A Look at a BlackJack Card-Counting System

[Ualaa]

First off the obligatory statement: If you are going to gamble, only play with entertainment money, not your rent/grocery/bills money. When I see a movie in the theatre, I might blow $30-40 on the movie and food. When I gamble for an evening, I won't spend more then that amount. Know your limit and play within it.





Disclaimer: This is presented for intellectual purposes. While the system is mathematically sound, there is no guarantee you'll win with it. Do not play with money you cannot afford to lose. I'd personally recommend only playing with pretend money such as poker chips.

My personal experience with this system resulted in a yield of 3 maximum bets per 100 hands (via computer simulation of several billion hands, using WinSim21 by Emubest) but only 1.5 maximum bets in actual play. The author of the system claims it is mathematically proven to hit 2.5 maximum bets per 100 hands played.

At the level I played ($2 table), a regular job would result in significantly more money earnt per hour.




The basic game of Blackjack is fairly simple. The dealer has a visible upcard and a hidden hole card - in many places the dealer does not take a hole card until after each of the players has resolved their hand. Each player receives two cards. The goal of the game is for the players total to exceed the dealers total, without busting by going over twenty one. The players have only part of the dealers hand to go off of.

Player options include Stand (take no more cards), Hit (take an additional card), Double-Down (double the initial bet and take one additional card), Split (double the initial bet, and split two numerically identical cards into two separate hands), Surrender (keep half your wager, losing the rest before any player takes a card), and additionally to take or reject Insurance (which is a side bet, when the dealer's upcard is an Ace). Without counting, Insurance should always be declined.

If the players final total exceeds the dealers final total, without busting, the player wins a value equal to their bet. If the players initial two card total is an Ace and a Ten value card, they have what is called a blackjack which means they win 150% of their initial wager. A tie with the dealer is a push, and no money changes hands. If the dealers hand exceeds the players hand total, again without busting, the dealer wins and collects the players wager.

Suits mean nothing in blackjack, and all face cards plus the 10's count as a 10 value. You could split a King and a Ten if you wanted to; they both count as a 10 value card.

The dealer (house) acts after all players have finished. The house has to continue hitting until their total is 17 or higher. Unlike players, the dealer cannot make any strategic decision, but instead plays according to strict rules. In most games, the dealer stands on any 17, but in some less favorable games, the dealer will hit a soft 17 but stand on a hard 17.

An Ace can count as either 1 or 11. If a given hand is 21 or under, with the ace counting as an 11, this is a soft hand; essentially even with a 10 value card, another card will not bust your hand. If the hand does not contain an ace, or if the ace can only be counted as a 1 (example, Jack, Three, Ace), the players total is a hard value.

The entire house advantage is based on players acting first. If the player busts (goes over 21), they lose their money, even if the house also busts later in the hand.

Each player is playing against the house, and decisions of the other players have little impact on your hand. Sure, if a given player who acted before you had hit instead of stood, the card order would have changed, but because the cards are randomized, it is just as likely to help as to hurt you, no matter how well or poorly they play.




The basic premise of a card counting system is that because of the rules of the game, high value cards favor players while low value cards favor the house. With a sixteen showing, a player has the option to stop, but the house must hit until they reach at least 17. With a lot of high value cards, players will frequently successfully double down or split, and the house will bust quite often. With a lot of low value cards, player double-downs and splits will result in weaker hands, with the house quite often not busting despite a high initial two-card value.

Per deck of cards in play, there are a fixed number of cards of each value. There are sixteen 10-value cards, and four each of the Aces, 2's, 3's, 4's, 5's, 6's, 7's, 8's and 9's. As these cards are depleted from the deck, the remaining cards are either higher in value, lower in value or about the same in value as a freshly shuffled deck.

When the remaining cards contain a disproportionate amount of high cards, the deck is rich. While the deck is rich, you will win a larger percentage of hands then you lose. If you were to bet more per hand, while the deck is rich and less per hand while the deck is poor, then you'd win more of your larger bets and lose more of your smaller bets. This is essentially what card counting is all about.

[Ualaa]

Basic strategy is the mathematical best option for a given dealer's upcard. If you follow basic strategy without employing any card counting strategies, you will eventually lose all of your money. However, if you were to play many billions of hands at a dollar per hand, ie in the long-run, basic strategy would have your money last longer then any other non-counting method of play.

A player gains the most (as a percentage) through correct Hit/Stand actions, less through correct Doubling actions, and the least through correct Splitting decisions. However, with basic strategy, we first determine if we can split our pair. Once that decision is made, we determine if we should double or not. Once that decision is made, we determine whether we should hit or stand.


HARD TOTALS
......................... 2........3........4........5........6........7.... ....8........9........T.........A
8 or Less.............H........H.......H........H...... .H........H........H........H.......H.........H
9........................D........D.......D....... D........D.......H........H........H........H..... ....H
10......................D........D.......D.......D ........D.......D........D........D........H...... ...H
11......................D........D.......D.......D ........D.......D........D........D........D...... ...D
12......................H........H.......S........ S........S.......H........H........H........H..... .....H
13......................S........S.......S........ S........S.......H........H........H........H..... .....H
14......................S........S.......S........ S........S.......H........H........H........H..... .....H
15......................S........S.......S........ S........S.......H........H........H........H..... .....H
16......................S........S.......S........ S........S.......H........H........H........H..... .....H
17 or More..........S........S.......S........S........S ........S........S........S........S..........S


SOFT TOTALS
......................... 2........3........4........5........6........7.... ....8........9........T.........A
A 2.....................H........H.......H........D. ......D........H.......H........H........H........ .H
A 3.....................H........H.......D........D. ......D........H.......H........H........H........ .H
A 4.....................H........H.......D........D. ......D........H.......H........H........H........ .H
A 5.....................H........H.......D........D. ......D........H.......H........H........H........ .H
A 6.....................D........D.......D........D. ......D........H.......H........H........H........ .H
A 7.....................S........D.......D........D. ......D........S........S........H........H....... ..S
A 8.....................S........S.......S........S. .......S........S........S........S........S...... ....S
A 9.....................S........S.......S........S. .......S........S........S........S........S...... ....S


PAIRS
......................... 2........3........4........5........6........7.... ....8........9........T.........A
2's......................H.......SP.....SP......SP ........SP.......SP......H........H........H...... ..H
3's......................H........H......SP.....SP ........SP.......SP......H........H........H...... ..H
4's......................H........H.......H....... H........H.........H.......H........H........H.... ....H
5's......................D........D.......D....... D........D.........D.......D........D........D.... ....D
6's.....................SP.......SP.....SP.....SP. .......SP........H.......H.........H.......H...... ..H
7's.....................SP.......SP.....SP.....SP. .......SP.......SP.......H.........H.......H...... ..H
8's.....................SP.......SP.....SP.....SP. .......SP.......SP......SP.......SP......SP....... SP
9's.....................SP.......SP.....SP.....SP. ......SP.........S......SP.......SP........S...... ..S
T's......................S........S.......S....... S..........S........S........S........S........S.. .......S
A's.....................SP.......SP.....SP.....SP. .......SP......SP.......SP.......SP......SP....... SP

KEY
H = Hit
S = Stand
D = Double
SP = Split

[Ualaa]

The Count:

2 = +1
3 = +1
4 = +2
5 = +2
6 = +2
7 = +1
8 = 0
9 = -1
T = -2
A = 0



Steps to Count Mastery

1. Take a deck of cards, turning over one card at a time and call out the count value: +1, +2, 0, -1 or -2. Do this until you instantly recognize the value.

2. Go through a deck of cards, one card at a time and keep a running count, adding or subtracting the value of the next card to the previous total as it is exposed. The count starts and ends at zero.

3. Go through the deck turning over two cards at a time. Total each set. For example a 5 and a 10-value -- the total is zero. Don't do a running count at this point, just practice until you know any two card value instantly.

4. Run through the deck, two cards at a time, and keep a running count. After you're good at this, alternate between one, two and three cards at a time, keeping a running count.



Exact Count vs Running Count

The exact count is also referred to as the "True Count". It is the basis for the mathematics in this system. Both playing and betting decisions are based on the exact count. The exact count extracts the significance of the running count at a given time.

The running count is a cummulative count of all the cards that have been removed from the deck. The exact count converts this raw data into something useful. You will need to remember the running count at all times, periodically converting to an exact count for a decision, then revert to the running count as cards continue to be played.

The exact count is an estimate of the count per half deck remaining to be dealt. If there is only half a deck remaining, then the exact count and running count are the same value. With a full deck remaining in the shoe, the exact count is half of the running count, because there are two half decks remaining to be dealt (Running Count divided by 2 <Half Decks>). With a deck and a half (3 half decks) the running count is divided by 3, to reach an exact count.

Casino's will deal from a shoe, which is most commonly six decks of cards. Therefore at the outset, there are twelve half decks remaining to be dealt. Usually, the casino shuffles with one and a half to two decks of cards remaning. With a shuffle, the running count is reset to zero.

If the running count is seven, and you estimate two decks remain (four half decks), the true count is basically plus two. If the running count is three and there are four decks remaining to be dealt (eight half decks), the true count is closest to zero. We don't need an exact calculation, going to the nearest whole number is easily sufficient.

Any time you need an exact count, you compute it from the current running count. Once you have the exact count and have made your decision, go back to the running count. Extremely important, go back to the running count.

[Ualaa]

Overcoming the House Advantage

First you need to know the house advantage, which varies according to the rules the casino plays with. Simply total the gains and losses according to the rules the house plays by. The total is the house percentage. Typically Vegas will offer amongst the best options for the player, with Atlantic City offering these least favorable options.

Gain or Loss
in Percentage................Rule Variation

- 0.19...........................Dealer draws to soft 17.
- 0.34...........................Two deck game.
- 0.50...........................Four deck game.
- 0.60...........................Six deck game.
- 0.66...........................Sixty deck game.

- 0.89...........................Doubling forbidden on Hard 11.
- 0.56...........................Doubling forbidden on Hard 10.
- 0.14...........................Doubling forbidden on Hard 09.
- 0.14...........................Doubling forbidden on Soft Totals.

+ 0.17..........................Allows doubling after splitting.
+ 0.19..........................Allows doubling on three cards.
+ 0.20..........................Allows doubling on any number of cards.
+ 0.02..........................Further splitting of all pairs except Aces.
+ 0.05..........................Further splitting of all pairs, including Aces.
+ 0.14..........................Unlimited draws to split Aces.
- 0.16...........................Forbid splitting Aces.
- 0.46...........................Forbid splitting any pairs.

+ 0.15...........................Surrender offered
+ 2.33...........................Blackjack pays 2 to 1. (Normal is 1.5 to 1).
- 2.33............................Blackjack only pays 1 to 1 (No bonus).


For example, a casino near me offers these rules: Eight deck game (- 0.60), can Double after Splitting (+ 0.17), re-split any pair except Aces (+ 0.02), and Surrender is offered (+ 0.15) for a total of - 0.26% against me.

Once you know the house percentage, you need to calculate when your advantage (exact count) exceeds the house advantage. Each point in the exact count equates to a 0.50% gain or loss of advantage.

In order to realize a significant enough advantage to begin moving your money towards bigger bets, you have to overcome the houses advantage and then gain a half percentage in your favor.

In the casino near me, the house advantage is 0.26%. At an exact count of +1, I have a 0.24% advantage. At an exact count of +2, my advantage has exceeded the houses by more then half a percentage (+1.00 minus 0.26 house advantage equals +0.74 percent in my favor).






Betting Technique

All bets are made in units. The unit, is your minimum and default bet. Generally at a $5 table, your minimum bet is $5, and at a $25 table your one unit bet will be $25. A lot of tables have a betting range of $5 minimum through $50 maximum. This means you cannot bet less then $5 or more then $50 as your initial starting bet. If you're playing at a $5 table, you could easily go with $10 is your minimum one-unit bet.

In order to maximize your advantage, you need to bet more money when you have the advantage, and less money when the odds are even or in the houses favor.

The larger your betting spread, the more likely you are to be suspected of counting cards. In general, you should limit your spread to a maximum of 1:5 units. As in, if your small bet is $10, then your maximum bet will be no more then $50.

Your ideal bet will be one unit most of the time, two units when you have 0.50% in your favor, three units at 1.00% in your favor, four units at 1.50% in your favor, and five units with 2.00% or more in your favor. Remember, with each point of the exact count, the odds change by 0.50%. Also remember you have to overcome the houses advantage first, and then exceed it by half a percentage before you increase your bet.

Typically, at an exact count of +2, you will have approximately 0.50% in your advantage. Most casino's have somewhere near 0.50% in their favor. At an exact count of +1, the odds are too close to even to make increasing your bet a good decision.

It all depends on the casino though. If the rules are vastly in their favor, you may need an exact count of +2 to break even, and not have the odds in your favor until +3. Remember though, you have the option to choose where you play. If the casino is offering rules which are very unfavorable, you can play somewhere else instead. If however, the only game in town has unfavorable rules, you at least know when to increase your bets.

If the exact count is +2, your ideal bet will be 2 units (+1 to negate the house advantage, +2 to gain 0.50% in your favor). At an exact count of +3, your ideal bet will be 3 units. At an exact count of +4, your ideal bet will be four units. And at an exact count of +5 or higher, your ideal bet will be 5 units. At any negative running count, the exact count is also negative so you'll bet just 1 unit without needing to compute the exact count.

I say ideal bet, because even if the true count is +9 and you'd like to bet your maximum 5 units, to maintain deceptive technique, you won't want to increase your number of units too quickly. Generally, a lot of players will allow their winnings to ride on their next bet. This means if you bet $10 and win, many players will put the $10 winning onto their next bet for a new bet of $20; this looks very natural. Generally speaking, you don't want to increase your bet more then 1-2 units at a time, unless you think it will look natural to do so.

[Ualaa]

Fluctuation and Bankroll

For example, your initial bet is $10. The freshly shuffled shoe gives the house approximately 0.50% in their favor. This means in the long term, the house will win 50.25% of the bets and lose 49.75% of the bets, for a net gain of 0.50% more winning hands then losing hands. If you were in this situation an infinite number of times, per 100 times in the situation you would wager a total of $1000. Of that $1000 wagered, you would lose $502.50....but despite your 0.50% disadvantage, you'd still win $497.50.

Take an exact count of +11 in a game where the house has a 0.50% advantage. Your first +1 exact count will counteract the houses advantage. The next +10 of the exact count gives you a phenominal +5.00% in your favor. This means, in the long term you will win 52.50% of the hands in this situation, but will still lose 47.50% of the hands. If you had a $10 bet out, per 100 times you are in this situation, you will have $1000 wagered. Of that $1000, (in the long-term) you expect to average $525 won and $475 lost, for a net gain of $50 won more then lost.

Fluctuation is when you win your smaller bets despite being at a disadvantage or when you lose your larger bets even with an advangate. We're not so concerned with winning smaller bets when at a disadvantage, but losing the larger bets in the short term can be nasty if your bank roll is not large enough to absorb this fluctuation.

If you were to play a single hand, at a high limit table with $5000 running on a single bet, even with 10% in your favor, there is a good chance you could lose the entire amount on a single bet. That is the nature of fluctuation. The casino effectively has an infinite sized bankroll, which allows it to ride out its streaks of bad luck so the mathematics of the long term percentage in its favor can assert itself.

If you were to play at a $5 table, with a $5000 bankroll, that is to say 1000 units, your bankroll is sufficiently large to ride out your streaks of bad luck and reach your long term potential. That is assuming you play the system error free and that you play enough hands for the long term results to realize themselves.



First off, a bankroll is money which has been designated for gambling. This means it is not your rent or mortgage money nor is it needed for groceries or other bills. It has been set aside entirely for gambling and for no other purpose. It won't be tapped for any expense other then gambling. If the entire bankroll were lost, you would not be out in the street.

Generally speaking, you would like your bankroll to be at least 500 units in size. Of that 500, bring a maximum of 50 units to a given session. If you're playing at a $5 table, this translates into having $2500 in your gambling bankroll, but bringing no more then $250 to the table with you.

In the long term, mathematically speaking 7 in 10 playing sessions will be profitable, but 3 in 10 sessions will result in a loss of money. By having 10 session bank rolls, you have a significant cushion against fluctuation.

If you play a given session and are losing constantly, stop the session before you lose your session bankroll. If on the other hand, you typically play for an hour or so, but are winning constantly, by all means continue to play. In short, play it by ear.



Moving up the scale

If you play at the $5 tables, you need a total bankroll of $2,500 and a session bankroll of $250 to overcome fluctuation.

If you play at the $25 tables, you need a total bankroll of $12,500 and a session bankroll of $1250 to overcome fluctuation.

If you'd like to play at the $100 tables, you need a total bankroll of $50,000 and a session bankroll of $5,000 to overcome fluctuation.



Assuming you play basic strategy perfectly, maintain an error free running count and exact count, bet accurately according to the system, in the long term you will average approximately one maximum bet won per 100 hands played. With the adjustments to basic strategy, based on the exact count, this increases to an average of approximately two maximum bet won per 100 hands played.

If you make mistakes, such as betting four units at an exact count of minus four, this will substantially cut into your long-term results.

Let's say you would like to play professionally. You learn the system inside and out, including all of the modification tables (which will be in later posts). You've played with poker chips at home until the system is second nature. You'd played in the casino environment for the lowest stakes possible for many sessions. It is highly recommended that you play up the scale, starting at a lower dollar amount and gaining experience through actual play.

If you're serious about professional play though, you'll probably want to start at a mid-range level of play. For example, playing at the $5 tables means your maximum bet is $25, and you can expect a long-term winning rate of only $25-50 per 100 hands played. However, if you have the bankroll to start at the $25 level, your maximum bet is $125, which correlates to $125-250 per 100 hands played. The 25/125 portion assumes the basic system and the double amount assumes the entire system including the modifications to basic strategy based on the exact count.

Number of hands played will vary based on a number of factors including how many hands you play simultaneously, number of players at your table, the shuffle point, how fresh you are etc. As the only player at a table, and playing two hands at once, you can average 100 hands played per hour. As one of four players at a table, and only playing one hand at a time, you will be lucky to average 50 hands per hour.

If you're playing at a $25 table, with a table spread of $25 to $250 (1 to 10 units), how long until you can move up to the $100 tables? The $25 level requires a bankroll of $12,500. If you were to play at the $50 level, you'd need twice the bankroll to be safe. With a 50-100-150-200-250 spread, you could play at the same table.

Playing perfectly, at the $25 level, and averaging $125 won per 100 hands played, it will take you somewhere in excess of 100 hours played to make enough for a sufficient bankroll to play at the $50 level. Once you have the bankroll ($25,000) to be playing with a unit of $50 at the $25 tables, your per hour will increase to $250. Depending where you live, you might have ready access to a casino. If you're limited to a four day vacation in Vegas per year, it will take a lot longer to reach 10,000 hands played.

[Ualaa]

Modifying Basic Strategy

The decisions within a range of +6 to -6 account for more the 90% of the gains through modifying basic strategy. The actual numbers for when it becomes beneficial to alter basic strategy are given, but in actual play situations beyond +/- 6 will almost never come up.



Insurance
When the dealer has an Ace up, take insurance at an exact count of +3 or higher (including all visible cards on the table). Decline insurance at an exact count of +2 or any lower value.



Hard Hit/Stand Decisions

......................... 2........3........4........5........6........7.... ....8.........9........T.........A
Hard 12..............3.........1........0.......-1.........0.......H.......H.........H.......H..... .....H
Hard 13..............0........-1......-2........-4.......-4.......H.......H.........H.......H.........16
Hard 14.............-3.......-4.......-5........-6.......-6......14......17.......16.......8.........12
Hard 15.............-5.......-5.......-7........-9.......-8......12......12........8........4.........10
Hard 16.............-7.......-8.......-9.......-11.....-10.......8.......8.........4........0...........8
Hard 17..............S.........S........S........S..... ...S........S.......S.........S........S.........-5
Hard 18+............S.........S........S........S...... ..S........S.......S.........S........S..........S

H = Always Hit.
S = Always Stand

Stand if the exact count is equal to or greater then the number in the table. Hit if the exact count is less then the number in the table.



Soft Hit/Stand Decisions

......................... 2........3........4........5........6........7.... ....8........9........T.........A
17 (or lower).......N........N........N........N........N .......N........N.......N........N.........N
Soft 18.............-13.....-14.....-13.....-13.......S........S......-11......H........H.........0
19 (or higher)......S........S.......S........S........S. .......S........S.......S........S..........S

H = Always Hit
S = Always Stand
N = Do Not Stand (Hit or Soft Double Decision)

Note, hit/stand is the last decision we make.... 1) Do we Split; 2) Do we Double; 3) Do we Hit/Stand. Many of these decisions, would be soft doubles.




Hard Doubling

......................... 2........3........4........5........6........7.... ....8........9........T.........A
....7...................21......15.......12......1 0........9.......H........H........H........H..... ....H
....8...................14........9........6...... ...4.......3......16........H........H........H... ......H
....9....................2.........0.......-2.......-4......-5........3........9........H.........H........H
...10..................-7........-8.......-9.....-10.....-11......-6.......-4.......-1.........4.........4
...11..................-9......-10......-10.....-11....-12.......-7.......-5......-3........-3.........1

H = Always Hit

Double down if the exact count is equal to or greater then the number in the table. If the exact count is less then the number in the table, do not double down (hit instead).



Soft Doubling

......................... 2........3........4........5........6........7.... ....8........9........T.........A
Soft 13..............10.......6........3.........0..... ...-2.......H........H........H.......H.........H
Soft 14..............10.......5........1........-2.......-4........H........H........H.......H.........H
Soft 15..............11.......4........0........-3.......-6........H........H........H.......H.........H
Soft 16..............10.......3.......-1........-5.......-8........H........H........H.......H.........H
Soft 17...............1.......-2.......-5........-8.....-10.......13.......H........H.......H.........H
Soft 18...............1.......-1.......-4........-6.......-6.......16.......X........H.......H.........X
Soft 19...............8........5........3.........2.... .....1.......16.......S........S........S......... S
Soft 20..............10.......9........7.........6..... ....5.......16.......S........S........S.........S

H = Always Hit
S = Always Stand
X = Do Not Double (See Soft Hit/Stand Table)

Double Down if the exact count is equal to or larger then the number in the table, otherwise do not double.

[Ualaa]

Splitting Pairs (Doubling after Splitting *IS* permitted)

......................... 2........3........4........5........6........7.... ....8........9........T.........A
Pair of 2's...........-4.......-5.......-7.......-9.......SP......SP.......8........H........H...... ...H
Pair of 3's...........-1.......-6.......-8.......-9.......SP......(8)......H........H........H...... ...H
Pair of 4's..........16.........8........4........2....... .0........X.......H.........H.......H.........H
Pair of 5's............X........X........X.........X...... .X........X........X........X........X.........X
Pair of 6's...........-1.......-3.......-4.......-6......-11...(-10)......H........H........H........H
Pair of 7's...........-8.......-9......-11......-13......SP.....SP........0........X........X...... ...X
Pair of 8's...........SP......SP.......SP......SP.......SP ......SP......SP......(21).....(6).....-13
Pair or 9's...........-2.......-4.......-5.......-6........-7.......4......SP.......SP........S........S
Pair of 10's.........10........7........6.........5....... ..4......14.......S........S........S.........S
Pair of Aces........-9.......-10.....-10......-11.....-12......-8......-7.......-7.......-7.........4

H = Always Hit
S = Always Stand
SP = Always Split
X = Do Not Split (Double or Hit/Stand Decision)

Split if the exact count equals or exceeds the number in the table, otherwise do not split. Numbers in parantheses are read reverse, as in split if the exact count is equal to or less then the number in the table, otherwise do not split.



Surrender

Some casino's allow you to surrender you initial two-card hand by paying the dealer half of your bet and keeping the other half yourself. Typically, you must surrender before any player has taken cards. If the casino offers surrender, doing so is to your advantage if your expected win/loss is less then 50% no matter what you do.

......................... 7........8........9........T.........A
.....12.................H........H......16.......1 2........H
.....13................20.......15......11........ 7.......12
.....14................14.......11.......6........ .3........5
.....15................13........7........2....... ..0........1
.....16................12........5........1....... .-2.......-1
.....17.................S.........S......13....... 12........X
Pair of 8's...........SP.......SP.......8.........1....... .Z

H = Always Hit.
S = Always Stand
SP = Always Split
X = Hit/Stand Decision
Z = Spit/Hit Decision

Surrender if the exact count equals or exceeds the number in the table, otherwise do not surrender.

[TheMuffinMan]

/mind blown

[Nghtmr9999]

*head asplodes*

[Ualaa]

At least the spam is semi-relevant to casino gambling.
Wouldn't however recommend clicking spam links.