0 it means that you will be hitting when the TC<=-1 but standing when the TC>-1. Thus, the index is 0.
In a floored system a TC of -1 means any count between [-1,0) and hence the index will be -1.

Hope this helps.

Sincerely
Cacarulo

PS: For more about flooring, truncating and rounding check out the glossary.

Effects of sim standard error overstated

Francis

I think it is sufficient to use sim results for index usage. If I see the results of a 2,150,000 round sim with a standard error of .0025%, this will not produce very large discrepencies in indices. I don't believe that such a big discrepency between -1.3 and -1 could happen between the two methods of calculation. Are you sure that your -1.3 is for 6D, S17 ?

Plus 2.5 mil is a very very small sim. (nt)

Talking about discrepencies

What do you think about the discrepencies occurring between simulation results?With all due respect for Cacarulo, I don't think that the difference between index 0 and index -1 can be talked away with reference to truncating and flooring. Anyway rounding would be more appropriate. I'm still waiting to see a simulation result that will yield decimals instead of integers.
My -1.3 was obtained by calculation on the basis of an infinite deck and should be valid for any shoe game S17.

Francis Salmon

Explanations

What do you think about the discrepencies occurring between simulation results?With all due respect for Cacarulo, I don't think that the difference between index 0 and index -1 can be talked away with reference to truncating and flooring.

But that's the way truncating and flooring treat indices. There's nothing wrong with it. Allow me to explain the difference between flooring and truncating in terms of buckets or bins:

Truncating

+----+---------+

| TC | Bucket  |

+----+---------+

| +2 | [+2,+3) |

| +1 | [+1,+2) |

|  0 | (-1,+1) |

| -1 | (-2,-1] |

| -2 | (-3,-2] |

+----+---------+

Flooring

+----+---------+

| TC | Bucket  |

+----+---------+

| +2 | [+2,+3) |

| +1 | [+1,+2) |

|  0 | [ 0,+1) |

| -1 | [-1, 0) |

| -2 | [-2,-1) |

+----+---------+

Note that all buckets have size 1 (one) except for the truncated "zero bucket" which is double. Here comes the difference and the reason of why flooring is better than truncating.

Now, let's say the exact index is -1.0. So you will hit TCs < -1.0 but stand on TCs >= -1.0. What happen at the -1 bucket in both methods?
If you're truncating then you should hit the buckets <= -1 but stand on buckets >= 0. That's why the index is zero.
On the other hand, if you decide to use floored buckets then you should hit the buckets <= -2 but stand on buckets >= -1. Thus, the index is -1. Do you see the difference?

Anyway rounding would be more appropriate.

That depends. Some times rounding is better and some times flooring is better. The important thing of both methods is that the buckets have the same size (=1).

Rounding

+----+-------------+

| TC | Bucket      |

+----+-------------+

| +2 | [+1.5,+2.5) |

| +1 | [+0.5,+1.5) |

|  0 | (-0.5,+0.5) |

| -1 | [-0.5,-1.5) |

| -2 | [-1.5,-2.5) |

+----+-------------+

I'm still waiting to see a simulation result that will yield decimals instead of integers.

It can be done with SBA. There's a trick for doing it that works pretty well. Suppose you want an exact index with one decimal using Hi-Lo:

1) Multiply the Hi-Lo tags by 10 getting the following system:

(-10 10 10 10 10 10 0 0 0 -10)

2) Generate the index you want
3) Divide the index found by 10
4) voila! there's your index with one decimal

Believe me, this method works!

My -1.3 was obtained by calculation on the basis of an infinite deck and should be valid for any shoe game S17.

If instead of using an infinite deck approach you used a 6-deck approach you would obtain an index of -1.0.

Hope this helps.

Sincerely,
Cacarulo

My Method

I use true count indices that were the result of flooring in SBA.
My decision is to always hit/stand or hit/double to the left of the indice. Meaning...... if it's a hit/stand decision and the if indice is -1, then any count to the left (or more minus) then -1, then I hit. Even one running count more then my true -1 is considered to the left.

One more question

Thanks for your extensive comments.In other words, Wong wants his index of 0 to be treated like -1.0.But then this same index of 0 is quite unsatisfactory for plays like 16v10 and 12v4.
You seem to be pretty sure with your -1.0 for the 6-deck-approach.Have you done it? I always considered it to be too laborious. Furthermore I thought that indexes generated with the infinite deck approach wouldn't differ significantly from 6-deck figures. Here another question comes to my mind: Does the level of penetration affect these indices? I really don't know.

Francis Salmon

He's done it and won Post of Month in GC archives (nt)

sims

Straight probability calculations are precise, and don't beat around the bush like sims do. But in complex problems, it may be more practical to program a solution though simulation, even though you are wasting CPU time. Enough trials will lead to an acceptable margin of error.

D.I.L.T.I.

If you use floored indices then there's a method called DILTI which states: DON'T (stand, double, split) IF (TC is) LESS THAN INDEX.

Normally, you would stand, double or split if the TC is greater or equal the index. DILTI is the way of dealing with floored indices.

Sincerely,
Cacarulo

PS: BTW, DILTI should be in the glossary with a better definition of course.

Answer

Thanks for your extensive comments.In other words, Wong wants his index of 0 to be treated like -1.0.But then this same index of 0 is quite unsatisfactory for plays like 16v10 and 12v4.

You're welcome. No, an index of zero in Wong's book or in "truncating" mode refers to the bin or bucket where "standing" has an overall EV greater than "hitting". If you compute the overall EV at the TC of "-1" (meaning all counts between -1 and -2) and get that hitting EV is 15% but standing EV is 14% then you should look at the TC of "zero". Suppose that there hitting is 14% but standing is 15% then "zero" would be your EV-Maximizing (EM) index OR in other words the bin where you should "stand".

You seem to be pretty sure with your -1.0 for the 6-deck-approach.Have you done it? I always considered it to be too laborious.

Well, I'm pretty sure since I got that number with different methods and they all agree. Yes, a 6-deck approach is better than the infinite-deck approach.

Furthermore I thought that indexes generated with the infinite deck approach wouldn't differ significantly from 6-deck figures.

In general, there's no great variation but you have a couple of exceptions.

Here another question comes to my mind: Does the level of penetration affect these indices? I really don't know.

Very little. Mainly with borderline indices but the loss is not significant.

Hope this helps.

Sincerely,
Cacarulo