My point is that images on the I’Net are forever. Delete your social site images all you wish – they will still be there. If you ever want to retain any semblance of anonymity, stay away from cameras, and never post pictures of yourself. I don’t want to engender paranoia. But, there is no reason to make the casino’s jobs easier. ]]>

I’m not putting down people that enjoy vices. If you have the self-control to deal with vices, and it brings you enjoyment without harm to you or others, more power to you and take enjoyment where you can. But, the mindset in casino cities has completely changed over the decades. And, not to anyone’s profit. ]]>

OK, that’s an exaggeration. And yes, it is absolutely allowed, and can even be therapeutic, to vent about the nonsense that we all experience in casinos on a forum. And please do not let me stop anyone from venting. Blackjack card counting can be a lonely avocation; and venting publically has a value in reducing the personal toll of your “in-casino” interactions.

BUT, APs have a very slim advantage. I think that one should look at any reactions that they have to the, obviously, unpleasant parts of this enterprise, to make certain that they do not reduce one’s advantage. That is, getting pissed off can harm your bottom line.

Apparently I have been misunderstood on this question a few times. When you are in a casino, you must have a thick skin. That’s not even right. You must have the ability to think of insults as humorous, but sometimes act otherwise. Depends on your act. There must be a disconnect betwixt what you feel and how you act. If you’re not a trained actor, this can be difficult. Actually, even trained actors have famously had difficulties in separating roles from life.

Some people in casinos are there for diversion from their boring lives. Some are degenerate gamblers. Some (most, I hope) are just having fun. (Still allowed.) Some of these people are not pleasant company. Many are likely nice people. All of these people can appear to be “in the way” of our goals. (Or, on occasion, used for advantage.) This is why I say that you should act as if the casino is a video game. There exist characters in a video game that may or may not be helpful. It is your job to figure out which are which. But, having emotional feelings about them is ridiculous as they are fictional. If you can use this mindset about other players and dealers in a casino; you can reduce the energy-sapping effects of dealing with unpleasant people – at least to a degree.

Now, just as important: In my mind, you should avoid letting your in-casino experiences define your “real” life. Yes, don’t let “extras” on a movie set get in the way of your goals. But, don’t let the cynicism leak into how you feel about the other humans with which we share existence. I’ve seen too many advantage players succumb to cynicism. Oscar Wilde said: “A cynic is a man who knows the price of everything, and the value of nothing.” When you are in a casino, you are playing a game; and everyone else is part of the game – not just the cards. When you are out of the casino, regain your humanity. Don’t lose sight of real “value.”

At least that’s my way of dealing with the situation – when I have the strength to follow my own advice. ]]>

Nearly everyone uses integer indices these days as attempting to use indices like +1.4 provide little additional gain. This isn’t just because indices aren’t that sensitive. It is also because such theoretic indices aren’t even correct. The advantage over increasing counts for a decision is not a simple linear relationship. A decision may make sense at a count of 1.3 and 1.5 but not 1.4. When we focus in more closely and look at the advantage chart between two integer counts, we no longer see a smooth curve; but see a choppy mess.

Griffin tells us that there is an exception. Insurance is the only linear play in Blackjack. This is because insurance is based on a very simple relationship between tens and non-tens, does not depend on dealer draws, and does not depend on multiple player draws. So, some percentage of players do use non-integer indices for insurance. For example, we are told that the HiLo insurance index for double-deck is +2.4.

So, what is the floored insurance index for HiLo double-deck? Oddly, it is +3, not +2. The problem is that insurance is only linear theoretically. For a human, it is not linear. This is because humans do not calculate true count using the exact number of cards remaining. Instead, they typically estimate the remaining cards in increments of quarter, half or full decks. This estimation method destroys linearity.

Below is a chart of theoretic true counts. The x-axis is un-dealt cards. The y-axis is the true count. The lines are running counts of 5 through 50. For example, the red line is a running count of +5. With 13 cards remaining, the true count is 20. 5 divided by one-fourth remaining decks. What we see are nice smooth lines.

The second chart is the same, except that we estimate remaining cards by quarter-decks. The smooth lines are gone. We now have jerky lines. Linearity is gone when we calculate true counts as a human calculates them. If the linearity is gone in this calculation, then linearity must also not exist in the indices.

]]>Griffin tells us that there is an exception. Insurance is the only linear play in Blackjack. This is because insurance is based on a very simple relationship between tens and non-tens, does not depend on dealer draws, and does not depend on multiple player draws. So, some percentage of players do use non-integer indices for insurance. For example, we are told that the HiLo insurance index for double-deck is +2.4.

So, what is the floored insurance index for HiLo double-deck? Oddly, it is +3, not +2. The problem is that insurance is only linear theoretically. For a human, it is not linear. This is because humans do not calculate true count using the exact number of cards remaining. Instead, they typically estimate the remaining cards in increments of quarter, half or full decks. This estimation method destroys linearity.

Below is a chart of theoretic true counts. The x-axis is un-dealt cards. The y-axis is the true count. The lines are running counts of 5 through 50. For example, the red line is a running count of +5. With 13 cards remaining, the true count is 20. 5 divided by one-fourth remaining decks. What we see are nice smooth lines.

The second chart is the same, except that we estimate remaining cards by quarter-decks. The smooth lines are gone. We now have jerky lines. Linearity is gone when we calculate true counts as a human calculates them. If the linearity is gone in this calculation, then linearity must also not exist in the indices.

We have seen charts showing the advantage a player has by section of the shoe for each True Count when discussing Floating Advantage. But, what about unbalanced counts?

I created a chart showing the advantage by running count using REKO-F for the first deck in the shoe through the fifth deck in the shoe. In the earlier sections of the shoe, high counts are not possible as the initial running count is negative. This chart is provide with no editorialization.

Particulars: six decks, S17, DAS, LS, one player, five billion rounds per section.

]]>I created a chart showing the advantage by running count using REKO-F for the first deck in the shoe through the fifth deck in the shoe. In the earlier sections of the shoe, high counts are not possible as the initial running count is negative. This chart is provide with no editorialization.

Particulars: six decks, S17, DAS, LS, one player, five billion rounds per section.

Look around the web, and you will find dozens of sites that talk about dealer bust rates. Which is odd since it is a near useless statistic (not counting odd bonuses and side bets). What you do not see are discussions of player bust rates. Also generally useless. However, as it can be useful in the discussion of bonuses, I put together a chart:

This chart is only for six decks, H17, DAS, dealer peeks with ten or ace, basic strategy, and split hands count. Each bar indicates the percentage of hands that result in the player total on the x-axis. The player busts less often than the dealer as the dealer is forced to hit in bad situations. Clearly you can increase the numbers by hitting more often, which is of value if there is a bonus for busting.

]]>This chart is only for six decks, H17, DAS, dealer peeks with ten or ace, basic strategy, and split hands count. Each bar indicates the percentage of hands that result in the player total on the x-axis. The player busts less often than the dealer as the dealer is forced to hit in bad situations. Clearly you can increase the numbers by hitting more often, which is of value if there is a bonus for busting.

Over the years, many have tried to resurrect Martingale betting (doubling the bet when you lose a hand). As we all know, Martingale betting fails, in Blackjack or in any endeavor involving betting. So, what if we use Martingale betting as cover? That is, we use Martingale at times when counting cards to try to look like a poor player, in an attempt to assuage the fears of the casino. The ideas vary, but usually involve either using a Martingale when the count is negative and correct betting when the count is positive, or using Martingale when the count is positive, and flat betting when the count is negative.

The below chart provides the SCOREs for various methods of betting. We start with optimal betting. That is, the correct Blackjack card counting bets, with a spread of 1-16. The next columns provide the SCOREs for betting one unit on negative counts, and Martingale on positive counts. Spreads of 1-16, 1-8, 2-16, and 2-8 are used. The final three columns provide the SCOREs for optimal betting at positive counts, and Martingale spreads of 1-16, 1-8, and 1-4 at negative counts.

As we can see, any use of Martingale seriously damages advantage. Positive Martingale destroys advantage.

I did not include it in the chart, as it is not Martingale, but Neg 1-2 spread would result in a SCORE of 24.3.

]]>The below chart provides the SCOREs for various methods of betting. We start with optimal betting. That is, the correct Blackjack card counting bets, with a spread of 1-16. The next columns provide the SCOREs for betting one unit on negative counts, and Martingale on positive counts. Spreads of 1-16, 1-8, 2-16, and 2-8 are used. The final three columns provide the SCOREs for optimal betting at positive counts, and Martingale spreads of 1-16, 1-8, and 1-4 at negative counts.

As we can see, any use of Martingale seriously damages advantage. Positive Martingale destroys advantage.

I did not include it in the chart, as it is not Martingale, but Neg 1-2 spread would result in a SCORE of 24.3.

On card counting forums, the question is often asked “At what count do you win the majority of hands?” The long-known answer is at no count. Even at high counts, you win fewer than half of the hands. You make money because of Blackjacks, doubles, splits, insurance, and betting.

But, what about hole-card play? With hole-carding, you get a peek at the dealer’s downcard. Surely, you will win far more hands as you have such important information. And it is well-known that the advantages can be huge. So, I performed a couple of sims. I chose six decks, S17, DAS, 80% penetration. For the hole-carding strategy, I used a compromise strategy. That is, ridiculous plays like hitting 19 because the dealer has 20 are not taken. I assumed 100% of hole-cards are seen, but never took insurance. In practice, a hole-carder would sometimes take insurance, but must be careful not to win every insurance bet. The hole-carder did not use indexes. For the card counter, I used Hi-Lo with full indexes. Results:

What we see is that the hole-carder wins more hands, but still does not hit 50%, even at a Hi-Lo count of +10. An enormous advantage can be realized without winning half of the hands.

]]>But, what about hole-card play? With hole-carding, you get a peek at the dealer’s downcard. Surely, you will win far more hands as you have such important information. And it is well-known that the advantages can be huge. So, I performed a couple of sims. I chose six decks, S17, DAS, 80% penetration. For the hole-carding strategy, I used a compromise strategy. That is, ridiculous plays like hitting 19 because the dealer has 20 are not taken. I assumed 100% of hole-cards are seen, but never took insurance. In practice, a hole-carder would sometimes take insurance, but must be careful not to win every insurance bet. The hole-carder did not use indexes. For the card counter, I used Hi-Lo with full indexes. Results:

What we see is that the hole-carder wins more hands, but still does not hit 50%, even at a Hi-Lo count of +10. An enormous advantage can be realized without winning half of the hands.

I thought that I’d take a harder look a Blackjack card counting strategy difficulty. The point at which our minds are busiest with counting is just after the dealer has dealt the initial cards, or during the dealing of each player’s second card. At this point, we are counting pairs of cards. We know that many pairs of cards cancel each other, leaving a zero count for the pair, and that this greatly speeds counting as we can ignore that card pair. So, let us start by looking at the count of pairs of cards. The table below provides the percentage of card pairs that add to -6 through +6 for the more popular card counting strategies. For example, with Hi-Opt I, pairs of cards have a count of -2 10% of the time, -1 24% of the time, etc. Ignore the Difficulty column for now.

So, how do we come up with a difficulty number? First, let us assign penalties for non-zero count pairs. Obviously, it is easier to count up or down one than add or subtract 2, and easier to add or subtract 2 than 3, etc. I think it is also easier to count up or add than count down or subtract. Generally, even numbers are easier to deal with. Counting by twos is something the mind tends to develop at an early age. So, I came up with difficulty coefficients for each pair count as follows:

-6 8.0

-5 5.5

-4 4.0

-3 3.3

-2 1.7

-1 1.1

0 0.0

+1 1.0

+2 1.5

+3 2.8

+4 3.5

+5 4.8

+6 6.0

We can multiply the coefficient by the percentages in the table for a base difficulty level. The higher the number, the greater the difficulty. Now, let’s tweak this.

The number of columns with non-zero values is the number of different values that the counter must get used to adding or subtracting. Let’s add another penalty. Five times the number of non-zero columns.

Suit-aware strategies, like Red7, add a level of difficulty as this is another concept for the mind to deal with. Add a penalty of 10.

True counting is a clearly more difficult task. Add a penalty of 20.

Side counting is a very difficult additional task. Add a penalty of 40, 50 or 60 depending on the level of the strategy.

On the other hand, compromise indexes are a simplification. KO gets a bonus of 10, as it has three indexes, although some change according to number of decks. FELT gets a bonus of 20 with two indexes. REKO has only one index for any number of decks, which means it really has no indexes, but two basic strategies. Bonus is 30.

Now we have a formula for the difficulty column above.

Disclaimers:

]]>-6 | -5 | -4 | -3 | -2 | -1 | 1 | 2 | 3 | 4 | 5 | 6 | Difficulty | ||

HiOpt I | 10 | 24 | 34 | 24 | 10 | 125 | ||||||||

HiOpt I/ASC | 10 | 24 | 34 | 24 | 10 | 165 | ||||||||

Hi-Lo | 15 | 18 | 35 | 18 | 15 | 130 | ||||||||

K-O | 15 | 12 | 38 | 14 | 21 | 99 | ||||||||

K-O Full | 15 | 12 | 38 | 14 | 21 | 109 | ||||||||

REKO | 15 | 12 | 38 | 14 | 21 | 79 | ||||||||

Red Seven | 15 | 16 | 36 | 17 | 16 | 120 | ||||||||

Silver Fox | 21 | 7 | 43 | 7 | 21 | 128 | ||||||||

KISS 2 | 10 | 23 | 33 | 24 | 11 | 116 | ||||||||

KISS 3 | 15 | 16 | 36 | 17 | 16 | 120 | ||||||||

Hi-Opt II | 10 | 14 | 19 | 15 | 14 | 17 | 10 | 2 | 217 | |||||

Hi-Opt II/ASC | 10 | 14 | 19 | 15 | 14 | 17 | 10 | 2 | 267 | |||||

RPC | 15 | 12 | 12 | 26 | 5 | 12 | 10 | 10 | 234 | |||||

FELT | 15 | 12 | 12 | 26 | 5 | 12 | 10 | 10 | 214 | |||||

Omega II | 10 | 5 | 10 | 17 | 20 | 11 | 12 | 11 | 5 | 232 | ||||

Omega II/ASC | 10 | 5 | 10 | 17 | 20 | 11 | 12 | 11 | 5 | 282 | ||||

Zen | 10 | 5 | 10 | 17 | 20 | 11 | 12 | 11 | 5 | 232 | ||||

Mentor | 10 | 10 | 7 | 12 | 24 | 12 | 7 | 10 | 10 | 242 | ||||

UZBII | 10 | 5 | 10 | 12 | 24 | 10 | 12 | 10 | 10 | 216 | ||||

Halves | 15 | 6 | 7 | 13 | 21 | 12 | 7 | 8 | 8 | 4 | 1 | 273 | ||

Uston APC | 10 | 5 | 5 | 10 | 20 | 8 | 7 | 8 | 11 | 12 | 5 | 1 | 347 | |

Uston APC/ASC | 10 | 5 | 5 | 10 | 20 | 8 | 7 | 8 | 11 | 12 | 5 | 1 | 407 | |

Uston SS | 15 | 6 | 7 | 7 | 25 | 12 | 7 | 6 | 11 | 5 | 1 | 254 |

So, how do we come up with a difficulty number? First, let us assign penalties for non-zero count pairs. Obviously, it is easier to count up or down one than add or subtract 2, and easier to add or subtract 2 than 3, etc. I think it is also easier to count up or add than count down or subtract. Generally, even numbers are easier to deal with. Counting by twos is something the mind tends to develop at an early age. So, I came up with difficulty coefficients for each pair count as follows:

-6 8.0

-5 5.5

-4 4.0

-3 3.3

-2 1.7

-1 1.1

0 0.0

+1 1.0

+2 1.5

+3 2.8

+4 3.5

+5 4.8

+6 6.0

We can multiply the coefficient by the percentages in the table for a base difficulty level. The higher the number, the greater the difficulty. Now, let’s tweak this.

The number of columns with non-zero values is the number of different values that the counter must get used to adding or subtracting. Let’s add another penalty. Five times the number of non-zero columns.

Suit-aware strategies, like Red7, add a level of difficulty as this is another concept for the mind to deal with. Add a penalty of 10.

True counting is a clearly more difficult task. Add a penalty of 20.

Side counting is a very difficult additional task. Add a penalty of 40, 50 or 60 depending on the level of the strategy.

On the other hand, compromise indexes are a simplification. KO gets a bonus of 10, as it has three indexes, although some change according to number of decks. FELT gets a bonus of 20 with two indexes. REKO has only one index for any number of decks, which means it really has no indexes, but two basic strategies. Bonus is 30.

Now we have a formula for the difficulty column above.

Disclaimers:

- I assumed infinite decks so I didn’t have to deal with the different numbers for different numbers of decks.
- There are additional difficulty factors, and some of the factors have different effects depending on number of decks.
- Obviously, the difficulty coefficients used are solely my opinion. And, different people have different abilities. I am very interested in other opinions. And am certainly willing to recalculate this table in there is a consensus.

The question has been asked, if you have been trespassed, that is told to never to enter a casino again, what happens if you do and you make a large win? Can the casino to refuse to pay you? Suppose you put a dollar in a Video Poker machine and hit the jackpot?

This is a tough question, and varies by location and specifics. But, let us look at it from a practical point of view.

There exists an old maxim, ostensibly by Thomas Draxis in 1616, that possession is nine points of the law. It isn’t a de jure law anywhere. It’s just de facto. That is, it is what actually happens as opposed to what should happen. In AP play, I am more interested in what does happen than what should happen. If someone has something that you have a right to, you are the one that has to fight for it. And that fight may require large amounts of money and time, no matter how good your case or cause. So, in the case of a jackpot that requires someone to come out of the woodwork and pay you, they have the money. And, rightly or wrongly, they can hold it. So, in answer to your question, the casino keeps it.

I’m talking reality, not right-or-wrong. If you have been trespassed, keep your buy-ins small, don’t carry large numbers of chips, and don’t make bets with large ratio payoffs.

Disclaimer: This is my own opinion and I am not a lawyer.

]]>This is a tough question, and varies by location and specifics. But, let us look at it from a practical point of view.

There exists an old maxim, ostensibly by Thomas Draxis in 1616, that possession is nine points of the law. It isn’t a de jure law anywhere. It’s just de facto. That is, it is what actually happens as opposed to what should happen. In AP play, I am more interested in what does happen than what should happen. If someone has something that you have a right to, you are the one that has to fight for it. And that fight may require large amounts of money and time, no matter how good your case or cause. So, in the case of a jackpot that requires someone to come out of the woodwork and pay you, they have the money. And, rightly or wrongly, they can hold it. So, in answer to your question, the casino keeps it.

I’m talking reality, not right-or-wrong. If you have been trespassed, keep your buy-ins small, don’t carry large numbers of chips, and don’t make bets with large ratio payoffs.

Disclaimer: This is my own opinion and I am not a lawyer.

It should be no surprise that this is a common question. So, so many variables:

First, it needs to made clear that this is not Poker table stakes or a tournament. You can go in your pocket at any time and pull out cash. These days, betting cash is often not allowed. But, you can ALWAYS pull out cash, even in the middle of a hand, and get chips. Pure cash betting (no chips involved) is rare these days and is treated in different manners as follows:

In olden days, most anything was allowed if you didn’t look like a problem. For example, if you had no more chips, but had to double or split, you could just say “mark it” – even if you had no account and they did not know your name and you looked like a long-haired hippy, if they felt that you would continue playing. They, rightly, figured they would get the money eventually. As days have gone by, the rules have become tighter and tighter. In the old days, you could throw a C-note (from Roman numerals if anyone cares about the ref) on the table and say “money bet,” and they would take the bet. Win it and you could put the cash back in your pocket and continue playing with the winning chips. Now, they exchange it for chips before the hand.

I’m afraid I failed to answer the original question — What should be your initial buy-in at a table? That’s because there is no one answer. It depends upon your “act.” And, it should not be the same, in the same casino, anyhow, unless making it the same is part of your act.

In the past, I used to make cash bets often. I felt it made me look like a gambler. In the present, I never do this on entering a table. Partly because it brings more attention, it is usually traded for chips before the bet anyhow, and it slows the game. And, my current philosophy is that speed is one of the most important factors. Also, I don’t like to be an annoyance to casinos, and paying cash is a huge annoyance and can bring unwanted attention. Oddly, used judiciously, if you are playing higher stakes, it can also bring “wanted” attention.

OK, I still haven’t answered the question. I like short sessions. I also like an excuse to leave and I like an excuse to bet unusually small amounts (below one unit) if the count doesn’t increase or make odd increases if it does. Keeping a small number of chips in front of you, of different denominations, allows you to look as though you are making bets based upon the colors that happen to be in front of you, either unusually high or low. So, I tend to try to keep the number of chips in front of me fairly small. In fact, I sometimes (not often) even buy chips when I have chips in my pocket, to give me camouflage possibilities. The point is to look like a pure gambler. Not a system player, which can be a good act until you break from it, but a random gambler that doesn’t give a f***. They like that.

But, as I say, there are many ways to play. Comments and experiences are welcome.

]]>- Do you have chips from that casino?
- Are you known at the casino? Known in what manner?
- Do they allow money (cash) plays and in what circumstances?
- How big is the casino?
- What is your “act?”

First, it needs to made clear that this is not Poker table stakes or a tournament. You can go in your pocket at any time and pull out cash. These days, betting cash is often not allowed. But, you can ALWAYS pull out cash, even in the middle of a hand, and get chips. Pure cash betting (no chips involved) is rare these days and is treated in different manners as follows:

- You can or cannot bet cash on entering the table.
- You can or cannot bet cash after entering the table and running out of chips.
- You can or cannot bet cash on a DD or Split.
- Any of the above, but they immediately trade the cash for chips instead of allowing the cash to stand as a bet, and allowing you to withdraw the cash on a win.
- Asking for a marker on the bet, which requires no cash or chips.

In olden days, most anything was allowed if you didn’t look like a problem. For example, if you had no more chips, but had to double or split, you could just say “mark it” – even if you had no account and they did not know your name and you looked like a long-haired hippy, if they felt that you would continue playing. They, rightly, figured they would get the money eventually. As days have gone by, the rules have become tighter and tighter. In the old days, you could throw a C-note (from Roman numerals if anyone cares about the ref) on the table and say “money bet,” and they would take the bet. Win it and you could put the cash back in your pocket and continue playing with the winning chips. Now, they exchange it for chips before the hand.

I’m afraid I failed to answer the original question — What should be your initial buy-in at a table? That’s because there is no one answer. It depends upon your “act.” And, it should not be the same, in the same casino, anyhow, unless making it the same is part of your act.

In the past, I used to make cash bets often. I felt it made me look like a gambler. In the present, I never do this on entering a table. Partly because it brings more attention, it is usually traded for chips before the bet anyhow, and it slows the game. And, my current philosophy is that speed is one of the most important factors. Also, I don’t like to be an annoyance to casinos, and paying cash is a huge annoyance and can bring unwanted attention. Oddly, used judiciously, if you are playing higher stakes, it can also bring “wanted” attention.

OK, I still haven’t answered the question. I like short sessions. I also like an excuse to leave and I like an excuse to bet unusually small amounts (below one unit) if the count doesn’t increase or make odd increases if it does. Keeping a small number of chips in front of you, of different denominations, allows you to look as though you are making bets based upon the colors that happen to be in front of you, either unusually high or low. So, I tend to try to keep the number of chips in front of me fairly small. In fact, I sometimes (not often) even buy chips when I have chips in my pocket, to give me camouflage possibilities. The point is to look like a pure gambler. Not a system player, which can be a good act until you break from it, but a random gambler that doesn’t give a f***. They like that.

But, as I say, there are many ways to play. Comments and experiences are welcome.

Apparently, GM’s OnStar always tracks your car location, even if you drop your subscription. And everyone gets a free trial subscription. That is, they keep a database of your driving habits, and sell it. Now, they claim the info is anonymized, so that particular cars cannot be identified by the buyer. But, it seems it is possible to hack the data. Kinda rings my paranoia button. Like, a casino tracking your past movements.

Or, as David Crosby wrote:

“You know, it increases my paranoia, like looking in my mirror and seeing a police car.”

]]>Or, as David Crosby wrote:

“You know, it increases my paranoia, like looking in my mirror and seeing a police car.”

The most famous color-dependent card counting system is Red7, but there are several. In Red7, you count the red sevens, but not the black sevens. The idea is to realize results that are closer to a level 2 strategy, without using a more complicated level 2 strategy. In a level 2 strategy, you would have to count the sevens as .5, or double all the tag values.

Of course, counting half the sevens is less efficient. Betting correlation theoretically drops from 98.4% to 97.2% and playing efficiency drops from 54% to 53%. But, does this matter? Well, first off, BC and PE don’t really relate well to unbalanced counts. And, PE assumes a large number of indexes, not normally used in Red7. So, in that sense, the loss in using a Red7 type of compromise is not as bad as it may seem. On the other hand, we introduce a new opportunity for error. We must now pay attention to color. And, counting of card–pairs, necessary for speed, is more complex and error prone. The question then becomes, is the opportunity for error, and the extra level of practice, worth using a color dependent card counting strategy as opposed to a simpler count or any gain in ease worth using this compromise over a level 2 count? The answer, as usual, is, it depends. Everyone’s mind works differently. Some people have no problem with the addition of this new factor.

Related is the question of indexes. Is it worth it to take into account the fact that you are counting half of the sevens instead of all of them as .5 when you generate indexes. In my opinion, the error introduced by color dependent tags is introduced during play, and cannot be reduced via indexes.

]]>Of course, counting half the sevens is less efficient. Betting correlation theoretically drops from 98.4% to 97.2% and playing efficiency drops from 54% to 53%. But, does this matter? Well, first off, BC and PE don’t really relate well to unbalanced counts. And, PE assumes a large number of indexes, not normally used in Red7. So, in that sense, the loss in using a Red7 type of compromise is not as bad as it may seem. On the other hand, we introduce a new opportunity for error. We must now pay attention to color. And, counting of card–pairs, necessary for speed, is more complex and error prone. The question then becomes, is the opportunity for error, and the extra level of practice, worth using a color dependent card counting strategy as opposed to a simpler count or any gain in ease worth using this compromise over a level 2 count? The answer, as usual, is, it depends. Everyone’s mind works differently. Some people have no problem with the addition of this new factor.

Related is the question of indexes. Is it worth it to take into account the fact that you are counting half of the sevens instead of all of them as .5 when you generate indexes. In my opinion, the error introduced by color dependent tags is introduced during play, and cannot be reduced via indexes.

On page 464 in *Modern Blackjack*, I provide a chart of the advantages by card and by count if you know the first card. For example, if you know your first card is an ace, your advantage is about 51%. A staggering number. But, what if you are playing Blackjack pay 6:5?

The below chart is single-deck Blackjack, H17, nDAS, one player, four rounds, card counting with HiLo. The advantage for counts -10 to +10. Lower numbers, but still huge advantages.

]]>The below chart is single-deck Blackjack, H17, nDAS, one player, four rounds, card counting with HiLo. The advantage for counts -10 to +10. Lower numbers, but still huge advantages.

It has occurred to me that a full table of contents of Chapter 15, How Blackjack Works, would be useful. This occurred to me because I go searching through the chapter myself trying to remember where I put charts. So:

**How Blackjack Works 369**

**Basic Strategy 370**

**Data by Count 383**

**Data by Depth 401**

**Data by Penetration (SCORE Charts) 407**

**Wonging/Back-Counting Data 428**

**Error Data 435**

**Variance and Volatility Data 439**

**Effects on Other Players 446**

**Unusual Effects 452**

**Peeking Data 462**

**Voodoo Charts 465**

**Bankrolls, Goals, Risk Data 468**

]]>What hands do we get? 370

Single-Deck 371

What are the good Blackjack hands? 372

Single-Deck 373

What Blackjack hands get the money? 374

Single-Deck 375

What Blackjack hands do we get? 376

What are the good Blackjack hands? 377

What Blackjack hands get the money? 378

What’s the effect of Hit on 17? 379

What’s the effect of DAS? 380

What’s the effect of number of decks? 381

What’s the effect of ENHC? 382

Single-Deck 371

What are the good Blackjack hands? 372

Single-Deck 373

What Blackjack hands get the money? 374

Single-Deck 375

What Blackjack hands do we get? 376

What are the good Blackjack hands? 377

What Blackjack hands get the money? 378

What’s the effect of Hit on 17? 379

What’s the effect of DAS? 380

What’s the effect of number of decks? 381

What’s the effect of ENHC? 382

How often do we get each True Count? 383

Single-deck 384

Cumulative 385

How valuable is each True Count? 386

What is the change in advantage from TC to TC? 387

How do Blackjack indexes affect advantages of counts? 388

What is the change in advantage from TC to TC? 389

How do different manners of True Counting differ? 390

How does this affect count frequencies? 391

How does the count affect win/lose/push rates? 392

How does the count affect Splits, DDs, BJs, Insurance? 393

How is this affected by indexes? 394

Where do indexes come from? 395

How about reverse indexes? 396

How do rules affect indexes? 397

How often do we get each Running Count? 398

How do Running and True counts compare? 399

How valuable is each Running Count? 400

Single-deck 384

Cumulative 385

How valuable is each True Count? 386

What is the change in advantage from TC to TC? 387

How do Blackjack indexes affect advantages of counts? 388

What is the change in advantage from TC to TC? 389

How do different manners of True Counting differ? 390

How does this affect count frequencies? 391

How does the count affect win/lose/push rates? 392

How does the count affect Splits, DDs, BJs, Insurance? 393

How is this affected by indexes? 394

Where do indexes come from? 395

How about reverse indexes? 396

How do rules affect indexes? 397

How often do we get each Running Count? 398

How do Running and True counts compare? 399

How valuable is each Running Count? 400

Why is depth important in Blackjack? 401

What about unbalanced counts? 402

True Counts by Depth 403

Running Counts by Depth 404

What is the advantage at different depths? 406

What about unbalanced counts? 402

True Counts by Depth 403

Running Counts by Depth 404

What is the advantage at different depths? 406

How much does penetration matter? 407

What is the real gain? 408

What about unbalanced counts? 409

How much do card counting indexes matter? 410

Single-deck 411

How much do strategies matter? 412

Single-deck 413

What about Ace-Neutral strategies and Ace side counts? 414

Single-deck 415

What effect do Blackjack rules have? 416

How often should we recalculate True Counts? 417

Single-deck 418

Where should we sit? 419

What is the effect of seats on SCORE? 420

Should I bet by half counts? 421

What about Zen? 422

What if I play the strategy for the wrong rules? 423

What about Card Counting? 424

What if I use a ramp calculated for the wrong depth? 425

What about balanced strategies? 426

REKO versus Hi-Lo One Betting Ramp 427

REKO versus Hi-Lo Two Betting Ramps 427

What is the real gain? 408

What about unbalanced counts? 409

How much do card counting indexes matter? 410

Single-deck 411

How much do strategies matter? 412

Single-deck 413

What about Ace-Neutral strategies and Ace side counts? 414

Single-deck 415

What effect do Blackjack rules have? 416

How often should we recalculate True Counts? 417

Single-deck 418

Where should we sit? 419

What is the effect of seats on SCORE? 420

Should I bet by half counts? 421

What about Zen? 422

What if I play the strategy for the wrong rules? 423

What about Card Counting? 424

What if I use a ramp calculated for the wrong depth? 425

What about balanced strategies? 426

REKO versus Hi-Lo One Betting Ramp 427

REKO versus Hi-Lo Two Betting Ramps 427

Effect of Number of Players 429

Effect of Entry Point 430

Effect of Exit Point 431

Effect of Spreads 432

Exit Point Only 433

Back-Count Round 434

Effect of Entry Point 430

Effect of Exit Point 431

Effect of Spreads 432

Exit Point Only 433

Back-Count Round 434

How do dealer errors affect us? 435

What about errors that favor the dealer? 436

How do player errors affect us? 437

Single-deck 438

What about errors that favor the dealer? 436

How do player errors affect us? 437

Single-deck 438

What are long and short runs? 439

Candlestick Charts 441

What is the theoretical range of my results? 443

How many Blackjack sessions should I win? 444

How many trips should I win? 445

Candlestick Charts 441

What is the theoretical range of my results? 443

How many Blackjack sessions should I win? 444

How many trips should I win? 445

How does Back-Counting affect others? 446

Where did the lost winnings go? 447

How does splitting to multi-hands affect others? 448

Where did the lost winnings go? 449

How does card eating affect others? 450

What are the overall effects? 451

Where did the lost winnings go? 447

How does splitting to multi-hands affect others? 448

Where did the lost winnings go? 449

How does card eating affect others? 450

What are the overall effects? 451

What is the effect of the cut card? 452

What is the overall effect? 453

What is that hump in the single-deck charts? 454

What is the Floating Advantage effect? 455

Do we spend more time in positive or negative counts? 456

What are the percentages? 457

What does it all mean? 458

How many cards are dealt per hand? 459

How about different counts? 460

What is the breakdown of hand lengths? 461

What is the overall effect? 453

What is that hump in the single-deck charts? 454

What is the Floating Advantage effect? 455

Do we spend more time in positive or negative counts? 456

What are the percentages? 457

What does it all mean? 458

How many cards are dealt per hand? 459

How about different counts? 460

What is the breakdown of hand lengths? 461

What is the gain from peeking at player down cards? 462

What is the gain from peeking at burn cards? 463

What is the advantage if we know the first card dealt? 464

What is the gain from peeking at burn cards? 463

What is the advantage if we know the first card dealt? 464

How do targets and stop losses affect us? 465

What are dealer hand total and bust frequencies? 466

How about by dealer hands by true count? 467

What are dealer hand total and bust frequencies? 466

How about by dealer hands by true count? 467

What is my risk of ruin? 468

What is my Trip Risk of Ruin? 469

What happens when I include a goal? 469

What is the probability that I will achieve goals? 470

How many hands will it take? 471

What happens when I include a goal and hands? 472

How many hands will it take? 473

What about hands to goals? 473

How does changing risk affect win rate? 474

What is my Trip Risk of Ruin? 469

What happens when I include a goal? 469

What is the probability that I will achieve goals? 470

How many hands will it take? 471

What happens when I include a goal and hands? 472

How many hands will it take? 473

What about hands to goals? 473

How does changing risk affect win rate? 474

Most people know that two wrongs don’t make a right. From this, we can logically infer that three wrongs don’t make a right. A progressionist is a person that believes that if he could only be allowed no limitations on the number of wrongs, then he would be right.

]]>The questions seem to become more and more odd as strange bonuses and side counts abound. These charts show the percentage of hands that are 2, 3, 4, 5, 6, or 7 cards in length, but for each possible dealer upcard. Split hands are counted separately. The sims are for HiLo with full indexes, as that’s more interesting. Six decks, 78% penetration, S17, DAS, one billion rounds each. Obviously, with an upcard of five or six, the player is far more likely to stand pat with two cards. Of course, doubles are more likely, creating three-card hands. I’ll leave analysis to the reader.

As you cannot see 5, 6, and 7 card hands in the above, below is the same data with a logarithmic scale.

]]>As you cannot see 5, 6, and 7 card hands in the above, below is the same data with a logarithmic scale.

Saw an article today that huge sunspot activity at the end of next year may cause massive technology blackouts. Sounds bad. But, that was followed up by a commercial for a refrigerator that has built-in Wi-Fi. Now, I’ve been in tech for longer than most everyone. But, when my refrigerator starts tweeting me, perhaps it’s time for a vacation from technology.

]]>Below are the charts. The first displays the percentage of hands won, by true count, for the three sets of indexes. This is followed by hands lost and hands tied. The results are interesting. I will leave it to the reader to analyze the charts.