Since your bet spread will likely change with every true count (at least up to a true 4 or 5), you will need to know the true count every round to calculate the true count and bet accordingly. This is why practicing calculating the true count is so important! Playing Deviations: Whenever you are dealt a hand with a deviation index number. In calculating a blackjack standard deviation with a computer software program, though, you won't be testing a select group of five or ten numbers. You'll be testing well over a million deviations. The standard deviation in blackjack is simply calculating the probabilities you will win or lose and extracting your odds from that. Mar 26, 2014 So that means for 100 hands of blackjack, yields a standard deviation of 11.4 in this case. So betting, say, $1 per hand would yield an expected loss of 50cents, since the house edge is 0.5% (for 200 hands, this would go up to $1). If you play 100 hands, then there is a 68% chance you could win or lose $11.4, for example.

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I recently received this message:

Hello,

Standard Deviation Blackjack Calculator Solver

Well, I have it narrowed down to 2 counts: K-O or Hi/Lo. One is much easier than the other, but is there much difference in performance? I play single deck (SD) in Reno and spread 1-5. I play long sessions, about 4-6 hours at a time. I was told K-O is bad for SD in comparison to Hi/Lo but how much worse, I don’t know. Could you shed some light on this subject?

Thank you,
A reader

You may or may not know that the “K-O” (Knock-Out) count is what’s known as an “unbalanced” count, which does not require a True Count conversion. This is what I said about unbalanced counts in the series I did called “Counting Systems” that is archived right here on this page:

Almost all the counting systems we’ve examined up to this point are difficult to learn. Not impossible, but certainly not easy, either. If you’ve been discouraged by all the adding and dividing and memorization that it takes to fully utilize these counts in a casino, take heart. An unbalanced count can easily be learned by anyone who can operate a computer and guess what? You’re on a computer right now, so you can certainly learn one of these.

They are called “unbalanced” because, while they still assign ‘point’ values to the cards, when you add all the point values up in a deck or decks, it doesn’t result in zero. By doing this, these counts allow you to play without a ‘true count’ conversion that many people find to be the hardest part of balanced counting systems to learn.Yet, these are still quite effective in 4-, 6- or 8-deck games and the fact is, most ‘casual’ Blackjack players who go to casinos where the games offered are dealt from four or more decks should probably use an unbalanced count. I cannot recommend them for single- or double-deck play because they have their limitations in those games, but otherwise the unbalanced counts are pretty good.

How Effective are Unbalanced Counts?

Of course, we have to first define the word “effective” and throughout this series I’ve quoted a lot of statistics for Playing Efficiency, Betting Correlation and so forth.How the unbalanced systems stack up against all the others will be covered in each individual count’s section, but “effective” as it relates to unbalanced counts has to also be defined as “ease of use”. If you go to a casino only once or twice a month, you probably play for quite a few hours at a time, but I live half-an-hour from 6 casinos, so it’s easy for me to play for an hour at one particular place and move on. Spending more than an hour or two at a game while using a complicated counting system is mentally taxing and, inevitably, mistakes are made. Throw enough mistakes into the equation and the result may be that you’re not gaining any edge over the casino for all your effort.

Unbalanced counts are easy to use for long periods of time because they don’t require a lot of memorization or mathematics to be effective. You still have some work to do if you want to make any $$$ using an unbalanced count, but not nearly as much as it takes to master one of the balanced counts. Naturally, you’re giving something up, but in a ‘typical’ 6-deck, the dealer hits soft 17, double after split allowed-type game, it’s not much. In return for just a bit less advantage, you can have the whole family counting! Think of it: grandma, the kids, the significant other; all can become counters. But seriously, there’s really very little excuse for not at least giving one of these a try. You came to this site, I assume, to learn how to win at the casinos, so if you’re a Blackjack player who’s been losing for years, you can change that now.

The Primary Unbalanced Systems

There are really just two of these and each compares favorably to the other as well as to other single-level systems (which is what these are), at least in multi-deck games. Good books are available on both of these systems and there’s a lot of additional information available besides that out on the ‘Net. Both of these counts have been analyzed to death, each has its loyal followers and each will get the $$$ if properly used, so I don’t really have a favorite. Your first decision is to stop losing at the casino and the next decision is to pick one of these systems; hell, even the cost of the book is about the same.

The Red 7 Count

Point Values 2-6 = +1; red 7s = +1, black 7s,8,9 = 0; 10, A = -1

The ‘standard’ comparisons of Betting, Playing and Insurance Efficiencies don’t really apply here because of how these work, but when used in simulations against the Hi/Lo and other single-level systems in 4+ deck games, the win rates are similar.

Most Effective: When used in 6-deck games where a 1-10 bet spread can be achieved. Good Points: Easy to learn, yet can also be enhanced by an “advanced” version Bad Points: Not very effective in single- and double-deck games. The Book to Buy: Blackbelt in Blackjack by Arnold Snyder (1998 edition) $19.95

The Knock-Out Count

Point Values 2-7 = +1; 8,9 = 0; 10, A = -1

The ‘standard’ comparisons of Betting, Playing and Insurance Efficiencies don’t really apply here because of how these work, but when used in simulations against the Hi/Lo and other single-level systems in 4+ deck games, the win rates are similar.

Most Effective: When used in 6-deck games where a 1-10 bet spread can be achieved. Good Points: Easy to learn, yet can also be enhanced by an “advanced” version. Bad Points: Not very effective in single- and double-deck games. The Book to Buy: Knock-Out Blackjack by Vancura & Fuchs (2nd edition) $17.95

You can see I make the statement that these counts aren’t at their peak of effectiveness in a single- or double-deck game, but I wasn’t the first, so I don’t know if that’s where the reader got this idea. But where the idea came from doesn’t matter either way. What really matters is how these counts ultimately perform and I may be able to provide some insight through the use of simulations. As I’ve mentioned many times before, I run most of my “sims” on a fantastic piece of software called “Statistical Blackjack Analyzer” (SBA), version 5.05. One of the great features of SBA is that it can use a wide variety of counting systems when running your sims and K.O. is included. So all we have to do now is set up some games, keep all of the rules, conditions, bet spreads, etc., the same and just swap out the counting system used in order to get some sort of comparison of which count is better.

The reader quoted above plays mostly single-deck games in Reno where, for the most part, the rules suck: the dealer hits soft 17, you may double only on 10 or 11 and double after split isn’t allowed. Those rules don’t apply to the single-deck games at every casino in Reno, but it does cover most of them and the house edge is 0.44%. Like so many other games, penetration is really important because the more cards a counter sees before the shuffle, the bigger advantage you can get when counting. They know this up in Reno, so the penetration averages just about 60%, which means roughly 31 cards are dealt before the deck is shuffled. (For some tips on how that can be improved, see my article “The ‘Rule Of’ Rule”, which is archived on this page. You may also want to read the article called “Really Beat the Dealer”, which is archived on the GameMaster’s Secrets page here.) But for purposes of comparison, I’m going with a straight 60% penetration in a game where the dealer hits soft 17, you may double only on 10 or 11, no double after splitting pairs and insurance is available, but surrender isn’t. I’m also going to use the same 1-5 bet spread that the reader uses because it’s a spread one can usually get away with in the Reno area without attracting undue attention. The only difference will be the count that is used to size the bet. In addition, I’ll be using only the proper Basic Strategy to play each hand in order to keep the comparisons as simple as possible.

Standard Deviation Graph Calculator

As you’ll see, simulations based upon this data show a barely-acceptable (1%) overall advantage for the counter. For what it’s worth, I do not use the Hi/Lo nor the K-O count when playing a single-deck game, but instead use a count called Hi-Opt 1 where the Ace and 2 have a “point” count of 0, 3-6 are counted as 1 and 10s are counted as -1. This is a balanced count but for it to be at its most effective, one must keep a separate count of the Aces, especially for betting purposes. The Hi-Opt 1 count, when used with a sidecount of Aces and all of the Basic Strategy variations indices from -6 to +6 is very effective in a single-deck game. I think I’ll throw in a sim on that as well.

Simulation #1 – Basic Strategy for the play of the hands, player’s bet 1-5 according to the Hi/Lo count (1 at a TC of 1 or lower; 2 at a TC of 1; 3 at a TC of 2; 4 at a TC of 3; 5 at 4 or higher), never left the table regardless of how low the count got (“play all”). Penetration was 31/52.

Hi/Lo Results:
Initial Bet Advantage: 1.06%
SCORE: 56.82
Estim. Payoff per 100,000 rounds played is $10,253.40, with an estimated standard deviation of $4,301.40.
Average st. dev. per round: $13.60
Av. std. per round per unit: 1.111
Average bet per round: $9.64

Comments on Simulation # 1: Because I think you should play only when a 1% or larger edge can be gained, this game is barely acceptable. You need to remember that this sim is based upon “perfect” play, which can be attained by a software program, but not a human being. The real problem here is the relatively shallow (60%) penetration. The acronym “SCORE” means “Standardized Comparison Of Risk and Expectation”, which was developed by Don Schlesinger and others and is thoroughly explained in his book, “Blackjack Attack” 2nd edition, which every serious card counter should own. For our purposes here, it’s an effective way of comparing the value of each game or bet schedule or whatever that will be examined: the higher the SCORE, the more $$$ you’ll make. As a side note, a SCORE of 40-50 ought to be the minimum one should look for in the games they’ll be playing.

Simulation #2 – Basic Strategy for the play of the hands, player’s bet 1-5 according to the K-O count (1 at a running count of 0 or lower; 2 at 1; 3 at 2; 4 at 3; 5 at 4 or higher), never left the table regardless of how low the count got (“play all”). Penetration was 31/52.

K-O Results:
Initial Bet Advantage: 0.99%
SCORE: 53.69
Estim. Payoff per 100,000 rounds played is $11,177.45, with an estimated standard deviation of $4,823.70.
Average st. dev. per round: $15.29
Av. std. per round per unit: 1.1104
Average bet per round: $11.29

Comments on Simulation # 2: You can see that the K-O count compares very favorably with the Hi/Lo, at least in overall player advantage, which was a surprise to me. The big difference between the two is that the K-O count needed a higher average bet ($11.29 versus $9.64) to achieve approximately the same return and that means your risk is increased. One measure of risk is “standard deviation”, which I’ve written about many times. The value of knowing the standard deviation for a certain game and bet spread can keep you from playing in an unbeatable situation, thus saving you a lot of time and frustration. The SBA software gives us a lot of good information in that regard. You’ll see an “Estimated Payoff” section in each simulation, which comes from the SBA report. What it’s trying to tell you is that you may expect to win “x” $$$ by playing 100,000 hands at that particular game and one standard deviation for that play is shown as a dollar figure. To keep this as simple as possible, if you can expect to make, say, $10,000 after 100,000 hands of play and the standard deviation is $5000, as an example, then there is a chance that you could be at a loss or break-even point, even if you play the 100,000 hands perfectly. If one standard deviation is $5000, then a two standard deviation losing “event” could find you at even after all that play and a three standard deviation event to the losing side would put you at a loss after 100,000 hands of play! The probability of either a two or three standard deviation event is admittedly very small, but it can happen and it’s best avoided by playing games where the indicated standard deviation is a small fraction of the expected win. When that’s the case, say a $10,000 expected win with a less-than $3000 one standard deviation value, you’re virtually assured that you’ll be ahead by some amount after 100,000 hands of play. A good way to summarize all this is to say that these calculations show us what lies in the future – the “long run” that we all talk about. As a generalization, the bigger the expected win is, compared to one standard deviation, the better.

Simulation #3 – Basic Strategy variations from -6 to +6 used for the play of the hands, player’s bet 1-5 according to the Hi-Opt 1 count with a side-count of Aces (1 at a TC of 1 or lower; 2 at a TC of 1; 3 at a TC of 2; 4 at a TC of 3; 5 at 4 or higher), never left the table regardless of how low the count got (“play all”). Penetration was 31/52.

Hi-Opt 1 Results:
Initial Bet Advantage: 1.18%
SCORE: 70.84
Estim. Payoff per 100,000 rounds played is $10,799.55, with an estimated standard deviation of $4,057.55. Average st. dev. per round: $12.83
Av. std. per round per unit: 1.105
Average bet per round: $9.65

Comments on Simulation # 3: While there is not a big gain in the Initial Bet Advantage from doing all the work that’s associated with this count, there is a substantial increase in the SCORE and an overall lowering of your risk, as is shown by the standard deviation calculation for 100,000 hands of play. The average bet is almost identical to the Hi/Lo and quite a bit lower than the K-O game, so you’ll make more $$$ with less risk and that’s a good deal. From a sheer money-making point of view, the Hi-Opt 1 count isn’t all that impressive when compared to the other counts, but when risk is compared to reward it shows its strength, which is identifying the right time to make the right bet.

Weighing the Differences

Would it be that all we had to do was pick the counting system that would make us the most $$$ in the shortest period of time, but unfortunately, it doesn’t work that way. The Hi-Opt 1 count has a lot going for it, but it takes a lot of practice to use it correctly, what with the side-count of Aces and so on. Because of its relative complexity, I typically limit my playing sessions to one hour or less, although that’s a good playing tactic to use, regardless. The reader who started this whole thing said that s/he plays fairly long sessions and that’s where the K-O count shines; it’s easy to learn and easy to use, so it’s much less mentally fatiguing than either Hi/Lo or Hi-Opt 1. All of them will get the $$$, but I’d want a little bigger bankroll than usual ( about 70 maximum bets, rather than the 50 I usually recommend) were I using the K-O count, to lower my “risk of ruin”. The primary benefit of the K-O count, that of not computing a True Count, loses a little of its impact at single deck games, mainly because the True Count, as calculated in the Hi/Lo and Hi-Opt 1 games is almost always either equal to or very close to whatever the running count is. When you see one “extra” small card in the first round of a single-deck game, both the running count and True Count are one. It may get a bit more difficult to calculate as the dealer gets deeper into the deck, but with 50% or 60% penetration, the division that’s needed is never too complicated.

So, which is better? Hard to say, but at least now you and the reader who initially asked the question have some information that will help you make your choice.

I’ll see you here next time.

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Standard Deviation is a measure of how results are distributed within a range of possible outcomes. This score is useful when comparing averages – for example two scores may have the same average of ‘50’ with one comprising of results entirely between 45 and 55 and the other having results ranging from 1 through to 100. The second set of scores is more widely distributed than the first, which will be reflected in a higher standard deviation score.

In Blackjack the standard deviation can be used to show you what the probability of winning or losing a number of betting units is, based on the number of hands you play. We could use this score to answer questions such as ‘what is the probability of winning more than 20 betting units over the course of 100 hands?’ or “Is winning 30 bets over 200 hands a normal outcome, or did I get lucky?’

This article will show you how to calculate (with the help of a calculator) your standard deviation in Blackjack and how to use this information to your advantage, whether you play live or in an online casino.

Calculating The Standard Deviation In Blackjack – A Note About Distribution Curves

You get to the probability of an event occurring by comparing your standard distribution score to a ‘bell-curve’ of possible outcomes, known as a ‘normal distribution’. The score is calculated in such a way as to show that 68% of outcomes will fall within 1 standard deviation of your average, 95% of outcomes fall within 2 standard deviations and 99.7% of outcomes fall within 3 standard deviations.

In other words, once we have worked out what the standard deviation score is for a certain set of data we then compare this to the normal distribution curve to arrive at a probability of any single score being within the normal set of expected outcomes.

Blackjack Standard Deviation – How Can We Chart The Distribution Of Blackjack Outcomes?

Outcomes of a single blackjack hand can be mapped precisely – since we know the rules, probabilities and all of the cards in the deck. The most common outcome is to win or lose one betting unit, with splits, doubles and blackjack making it possible to win or lose more. With the larger number of single units dominating it is possible to work out that the standard deviation for a single hand of 6-deck Blackjack is exactly 1.1418 based on card distributions and rules alone.

This table reflects a standard deviation of 1.1418.

By applying this number directly to a ‘normal distribution’ – or bell curve - we find that over an infinite sample, in a single hand of blackjack you will win or lose 1.1418 betting units or less 68% of the time, win or lose 2 standard deviations or 2.2836 betting units or less 95% of the time and win or lose 3 standard deviations or 3.4254 units or less 99.7% of the time.

While this score is interesting, the application of it benefits from adding a second variable – the number of hands played.

Standard Deviation In Blackjack – Using The Information To Predict Win / Loss Runs

Finally we get to the key practical application of working out standard deviations in blackjack games – assessing the likelihood of winning or losing certain amounts of units over specified numbers of hands. Here is the formula to work this out based on your hand sample size:

(Square Root Of The Number Of Hands Played)*1.1418

Here are some working examples:

Standard Deviation Calculator For Sample Data

100 hands played, square root = 10 * 1.1418 = 11.418

This shows that 68% of the time you will win or lose 11.418 units or less over the course of 100 blackjack hands, 95% of the time you will fall within 2 standard distributions and win or lose less than 22.836 units – while 99.7% of the time your outcome over 100 hands will be within 3 standard deviations, or + / - 34.2 units.

300 hands played, square root = 17.32 * 1.1418 = 19.77

Here the distribution of blackjack outcomes predicts you will win or lose 19.77 units 68% of the time you play 300 hands, 95% of the time you will fall within 2 standard deviations and win or lose 39.54 units and 99.7% of the time you will fall within 3 standard distributions and win or lose < 59.31 units.

Population Standard Deviation On Calculator

As you can see, the higher the number of hands played the smaller the relative impact of chance. Of course you also need to take into account the house edge of 0.05% or so when making these calculations!

Do not worry if you do not have a pocket calculator with you at the casino, it is straight forward to work out the blackjack standard deviations for different sized sessions in advance and gain an insight into how the average distribution of outcomes affects your chances of either winning or losing certain amounts of cash. Once you get an idea of the types of swings which are normal in the game you will feel more comfortable at the blackjack tables, whether live or online!

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