Deck Estimation

[Felix Rue-de-Guerre]

Casino Verite gives you the options: 'round', 'truncate' or '%95 percentile' for deck estimation. I'm not sure if I have ever seen this idea expressed very well in anything I've read. The CV help file suggests that most people use the 'truncate' or '%95 percentile' options.

But, I have always assumed rounding was the proper way to approach this. I would see something like this, from "Professional Blackjack" by Wong:

"The running count is now +2. Since about 2/3 of the deck remains unseen, you divide by 2/3."

Assuming that the word "about" is roughly equal to the word "around", I have always rounded. When the tray has slightly less than four decks, I round to 4 decks. A little over 3.5, I round to 3.5.

I'm talking about 4+ deckers, for the sake of argument.

Questions:
1. What do you other guys do, and why?
2. Can anyone point to any math on which, if any, method is better?

-Felix

 

[Norm Wattenberger]

Rounding

is what nearly everyone does these days and is the default for deck estimation. One criticism I have of nearly all BJ books is all of the examples they provide for TC calculation involve integer quotients, depite the fact this rarely occurs in real life. And I've looked specifically at this in most of the books to try and determine how each calculated indexes.

Serious Blackjack Software​

 

[Anon]

alternative

Do you want to know TC for its own sake, or do you want to know your departure point?

see http://www.bj21.com/boards/free/free_board/index.cgi?noframes;read=145985

If this does not take you directly to the window, but only to the home page, copy the URL and paste it into the address block of your browser.

 

[Automatic Monkey]

Doesn't make a heck of a lot of difference

If I'm using a true count system I round to the nearest full deck because that's the way I run my sims. Truncating or rounding up will result in the errors all going in one direction. Also in my sims the difference between full deck resolution and single card resolution are minimal (in shoe games) so being I can't estimate decks any better than a full deck anyway, why try? This is a problem in SD or DD games where full deck isn't good enough so now I've switched to an unbalanced system for all games where I'm straight counting.

There's also a psychological component of deck estimation that concerns me. You've been taking a beating on your big bets, and all of a sudden that 2 decks left in the shoe looks like 3 because your subconscious has fear of putting out another big bet and losing. Or the opposite, you've been getting good variance and your subconscious is horny for more so the 2 decks looks like 1.5. In my system the bet is defined by a straight additive term to the RC so there's none of that.

 

[Felix Rue-de-Guerre]

This...

>>Also in my sims the difference between full deck resolution and single card >>resolution are minimal (in shoe games) so being I can't estimate decks any >>better than a full deck anyway, why try?

Is one of the things I expected to hear.

This "slushyness" is never discussed in anything I remember reading. It seems that it would be of value to any beginner who was trying to get his priorities in order.

-

 

[stainless steel rat]

this is common

In computer chess, my "long-time hobby" I noticed many years ago that when writing code to evaluate a position to see which side stands better, it is far more important to evaluate a well-known chess feature (good for white) as +X than to not evaluate it at all. But as to whether the feature is worth +.30 or +.50 is another matter. Often the exact "score" is not as important, which means that lots of computer chess experts around the world (including myself) have spent a lot of time tuning the evaluation numbers without getting much benefit from all the work.

Counting seems similar. Whether you stand on 16 vs 10 at -1, 0 or +1 really is not going to make you richer or poorer by any significant amount. Other plays such as splitting 10's vs 4, 5 or 6 can be big money-makers if they don't get you tossed. but if you split 10's vs 6 at +3, +4 or +5 is not that big a deal, although the bigger your bet (and it ought to be big at these counts) the more noticable the effect on your win rate if you fiddle with the indices.

And then there are the discussions about rounding, flooring or truncating your indices and TC calculations. Rounding has been used with great effect for years, yet recent analysis has shown flooring to be slightly better. "slightly" being the operative word...

 

[Mayor]

Exactly

Chess, a long time hobby?! You are too modest.

Exact values for indices and flooring/rounding issues are just not relevant to beating blackjack. As an example, splitting TT vs. 6. If the index is 5 or 4 it doesnt' really matter. Most of the time you won't split. Many times when you do split, you have a TC of 16 or something crazy like that. Those very rare times when the TC is 4.5 and you are debating to do it or not, the actual correct decision to do one or the other is worth pennies for a $100 wager. So, it is very rare to have a situation where the question for the count index will come up, and in those cases it does, the cost of one or the other (assuming you have done your division perfectly) is worth very little. Indeed, if you aren't sure and think you may make an error, always make the play with less variance (stand on TT vs. 6 instead of split -- hit 9 vs. 7 instead of doubling, etc.). That's a safe and sure guide to these sorts of questions.

I once asked Don Schlesinger about splitting 2,2 vs. 8 in certain counts. With the number of times that play comes up and the difference in edge between one play and the other, his comment was that "knowing this index wouldn't buy you a cup of coffee over your lifetime." I have since used his line many times, but with a much broader brush.

It's just not worth it to worry about this issue. Finding a good game is much more important.

--Mayor

 

[stainless steel rat]

it is truly remarkable

that players, particularly "newer ones" will spend so much more energy trying to move to "a better counting system", or learn more BS departure indices, or try to reach a point where they can count down a deck in 2 seconds, and spend so very little time scouting the tables for decent rules and good penetration. And then they wonder "why isn't my super-duper level 8 counting system with 1400 departure indices winning me any more money than my old hi-lo system with the I-18 indices?

If they'd play with something like CVCX (qfit) for a while, they'd see that penetration, not "playing efficiency" (of their counting system) is what this is all about...

 

[Automatic Monkey]

And the need for risk-averse indices

One thing it seems a lot of people don't realize is the need for indices to be risk averse when they change the amount of money you put on the table. If you believe in the Kelly Criterion and that your bet needs to be proportional to your advantage, there is no difference between using non-risk-averse indices and plain old overbetting. This is especially a problem with the uncommon split and double indices because they become even more uncommon when played risk-averse.

But the one place where I prefer to use full indices is the late surrender table. Even if the play doesn't add to my advantage, there is an advantage to getting the same win rate with half the money.

 

[jblaze]

RA indices

I ran CVCX sims using RA indices for my count system. I also ran CVCX sims using full indices. The results: after tinkering around with optimal betting and inputting my desired risk of ruin, full indices provide better EV for the same ROR than do RA indices.

 

[Mayor]

Of course they do!

Of course RA indices do not give the optimal EV -- that's almost by definition!

RA indices are designed to maximize the ratio: EV/SD, hence they optimize SCORE as well; regular indices maximize EV only.

--Mayor

 

[jblaze]

SCORE optimization

SCORE is a measure of EV weighted with ROR from what I understand. Therefore, if you can equilibrate RORs then SCORE is directly proportional to ROR. As I said, with the same ROR, regular indices give higher EV than RA indices. The regular indices (not only by deduction but by simming) yield higher SCORE than RA for the SAME ROR.

 

[Mayor]

Not quite

"SCORE is directly proportional to ROR"

SCORE assumes a fixed ROR, it is not proportional in any way to ROR.

However you are correct that I was being fuzzy about "SCORE." The SCORE of the game is based on certain fixed non-risk averse hi-lo indices, a 10k BR, and a specific bet spread.

What I was saying is that if one used RA indices then the ratio EV/SD would increase even if the EV decreased (as you noted). Most investors care much more about EV/SD than they do simply EV.

--Mayor

 

[jblaze]

oops

Meant to say - "SCORE becomes directly proportional to EV (if RORs are the same). I will rerun sims on my comp once I get CVData here to generate indices, but wouldn't players be most interested in gaining the most return possible on a given risk? I would rather play with a $100/hr expectation and 5% ROR than a $95/hr 5% ROR expectation.

 

[Automatic Monkey]

Non-RA indices require lower betting unit for same ROR

It's a very small amount, but it's calculable.

Think of it like this- for a given play, with a big bet out, the advantage of doubling down is 0.5% higher than just hitting. Sounds like you should double down, right?

But put it in these terms- would you put out a big bet if the count said your advantage was only 0.5%? Unless you have an infinite bankroll, most players save their big bets for around 2% advantage. The RA split and DD indices wait until the count is high enough to indicate an added 2% advantage, or whatever the necessary advantage is to justify an additional bet of whatever size. The RA surrender indices do the same thing but in reverse.

 

[stainless steel rat]

If they didn't..

You just solved the "perpetual motion machine" problem.

Anytime you decrease risk, you decrease gain as well. But as to how you got the same ROR with RA indices and non-RA indices is a mystery. Unless your RA indices were not very RA.. RA should decrease variance and ROR, assuming nothing else changes, I would think...

 

[jblaze]

Re

I dont know why this is such a challenge for people to understand here. Maybe my RA indices are off, but...

My point is:
No matter what indices you use, you personally have to determine the amount of risk you wish to take on, and adjust your bets accordingly. So, run your RA indices and determine what risk level you are comfortable with. Let us say that level is 5%. Now, run sims using 'normal' indices. For the 'normal' sims, adjust your bets to match that 5% ROR. Which indices provide the higher EV? Your answer is going to be the same had I asked the question which indices produce higher SCORE (since ROR is the same - you have made it the same.)

If the goal of RA indices is SCORE optimization, then these indices fail to produce.

 

[jblaze]

PS

You can increase gain and decrease risk with such rules as surrender.

 

[stainless steel rat]

I don't use 'em

but had always assumed the purpose of RA indices is nothing more than to reduce variance. And in doing so, also reducing the EV. Some might be happy to reduce variance since the swings can be so wild, and if reducing the swings doesn't greatly reduce the EV, some would consider that acceptable.

I simply try to play as accurately as possible, using the indices that produce the highest EV, and go from there, accepting the swings as part of the "deal"...

If you (or anyone else) use another definition of "risk averse" then my impression above does not count for anything, of course.

But for my definition, the idea might be that doubling a 10 vs an A could use the normal +4 index, or you could ramp it up a bit. The higher the index for this play, the lower the risk. Of course, the lower the EV as well. Lots of other plays come to mind, anywhere you might be tempted to get more money on the table, such as splits and doubles where the decision is a bit "shakey". double 9 vs 7 for example at +3. The higher the count, the more likely the dealer actually has a 17, and you are more likely to end up with 19. So I've always assumed the idea was to make the winning probability a bit higher before doubling or splitting because doubling your bet doubles the variance for that round.

 

[stainless steel rat]

yes,

but you can't force the casino to offer surrender. All offer some form of doubling and splitting, which allows you to increase your money on the table when you think it is favorable. Probably the best index to use for ramping your bet with hi-lo is +1. At <= 0, bet min, at +1 bet max. But that causes wild swings that a slower ramp (with a lower EV but better RoR) avoids...

I'm not sure why casinos offer surrender, except that I see ploppies surrendering ridiculous hands. For example, 19 vs dealer 10 up. So I guess they like to see that kind of thinking..