My EV? My variance?

I am new to blakjack... only been playing 2 weeks. I know basic strategy without thinking about it, and I use the high-lo count. So far I only use two strategy variations: I insure at +3 or more, and I stand on 16 vs 10 on + counts. Other than that, I play basic strategy.

At the casino where I play, they have $5-$100 tables, and that's where I play. The rules are 8 decks, S17, DAS, DOA, no surrender. The penetration is not great; they cut off about 2 decks. There is absolutely NO HEAT. They don't care. I saw a guy who I think was counting, jumping his bets from $5 straight to $100... no one cares.

So, here is what I do: When the true count is +1 or below, I bet $5. At +2 I bet $25, at +3 I bet $50, and +4 I bet $75, and at +5 or above I bet $100. If the true count drops to -3 or below, I take a "bathroom break", or swing by the bar, or just take a quick lap around the casino. Although, I try not to abandon two consecutive shoes.

My questions are:

1. What is my EV?
2. What is my standard deviation?
3. How would these numbers change if I learned all the "illustrious 18" strategy variations?
4. How good is my betting ramp? If I change it, can I increase my EV without increasing my variance? Or, similarly, can I decrease my variance without taking an EV hit?

Thanks in advance for any help,

Keith

8 decks is certainly difficult to beat, but with decent pen (80% preferable) and no heat it can be beaten. With regard to your EV etc, I suggest you get some decent software (www.qfit.com). You can then play with your spread/betting ramp and see the results. Since you have no heat, your optimal situation in your case would be to bet $5 until you have an advantage (say TC=2) and then jump to $100, but offcourse you must have a large enough bankroll. Again, simulation software should be your guide here. With regard to learning the "illustrious 18" I would suggest putting it off for now for 2 reasons: you are just learning the game, and, 8 deck games are primary beaten with a large betting spread (playing modifications only add a slight edge at 8 decks). If you have patience and can continue to spread 1-20, you should be able to beat your game with patience and a sufficient bankroll. Good luck!

If all you have is 8 deck, either learn poker or move to some other place. If all I had was 8 deck around me, I wouldn't play blackjack.

Or travel. I bet you have some better games within 10 hrs drive of you. Of course, you'd need a bigger spread to make it worthwhile.

Also, if you are an old lady, you can walk up with $1000 dollars and plop it down on the felt and tell the pit you are a card counter and they won't do a damn thing. I'm exagerrating a little but I've seen something close to this happen.

you should be playing two spots at all times...so if you spread 2x$5 to 2x$100...your optimum ramp would be...

-2 to +1 bet 2x$5
+1 bet 2x$25
+2 bet 2x$60
+3 bet 2x$100

You've got to hit your max bet early because of the poor penetration.

If you use this spread and the I-18 plus fab 4 indexes, you will win about $25/100 rounds. If you play 1x5-1x100 your eV will be $12.50/100 rounds.

Your standard deviation will be $572/100 Rounds for 2 hands of 5-100, for 1x5-100 your SD will be about $345/100 rounds

I can't tell you what the numbers would be based on your two indexes you currently use without taking the time to run a more extensive sim.

Regarding betting ramps, the optimum ramp for your game is above...your variance will increase, but so will your EV. The best thing you can do to improve your game is to play two hands, and try to wong into another game when wonging out of a bad shoe. If the tables are all packed/crowded and you can only sit out during negative counts, you should consider wonging out sooner than -3....for this poor a game you should wongout at -1 and try to find another table.

I`m sorry, this game is simply unplayable.

When I start crunching some of the numbers with my slide ruler, I`m gettin NOs of, like, 130,873.6 rounds

A good game is 10,000 rounds.

NO is the number of rounds you have to play to be reasonably sure (around 70%) that you are ahead. That your win rate has a reasonable chance to overcome the fluctuations.

If you don`t mind playing nearly 1300 hours, at full Kelly (13.5% ROR), to essentially break even, well ... you are insane.

Sorry, don`t mean to be cruel.

Incidentally, I dropped by bjstats.com, because these numbers looked a little harsh ... and they gave me SCORES of around $10 and NO`s of 94,000 rounds plus.

If you must play BJ ... rather than play your 1000 (or so) hours, take 5 or 10 of those hours and fly to some place with a real game.

Better yet, take up poker.

And if you don`t mind me offering a little more personal advice, think of quality of life issues. 1000 hours is a long time, you can learn another language in that span. I don`t mean to jump off track here, but you could become reasonably profficient in Japanese.

Why would I mention this?

Come to Tokyo, perhaps Shibuya, and you`ll understand.

So here`s what I would do, skip that game ... fly to Reno, play the single decks ... get booted. With the money you make, plan a trip to Japan,and with the 900 hours you saved ... learn Japanese and make love to all the little J-girls.

Not bad, huh?

Personally, I think this is some damn fine advice. But maybe my perspective is getting a little skewed.

Best,
Syph

I don't understand the rationale for playing two hands in TC's less than +1, when the house has the edge. Can you explain please.
Also where I play mostly, you have to bet double the min on each if you play two hands.

playing two hands is superior in negative rounds because you eat up the cards faster. It is better from a time situation. Now if the casino rquires you to play 2x the table minimum and the table min is going to be your ultimate low bet, then this presents a problem and it's better to just drop to 1 hand. Likewise, if you play at full or semi-full tables you can drop to 1 hand. It's far better, from a camouflage standpoint, and your win rate will be higher at full tables if you just always play two hands and get more aggressive at taking bathroom breaks during almost any negative count and let the other idiots at the table eat the negative rounds for you. I sure you can be creative in ways to avoid playing once the TC gets worse than -1. (bathroom, see how your imgainary wife is doing at the slots, take or make a phone call, make some tea, etc).

I play higher limit tables where I am often heads up and if you drop from 2x$100 to 1x$100 when heads up you don't save very much because the number of rounds in negative decks increases as fast (you cut your bet by 50%, but you get a 50% increase in hands to be played for no real net savings) and it takes more time to eat through the negative deck costing you $$/hour. The more civilians there are at the table the more you can use them to eat the negative shoes and the more effective dropping to 1 spot will become.

Too much sake (or was it Peachy Chu-Hi?) last night.

Re-crunched the numbers and Bigplayer is correct.

For one hand, I get a NO of 76,176 rounds with a win rate of $12.50/hr, and a bankroll requirement of about $9522.

($345/$12.50)^2 * 100 = NO)

If you can increase your bankroll by about 40% (to about 13-14K), you can play two hands and double your win rate with the same ROR (13.5%).

That said, not many play to Full-Kelly, so you might want to double your bankroll, to reduce your ROR to below 2%. Thus, you`ll need about 20K to make $12.50/hour.

The game still sucks, come to Japan.

(You to, Bigplayer)

Best,
Syph

Thanks for taking the time to answer. How many hands to play and when to spread or drop back seems to be a bit controversial judging from the reading I've done, (which includes Wong and Schlesinger).
I'll study your advice and decide how it applies to the game and conditions where I normally play.

playing two hands instead of one is so superior that he's suprised that people even have to discuss it. Run some sims and it's so obvious.

Besides hot women. I was there about 10 years ago. I was in downtown Tokyo. What a place but I didn't see any casinos. What kind of games do they have ? Do they back off counters ? The problem I would have is that I'd be playing a game and they would come over and tell me I couldn't play anymore in japanese and I wouldn't know what they were saying. I had a japanese girlfriend at the time and she would guide me around town. It was great.

Gambling is illegal in Japan (except for pachinko, slots, races, etc ...), however there is some BJ about.

The games are run by the Yakuza, and aren`t too bad from the reports I`ve heard.

6D, DAS, LS, good pen, limited to a 1-5 spread, but ...

You get a 25% buy-in bonus, at least in Okinawa.

That said, there have been reports of "exit fees" for big winners.

LOL!

Honestly, I would never come to Japan for anything other than the girls (and rebuilding a bankroll that went poof). Even so, the Japan today is not the pre-bubble burst Japan of yesteryear.

It`s still pretty good, though.

Best,
Syph

(ps Vietnam is pretty hot now, and Thailand always rocks)

Thanks for the advice, bigplayer. Unfortunately, I'm not sure if I can follow any of it. The casino where I play (a charity casino in ontario, canada) has a $100 limit on all it's tables. The difference between the "low limit" and "high limit" tables is only the minimum bet... it goes as low as $5 and as high as $25. The max bet is always $100. Clearly, the $5 tables are the ones I want to play.

Having said that, they generally only have two $5 tables going at once (this is not a big casino). Also, they don't allow you to play 2 spots if someone else is waiting for a seat (which is just about all the time) so playing 2 spots is impossible 90% of the time. Also, you must bet at least double the minimum when playing 2 spots.
So, basically, I am stuck playing 1 spot at a full table almost all the time. Occasionally I'll get lucky and someone will leave when the count is good, which will allow me to play 2 spots for a few +EV hands. But this is pretty rare.

As far as my betting ramp.. why would I want to increase my bet to $25 when the count is +1? My edge here is quite low (only a few hundredths of a percent) so it seems that I'm increasing my variance without much of an EV payoff. What am I missing here?

As far as hitting my max bet at a count of +3... that would be nice, but I don't think that I have the bankroll for it.

As far as the wonging in/out goes... it's tough. They don't care how much you range your bets, but they don't like it when you sit out and there are people waiting. You can get away with it for a couple of hands but then they start threatening to give your seat away if you don't play the spot. Having said that, I can ask for a lammer and get up, and they will hold my seat for up to 15 min. Someone else can play in that spot but they have to give the seat back when I get back. Basically I use this strategy to abandon shoes where I feel that the count is unlikely to ever go high enough for it to be worthwhile for me to sit through it. I generally mumble something about going to the bathroom or going to get a drink as I am leaving.
Then I try to get back as the shoe is about to end, and I let the guy who is playing my spot keep it "until the end of the shoe". Also, if the count is low AND things are going bad, I will sit out a couple of hands, saying something about "changing the order of the cards", which generally seems to be appreciated.

As for the indices, I definitely want to add them to my game. I am trying to do it slowly, one at a time, until I get all 18. This shouldn't take too long... within a month I should have all 18.

Thanks for the advice,

Keith

As I understand it, the NO is the number of rounds which must be played so that your EV exceeds your standard deviation. If this is the case, then you would in fact be about 5/6 (83%) sure that you would be ahead after this many rounds.

The math here is easy. About 2/3 of observed results will fall within 1 standard deviation of the mean. of the remaining 1/3, 1/2 of them (ie 1/6) will be above the mean by more than one standard deviation, and the remaining 1/6 will be below the mean by more than one standard deviation. Furthermore, of the few times that you are down, very few of those times will you be significantly down. I don't see how you could possibly call this "essentially breaking even". In fact, it is a situation where you are probably up, and more likely to be up a lot than up a little, AND if you happen to be down, you are probably not down very much.

Keith

I dug around for a sim or two that might help illustrate my concerns. For those who wish to jump in and play BJ without knowing what they are in for, I came up with this one from John Austin.

S17DASLS, good pen, 1-12 spread play-all, hi-lo.

Win rate: 2.61
SD: 45.50
$8000 bankroll,
$26.10 win rate.
NO = 30,000 rounds

(Essentially, twice the game you have access to. But if you increase your bankroll to $14,000 and play two hands with your game, the win rate is about the same. So to, is the risk of ruin.)

Now, lets look at what can happen:

After 305 hours...

(drum roll please!)

Within a 1 SD event, you will profit a minimum of $14.

Now, many do not consider a 1/3 chance of being outside of expectation to be the long run. Most want a little more assurance than that so some consider a 2SD to be the long run, and others prefer a 3SD.

So...

After 1216 hours (within a 2SD event) you will profit at least $5.

And after 2740 hours (within a 3SD event) you will profit at least $63.

(All these numbers, incidentally, were calculated with an INFINITE bankroll. If you play Kelly, you have about a 1 in 7 chance of going bust.)

This is without cover or tips, perfect play, etc...

I`m not sure how much more I can illustrate how terrible this game can be. It`s true, I tend to focus on the nasty stuff (previous experiences color my attitudes). But my point is ... if you play for any length of time, you WILL be at the wrong end of the curve.

That is a certainty.

(and I intentionally did not post the OTHER numbers because I felt it necessary to show the dark side of this game.)

Please, save your money and come to Japan.

But if you must play BJ, go frolick around Northern Nevada where good single deck games can still be found.

Best,
Syph

Please do not take this the wrong way, but your posts lead me to believe that you don't understand the math / numbers you are using.
First you said that your NO represents the number of hands that you would play to be 70% certain of being up. As I pointed out, the number is much higher than this (it is actually 84.13%, not 83% as I had guesed in my last post), since if you are outside a 1 sigma range, you have just as much chance of being above it as below (this is important... normal distributions are symmetric around the mean)

Now you are talking about winning a "minimum" amount if you play for a certain number of hours. I'm just not sure what you mean here. Of course, no matter how long you play and how good the game is, you can play for any length of time and there is a non-zero probability that you will be down. They could play one deck with blackjacks playing 1000-1 and you could still theoretically lose. This is a game of expectation and variance, not of guarantees.

Then you say "if you play for any length of time, you WILL be at the wrong end of the curve". I'm not quite sure what you mean by this statement, but of course you have just as much chance of being ahead of your expectation as you do of being below it. You are worried about being 3 sigma below your expectation after 2470 hours (probability = 0.00135) when in fact you are just as (un)likely to be 3 sigma above your expectation.

Instead of being so paranoid about variance, I prefer to just do my best to maximize my expectation, within reasonable limits. Being worried that I might only break even one out of every 740 times is not something that I am going to take the time to worry about. I may as well refuse to step outside for fear of being run over by a bus or being struck by lightning.

In case you think that I am new to gambling, or that I am just being gullible about variance here, let me share some of my background here. I have played a fair amount of poker, including low limit hold'em against people who chase any crappy draw all the way to the end. I know what it's like to take bad beat after bad beat and lose your money to people who have no clue about the game. I know what it's like to be on the "wrong end" of the curve. I ALSO know that if you keep playing, the money eventually (over days, weeks, months) comes back. The thing about variance is that it can go both ways.

Keith

"Please do not take this the wrong way, but your posts lead me to believe that you don't understand the math / numbers you are using."

Have you been talking to T-Hopper?

"First you said that your NO represents the number of hands that you would play to be 70% certain of being up. As I pointed out, the number is much higher than this (it is actually 84.13%, not 83% as I had guesed in my last post), since if you are outside a 1 sigma range, you have just as much chance of being above it as below (this is important... normal distributions are symmetric around the mean)"

Yes, yes ... here let me add:

"within one standard deviation"

Brett tells us that N0 is "equal to the number of rounds that must be played, with a fixed betting spread, such that the accumulated expectation equals the accumulated standard deviation. As such, it is a measure of how many rounds must be played to overcome a negative fluctuation of one standard deviation with such a fixed spread."

Moving on ...

"Now you are talking about winning a "minimum" amount if you play for a certain number of hours. I'm just not sure what you mean here. Of course, no matter how long you play and how good the game is, you can play for any length of time and there is a non-zero probability that you will be down. They could play one deck with blackjacks playing 1000-1 and you could still theoretically lose. This is a game of expectation and variance, not of guarantees."

Vary true, unfortunately many seem to neglect this fact when they first start to play. My point from the start is that once you start looking at the variance and expectation of BJ, you have to be very selective of the games you play if you wish to have any chance of getting into the long run.

The game you are contemplating playing is a waste of time.

"Then you say "if you play for any length of time, you WILL be at the wrong end of the curve". I'm not quite sure what you mean by this statement, but of course you have just as much chance of being ahead of your expectation as you do of being below it. You are worried about being 3 sigma below your expectation after 2470 hours (probability = 0.00135) when in fact you are just as (un)likely to be 3 sigma above your expectation."

If you play for any length of time, you will find yourself at the wrong end of the curve.

It is a dark, lonely place.

"Instead of being so paranoid about variance, I prefer to just do my best to maximize my expectation, within reasonable limits. Being worried that I might only break even one out of every 740 times is not something that I am going to take the time to worry about. I may as well refuse to step outside for fear of being run over by a bus or being struck by lightning."

Every professional I have heard of, or have had the privilege of meeting, using your analogy, has been struck by lightning and/or ran over by a bus.

(DD, BP, if you are out there, please feel free to chime in.)

As long as you are aware what can happen, and that IT DOES happen, and HAS happened (and far worse, for that matter) to EVERYONE who has played this game long term, my work is done.

"In case you think that I am new to gambling, or that I am just being gullible about variance here, let me share some of my background here. I have played a fair amount of poker, including low limit hold'em against people who chase any crappy draw all the way to the end. I know what it's like to take bad beat after bad beat and lose your money to people who have no clue about the game. I know what it's like to be on the "wrong end" of the curve.

Low limit no fold`em? Uh ... no offence (my turn :), but get ready for a whole new world of pain.

"ALSO know that if you keep playing, the money eventually (over days, weeks, months) comes back."

Heh ... I talked to one semi-pro who was for 7 years (averaging about 200-300 hours a year) in the red, playing BJ. He told me the same thing,

I told him he was a strong man.

"The thing about variance is that it can go both ways."

Virtually everyone is unprepared mentally, emotionally, and financially when it swings against them.

If you haven`t read this article, please do:

http://www.bjfonline.com/Library/wontwin.htm

I confess, I am a little vexed as to why you are/were contemplating playing this specific game. But I wish you all the best, and my hat is off to you if you can make a profit.

Best.
Syph

Well I don't know who T-Hopper is (I'm new here) but you say some things which, at best, give a very wrong impression of how the math actually works.

First, your statements seem to imply that you are more likely to end up below your expectation than above it. This is, of course, not true. A normal distribution is symmetric around the mean, which means that you are JUST as likely to end up above your expectation as below it. Furthermore, for any particular x, you are just as likely to finish $x above your expectation as you are to finish $x below your expectation.

Also, you seem to imply that if you play long enough, the variance will eventually catch up with you and you will lose. This is the exact opposite of what is true. In fact, your edge grows quadratically faster than your standard deviation, and so if you play long enough, your edge will outpace your standard deviation and you will win. This is the same concept that guarantees that casinos will continue to make money at unbeatable games where they have a fixed edge, like, for example, roulette.

Although you don't actually say these things, and I certainly don't mean to put words in your mouth, I'm not sure how else to interpret statements such as "If you play for any length of time, you will find yourself at the wrong end of the curve." This statement falls somewhere between flat-out wrong and incredibly misleading, depending on exactly what it is that you mean. A correct version would be "If you play for long enough, you will find yourself close to the middle of the curve". This is just basic stats.

As for your story about they guy who is in the red over 7 years playing 200-300 hours per year... let's analyze this and see what we can come up with.

200-300 hrs / year over 7 years is about 1750 hours. If he is playing at a full table this probably works out to about 87,500 hands, while if he is playing heads up or close to it, it is probabvly closer to 175,000 hands. Let's split the difference and say 120,000 hands over those 7 years.

This is where the value of NO would come in handy. Remembering that expectation grows quadratically as standard deviation grows, here are some numbers:

He is at least 1 sigma below expectation if his NO is 120,000
He is at least 1.5 sigma below expectation if his NO is 53,333
He is at least 2 sigma below expectation if his NO is 30,000
He is at least 2.5 sigma below expectation if his NO is 19,200
He is at least 3 sigma below expectation if his NO is 13,300

Now, the probability of being 3 SD below the mean is about 0.0013 (about 1 in 769) and the probability of being 2.5 SD below the mean is 0.0062 (about 1 in 161). These are unlikely results, but certainly within the realm of possibility. He is either playing in a game where he has a high NO, or he has had a REALLY unlucky 7 year stretch, or he just isn't a +EV player (have you seen him play? does he know what he's doing?).

Anyway, to suggest that results like these are typical is ridiculous. Even if his NO is 30,000 and he is "only" 2 sigma below his mean, the probability of that happenning is about 0.0228 (about 1 in 44). In other words, if 44 people played for 7 years each in conditions like this, you would expect 1 of them to break even, and the other 43 to make money. Kind of sucks for that one guy, but overall it's a pretty good deal.

As for your being "vexed" by my choosing to play in this game... "vex" means to anger or annoy. I'm not sure why this would anger or annoy you. If you meant to say that you are confused by it, my reasoning is simple. It's the only casino that is within a 1 hr drive of where I live. There are many casinos that are about 3-4 hours away, but that is too far to play regularly. Playing at one of those casinos would require spending the night, which would certainly eat my profits. Also, most of them have pretty much the same conditions (although one offers better penetration... they don't have shuffling machines so they deal 7 decks out of an 8 deck shoe before they shuffle in an attempt to get more hands in) I know that this makes the game SIGNIFICANTLY better, but it is a 4 hour drive from where I live. It is not reasonable to play in this game regularly, or even semi-regularly. Basically, I either play at this casino with the $5-$100 tables and 6/8 penetration, or I don't play at all. I choose to play. I enjoy playing. If I ever stopped enjoying it, I'd stop playing. And, once I'm going to play, I'm going to get every edge that I can. And I WILL win. Or, at least, I'm more likely to win than I am to lose. Which is really all that I can ask for.

Keith

And lets hope you hit one of those three sigmas above expectation.

Take care,
Syph

("Vexed" = To cause perplexity in; puzzle.)