Relationship between independent events!

It seems common sense, that many short bj sessions would add up to one long session, but in running 10 sims of 100K hands, the added results don't seem to assimulate or converge with a continuous running sim of 1 million hands.

If you were to add all you playing sessions and produce a total, I can see the relevance of each session to that total because they make up that total, but taking the results of an independent/event sim run equal to your tatal playing sessions, makes me wonder if independent events can really be assimulated.

also,

playing two positions at a bj table, is this two independent events or one?

swithching tables, is switching to another table, the same event or another event?

when a player finishes play for the day and starts up the next day, is he starting another independent event or is it considered the same event?

This is probably a poor example to get my thought across, but

The space shuttle is an "ideal" to which they strive but the body of knowledge would come from the actual independent shuttles and not the "ideal".I would think the "ideal" would change as the independent events of the separate shuttles were analyzed.

Two events are independent if there is no linkage between them.

Starting with your Space Shuttle analogy (as one of the original design team), all Shuttles derive from a common design and are (therefore) not independent. Further, individual subsystems on different Shuttles were manufactured by the same people. If you find bad O-ring seals on one solid motor, you are likely to find them on another.

The purpose of a shuffle is to eliminate the linkage between individual cards in a pack and make each shoe independent of each other shoe. In a new deck, the cards are suited and ordered -- definitely not independent of each other. Given enough shuffles of sufficient quality, the pack can be rendered random, with each card independent of each other card. However, it generally takes more shuffles than a casino is willing to put into it to achieve true randomness. Any lack of randomness after the shuffle is called "memory," and is the basis of shuffle tracking. Studies have shown that most casinos put enough effort into shuffling to make the pack random for practical purposes. For practical purposes, after the shuffle each pack can be considered independent of previous packs, unless the casino has a defective shuffle.

Given an effective shuffle, each pack at each shuffle at each session at each table at each casino can be considered an independent event. Changing tables, changing casinos, or starting and stopping don't change a thing. Independence starts at the shuffle.

However, within a particular pack, events are not independent. That's the basis of counting. When the counter sees a lot of small cards played, he knows to bet big. The cards may have been distributed randomly and without memory at the shuffle, but the remainder of the pack is not independent of which cards ended up at the beginning of the pack. Likewise, playing two hands is not the same as playing one. The technical term is "covariance."

About simulations. Run another one-million round simulation. I'll bet you get a different answer. Run another ten 100K sims. I'll bet you get a different answer. It takes a LOT of hands to settle a sim toward the end result.

Incidentally, it can be demonstrated mathematically and by simulation that playing errors by other players at your table to not affect your results. Additional players cut your win-per-hour (because you get less hands per hour), and may make cover betting more expensive (they eat cards and cut your average bet when using cover betting), but their playing errors don't affect you.

Don S.'s book, "Blackjack Attack," gives a comprehensive treatment of these matters. Covariance and multiple hands is a particularly complex topic that he treats well, among many others.

first of all, Curious, I want to add my appreciation for giving us a direct and clear answer to the questions North Wind asked. It is a good post, well written.

In my practice software there is a choice between 'random' and 'casino' shuffles and I have found that the results from my small samples indeed are different in using two varieties offered. It is also important to understand that a hundred thousand trials or even ten million trials are really not enough and can lead to quite different conclusions. I think Norm's software (CVData) suggests that anything less than 40 million trials will give you statistically insignificant results. Using CA to guide your playing decisions is essential, but in the course of one player's lifetime of play, it is practically impossible to predict which sample will be represented within the parameters of tens of millions of trials. My incomplete understanding of the statistics of probability makes me hesitate to open my mouth on these topics, but with ET Fan, Maverick, and yourself on this thread, I am sure to learn something.

I have been experimenting more and more with playing two hands in shoe games, off the top. While downtown, I realized that I could sit at a SD table with two other players, and while using two boxes, be dealt an extra two hands during a RO6 game. I actually had one dealer on Fremont deal three rounds, amounting to an average of 40 cards per shuffle played. When I am seeking cover or comps, playing two hands allows me to disguise my spread and average bet in a way that gives me an option to drop my bet down 75% when I encounter negative EV within a given shuffle. The pit thinks I am playing with an average bet of $40, when my actual unit is $10. Pretty common stuff, I know. But are these ploys pure cover or helping me win?

What I seem to understand is that when I bet two boxes of $20, I am betting $40 with the same risk level as if I was betting $30 on one spot. The covariance gives me additional protection and also the potential of making more money than if I were playing one box of $40. How do you experienced players utilize this into your bet stategy and ramps? What are the specific references in BJA for me to build a plan to improve my game with these interdependent hands and how does it relate to indices when you have two separate but linked chances to beat the dealer?

If you have read some of my recent stories, you may have noticed I am often finding success more quickly and with less variance by playing two hands in all neutral or positive counts, especially with shoe games. Am I lucky or is there some CA to back up what I am seeing in real casino action? I guess what I am thinking is that I am taking on more risk than I realize, and have only anecdotal evidence that it is justified, since it has been working out in my favor of late.

ET Fan is always warning me that 'common sense' has no place in guiding your playing tactics and I tend to agree. But sometimes when I try to dig into Don's research all I get out of it is a bucket of muck. I realize this is my problem, and not question of clarity in the results of simulations.

So thanks for any suggestions, examples, or directions as to where to look and what is proscribed by mathematical formula. I hate to think I am setting myself up for destruction playing too many hands and higher stakes while under the misconception that co-variance is acting as a safety net.

scobee

I once used an amp fuse as an analogy for a stop loss in bj and Curious Amateur responded as an electrical engineer. This time I use a space shuttle as an analogy and Curious turns out to have worked on the shuttle program. I have no specific knowledge about electricity or the space shuttle and will have to be more careful with my analogies from now on. Using analogies in my thinking seems to help me observe how certain problems are overcome.

Thanks for the response,although it changed the direction of the post. I meant to suggest that a large sim levels the playing field, while the player must climb the mountain directly in front of him. If you turn out to be a mountain climber, I throwing in the towel.

Thanks again.

ET Fan is correct: intuition is not a good guide. Math is supposed to be meat and drink to engineers, but probability and statistics were considered killers.

When you are talking about things like covariance and sizing bets for two hands, you have to understand your criteria of success. Most of us low-rollers tend to adopt a minimum bet "unit" and ramp up from that, replinishing bankroll from income as necessary. There is another concept called "ruin," which is the amount of money lost that will cause you to leave the game permanently. That amount is called the "bankroll." If one uses the concept of "ruin," there is a bet-sizing principle called the "Kelly Criterion." The Kelly Criterion provides guidance on the percentage of bankroll to bet at any given advantage to maximize the probability of doubling the bankroll with a given likelihood of ruin. Be careful to know the criteria being used by authors such as Wong and Don S.

Beyond these comments, the subject is too complex to cover in a post. That's what the books are for.

I have climbed mountains -- at least cliffs. My younger son is a climber, and he put me in a harness and sent me up a top-roped 90-foot cliff. He had to pull on the rope to get me past a couple of overhangs, but I got to the top. He's climbed Ranier and the five tallest mountains in Ecuador.

I like analogies, and this climbing analogy is useful. If one were to hike from Eastern Colorado to the Continental Divide, the route would not be all upward. There are a number of individual ridges of mountains on the way, each ridge followed by a valley. If the hiker has enough stamina, he'll eventually make it. Likewise, if the counter has enough bankroll, he'll eventually reach the point at which the probability of being ahead is arbitrarily large.

I think of shoe games like going elephant hunting... you drive for hours and find a location that has a reputation for elephants. You sit and sit and hope that you eventually will see an elephant. When you see one, you fire your highest caliber rifle at it repeatedly... the target is so huge that you think it impossible to miss. The elephant rushes you and you high tail it out of there, lucky to escape alive....

Ever go elephant hunting, Curious?

This thread is making me pee, it is so unprobable. Nice comebacks for you both.

I think the lesson here is that mountains can be climbed, if you prepare and have a sturdy lifeline. Combinatorial analysis and probability theory are the best guides to take you to the summit, but the route to the top has many paths. Oh yeah, forget about predicting the weather. When you say we had a mild winter, that can mean mostly warm except for that week when it was -20 with 40 mph headwinds. Sorry North Wind, for taking a southerly route off topic. It seems that anything you serve to Curious Amateur, he hits back for a winner

This thread is platinum plus. thanks guys.

scobee

As far as I know, there's no elephant hunting in the U.S. It was one of my ambitions to retire from Federal service never having held a passport -- an ambition in which I succeeded. And I've seen no reason to have a passport since. I'm not a good traveler.

I was almost forced to travel overseas. Many years ago I was in the military and was to make a trip starting in the Aleutians and traveling through Japan, Korea, Pakistan, Turkey, Greece, Italy, Germany, Belgium, and England. There may have been another stop or two along the path. Anyway, I had every shot known to medicine before they cancelled the trip. Even on this trip, I don't think I'd have seen elephants. And had I been in elephant country, and been inclined to hunt them, I probably wouldn't have been successful. While I can hit pretty much what I want to shoot, I don't have the patience to hunt (or fish).

in this country-Politics "you know ?"

We promise you won't be busted if you decide to post more than a NT.

Can you believe that exchange between Curious and Northwind!?

er....Please hang with the players, again, okay? I can get you a deal on red chip membership.....but only if you act now.

This is the Phoenix, not a trash heap. Welcome back. The whether is fine. The posts are popping..

Frank has promised never to reveal his 'flaw' at the Venus Pool Cabana and you can't imagine the volume and quality of the traffic on green chip.

The only mafia here is Godfather Wong and his family of Green Chip Capos.... dip your toes in the bandwidth.....you won't be sorry...well, that could alway change...but for now

Wow.

Regards,

scobee

Combinatorial analysis and probability theory are the best guides to take you to the summit, but the route to the top has many paths.

Your friendly mountain guides have more knowledge than you credit to them. They can tell you precisely the path to get you to the top in the shortest possible time.

This mountain is notoriously trecherous -- life threatening, in fact. All paths, other than the tried and true recommended by Msrs. CA and PT, are highly likely to lead to ruin.

ETF

Please send a membership application for red chip. Hopefully the process is somewhat less cumbersome than an IRS form.

Will try to toss in a few words here and there along the way.

I hope all had a good time in The Meadows not long ago.

BTW, my trip to Grand Teton and Yellowstone was superb! If you've never been, I highly recommend the trip, in particular, hiking into areas well off the beaten path. There is an outstanding hike along the Upper and Lower Falls in Yellowstone that is excellent. Old Faithful was a little less than exciting...not sure what I expected from a geyser, but that particular area is rife with commercialism.

The bison are everywhere, and often times on the road itself...they of course have the right of way. Lots of elk, coyote, and moose. No bears, and thankfully none on the lengthy hikes we took. A few trails were prime bear areas, but I guess we got lucky and made enough noise as we hiked along.

Grand Teton is very impressive...I highly recommend the Jenny Lake ferry and the hike to Inspiration Point. If anyone who reads this is headed that way, I'd be glad to share my info.

BTW, your post near the top of the page was priceless! :-)

Regards,
Wildcard

but it seemed to fit better if I orphaned Frank and then zinged in there with my answer.

Wow, what a trip! You must be all enlightened now. I will pay special attention to your comments from now on.

I think all the bears were vacationing on Wall Street.

We missed Titanium Man, but indications are good for the spring.

Regards,

scobee

"This mountain is notoriously trecherous -- life threatening, in fact. All paths, other than the tried and true recommended by Msrs. CA and PT, are highly likely to lead to ruin.
ETF "
Yes, I lie in ruin many times because I didn't follow the recommended path, but there is usually another paycheck and another opportunity to travel a parallel path. Counting is a bright light that captures everyones' attention but blinds everyone from seeing other possibilities. Try putting counting aside temporarilly and emphasize other math aspects that you're aware of. Your an ET fan, while I'm EVeryone's fan.

I can only afford to climb imaginary mountains.

a great song with that name 40 years ago. On subject, risk of ruin
is a subject not discussed in one author's books. That is because
all his methods are desigined to keep you from "busting out". Now
the majority of folks here prefere financial suicide. As a child,
I was taught better. So the talk is pie in the sky;but I have yet
to see the math boy author that can match John Patricks-in casino time. They have degrees to fall back on if thy bust out or turn sour.
John is blessed with a HS diploma and 40 years of continuious casino
experience. What does this prove ? That experience counts just as
cubic inches count in engines. All of John's methods are fo the $5
bettor; but some of the big DAWGS like it as well.

I had a long post up for a few hours about parallel paths and individual choices, but I decided not to pursue the thought just then. I am a little TIC with my post about sherpas. Many advantage players do indeed travel paths outside of counting, and even counters must make choices about when, where, and which kinds of games to play. Even within the counting community there are conflicting opinions about using combinatorial analysis religiously or pragmatically, as cover and longevity are also considerations to be incorporated into your game. It could be said that a pro who plays purple has the same guidance from the probability theory lighthouse as the nickel player, but he is certainly on a different path through steeper terrain.

Ask ten players what to do on an Ace-eight and see how many different answers you receive....narrow it down to A-8 against a 2 and you may even get more answers than you have respondents. Poll the membership about which counting system is the best for DD....or ask them when to leave a good game... Mountain climbing may be a religion to some, but for others it is an individual sport with exhilarating moments of personal insight.

scobee