Blackjack Card Counting Systems

Tuesday, 19th September 2017

Card counting systems in blackjack are a means of advantage play in which you gauge how favorable or unfavorable the deck is, and then betting more or less based on that estimate. This estimate is arrived at, not by memorization, but by a heuristic system which assigns a point value to various cards in the deck. Once a card has been removed from the deck, it either makes the deck more favorable for the player or less favorable for the player. This effect is tracked by adding and subtracting numbers from a mental tally called “the running count”.


How and Why Card Counting Systems Work

Imagine that you’re playing roulette, and you place a bet on red, and you want to know what your chances of winning are. The calculations are simple enough; you simply divide the number of red slots on the wheel by the total number of slots on the wheel. On an American roulette wheel, you’d have 18 red slots, 18 black slots, and 2 green slots, for a total of 38 slots on the wheel. 18 divided by 38 is 47.37%, which is your chance of winning. No matter whether you win or lose on that bet on red, if you bet red again on the next spin of the wheel, your odds of winning are the same: 47.37%. They don’t change based on what’s happened before.

Now suppose you’re playing a card game similar to roulette, where the dealer turns over a card, and you bet on whether or not the next card is going to be red or black. The deck of cards has 18 red cards in it, 18 black cards in it, and 2 jokers. If you bet on red, you have a 47.37% chance of getting a red card. Now suppose that card is discarded, and you’re dealt another card. Have the odds of getting another red card changed? The answer should be obvious, because now there are only 37 cards total in the deck, and only 17 of them are red, so the odds of winning become 17/37, which equates to 45.95%. The odds of getting a black result have increased to 18/37, or 48.65%.

Now suppose you get red five times in a row. If you’re playing roulette, then your odds of winning your next bet on red is still 47.37%–they don’t remove red slots on the wheel when you’ve won. But in this imagined card game we’ve come up with, the difference is significant after five red wins in a row. The chances of being dealt a red card on the next play have gone down to 13 divided by 33, or 39.4%. Meanwhile, the chances of being dealt a black card on the next play have gone up to 18/33, or 54.54%.

Now suppose you only bet a single dollar on the first five bets, so you’ve lost $5. But now that your odds of winning (by betting on black) are more likely than not, you raise the size of your bet to $20. Your expected value is 54.54% of that $20, or $10.90. And if you kept playing long enough, you’d continue to find opportunities to make bets with a positive expectation.

That’s a remarkably accurate description of how card counting systems work, but instead of tracking the colors of the cards, you’re tracking whether the cards are high or low. In some systems, what constitutes “high” or “low” varies based on goals having to do with accuracy and ease of play. Either way, you’ll know when the deck is in your favor, because when the deck has lots of high cards in it, you’re more likely to get a 3/2 payout on a natural 21, and you can bet more to take advantage of the situation. You’ll bet less when the deck has lots of low cards in it, because the dealer is less likely to bust, which isn’t a favorable situation for the player.

Some of the most commonly used counting systems include the following:


What Kinds of Different Systems Are There?

Each card has a value to a blackjack counter, and that value is called “the effect of removal”, or “EOR”. The EOR for the aces and fives have the largest effect on a player’s chances. If you remove all the aces from the deck, then a natural 21 is impossible, which subtracts considerably from the player’s chances of getting ahead. On the other hand, if you remove all of the fives from a deck, the EOR is so great that it would make almost any blackjack game a positive expectation game for the player.

The simplest card counting system is called an “Ace-Five Count”, and you simply add 1 to the count every time a five is dealt and subtract 1 from the count every time an ace is dealt. The higher the count is, the more you bet. If you have a wide enough betting range, say anywhere from 1 unit to 10 units, this is a remarkably easy and effective system. Most people are looking for more of an edge than this simple count offers, though, and they use slightly more complicated systems. (Something to notice about this system is that there are just as many +1 cards in the deck as there are -1 cards in the deck—this is called a “balanced” counting system, as a result. Not all systems are balanced.)

All card counting systems estimate multiple factors related to their effectiveness. The first of these is called “betting correlation”, and it’s probably the most important one. This number determines how well the count estimates the player’s edge—this is important for making decisions about betting amounts. The second of these is called “playing efficiency”, and this estimates how well the count takes into account changes to basic strategy. This factor isn’t as important as it may seem, but players who want to squeeze every percentage point of value out of their blackjack card counting system pay attention to it. The third and possibly least important factor is the “insurance correlation”, which is an estimate of how well the system predicts whether or not insurance is a good bet.

We already discussed balanced systems versus unbalanced systems, but just to reiterate, a balanced system is one in which the count evens out to 0 when you count through the entire deck. For example, the Hi-Lo system, which is quite popular, is a balanced system that counts aces and tens as -1 and counts any card ranked 2 through 6 as +1. There are 20 cards in each category, positive or negative, and when you finish counting through a deck, you’ll have a total running count of 0. In an unbalanced system, this isn’t true.

The Hi-Lo system is also an example of a single level system, because the cards are all valued at either +1 or -1. A higher level system might give different values to different cards. For example, if a system counts aces as -2 and fives as +2, and then counts tens as -1 and 2s, 4s, and 6s as +1, then the system would be a multi level technique.

Some card counting systems go even further and require you to keep a side count of the aces that have been dealt. The more complicated the rules for the system are, then the more accurate it is, but you need to remember that your system should also be practical. You’ll be counting cards in a crowded and noisy casino, so you need to be able to concentrate without looking like your concentrating. Practice is necessary, but so is a simple enough strategy.


Roulette Systems – Most Popular Roulette Betting Systems to Win

Tuesday, 22nd August 2017

Roulette betting systems are always worthless. Don’t bother with them. If you’re going to play roulette, the best approach is to accept that it’s a mathematically losing proposition if you play long enough. As long as you’re getting your money’s worth in terms of entertainment, you’re doing fine.

Why don’t roulette betting systems work? It’s all in the math.


How Casinos Stay in Business

Casinos are some of the most profitable businesses you’ll ever find. That’s because the games are all set up in a way which guarantees the casino a mathematical certainty of winning over time.

They do this by offering payouts that are slightly less than the odds of winning. In roulette, for example, a straight-up bet pays off at 35 to 1. The odds of winning, though, are 37 to 1. It doesn’t take a nuclear physicist to understand why this results in sure winnings for the casino over the long run, but here’s a clarification.

Assume that you play exactly 38 spins on a roulette wheel, and you see mathematically perfect results. You’ve bet on the same number for all 38 spins. In a mathematically perfect example, you’ll have won once, and you’ll have lost 37 times.

If you’re wagering $100 per spin in that situation, you’ll have won $3500 on the hand which you won. But you’ll have lost $3700 on the other losing spins. Your net loss for this hypothetical situation is $200.

Of course, in reality, you don’t see mathematically perfect sessions like this. The rule of thumb is that over time, the more results you see, the closer they get to mathematically perfect. That’s why a player who spends an hour or two at the table might walk away a winner, but the casino still makes a profit over the long term.

A small casino might have four roulette tables with an average of four players at each table per hour. That’s 16 players per hour placing an average of 40 bets per hour, or 640 bets per hour. Over 24 hours, that casino has taken 15,000+ bets. Over the course of a month, that’s about half a million bets. And over the course of a year, that’s six million wagers.

The casino will see close to mathematically true results over that volume of bets. A single player won’t even come close to that kind of long-run expectation.


How to Get an Edge over the Casino in Roulette

You can win at roulette. You just have to get lucky. But nothing you can do will affect your chances of getting lucky. The math stays the same no matter what you do.

That’s why roulette systems are nonsense. They’re unable to change the math of the situation.


Progressive Betting Systems

Most roulette systems are variations of progressive betting systems. The most famous of these is the Martingale System, in which you double your bet after every loss. At first glance, the Martingale System sounds like a sure thing. But it falls apart under closer examination.

A Martingale player will make a $10 bet on an even money bet on the table and hope for a win. But if she loses, she’ll double the size of her next bet in order to recoup her losses and still wind up a single betting unit ahead. If she loses twice in a row, she’ll double up again. This betting progression, if you’re on a losing streak, might look like this:

$10 – $20 – $40 – $80 -$160 -$320 – $640 – $1280

And so on.

The flaw in this betting system is that you’ll see losing streaks more often than you think you will, and when you do hit a bad losing streak, you’ll have lost a massive amount of money.

Another flaw is that eventually you’ll wind up needing to place a bet that’s either more than you can afford or that’s over the table maximum at the casino. In that case, the system breaks.

In the example above, if you’ve lost that many bets in a row, your next bet would be $2560. You’ve already lost $2550, so if you win after placing this massive wager, you’ll still only be up by $10.

And what are your chances of winning on this large $2560 bet? About 47.3%.

The odds of each roulette spin are independent of each other spin. You’re not more likely to win after losing 8 spins in a row.

Other progressive betting systems involve other, more complicated, methods of raising and lowering your bets depending on what’s happened on previous spins. But at the end of the day, math will win out.

You might be able to grind out a few small wins using one of these systems, but if you play long enough, you’ll eventually lose all of those and then some when you come upon the inevitable losing streak.


Daniel Rainsong

Michael Shackleford runs a website about gambling math called The Wizard of Odds. At one time he offered to bet $20,000 versus $2000 that any betting system would lose over a billion wagers. Daniel Rainsong contacted him via email and agreed to take him up on the challenge.

This simulation used blackjack rules rather than roulette rules, and the house edge on the game variation used was 0.26%. That’s 5% better than you’ll find on a roulette game, so the chances of his betting system working should have been significantly better than if he’d used roulette.

It would have taken 14 hours to run through a billion blackjack hands via the simulator, so they did a test run of just 10 million hands. The system showed a profit of and on for the first 168,000 or so hands, but after that, the losses piled up, and the simulated player was never ahead again.

This is as good a real life demonstration as you’ll probably ever see of why betting systems don’t work on games with a negative expectation.


Craps Betting Systems

Betting systems of any kind are exercises in futility. No manipulation of your betting amounts can change the fact that all casino games have an insurmountable edge over the house. This includes craps betting systems.

The big error that most betting systems make is assuming that the odds of something happening change because of what happened previously. This is true (to an extent) in a game like blackjack, but that’s because the deck has a memory—once a specific card has been played, it can’t be played again until the deck has been re-shuffled.

In other games, like roulette and craps, each outcome is an independent event. Just because someone has been rolling hot all night doesn’t mean she’s statistically likely to continue rolling hot. It also doesn’t mean that she’s due for a loss. The odds of each outcome of each roll remain the same regardless of what happened on the previous one, two, three, or even thirty rolls.

The rest of this page explores and examines some craps betting systems.


Hedge Bets

Some of the worst systems you’ll come across involve what’s called “hedge betting”. These bets are supposed to reduce your risk. For example, you might try to hedge your bet on a pass line bet by also placing a bet on any craps. This seems like a can’t lose system, but once you examine the math, the system falls apart.

Suppose you make a pass line bet of $20. You have 8 ways to win, 4 ways to lose, and 24 results which are essentially “no result”.  After 36 rolls, on average, you’ll have won $20 eight times, lost $20 four times, and seen a “no effect” the rest of the time, for an average win of $80.

Now suppose you make a pass line bet of $20 and a $5 bet on “any craps”. You now have 12 ways to win and 24 ways to lose. You’ll only win an average of $60 over 36 rolls with this system.

You’re better off just sticking with the pass line bet, obviously, right?


The Rothstein System

Another craps betting system that might be familiar to some players is called “the Rothstein system”. It’s just a variation on a popular betting system called the Martingale System, and it’s equally worthless.

The way this system works is that you begin by placing a single betting unit on the pass line. If you lose, you bet again, but this time you bet three units. If you lose again, you bet seven units. In other words, any time you lose, you double your last bet and add one unit.

If you win after your first bet, you’re up by one unit. If you win after your second bet, you’re up by two units. And so on.

Each time you win, you go back and start over again with one unit.


The Watcher System

We’ve also seen this one called “the Patience System”. Your goal is to win $10 a day with this system. You need a bankroll of $500 minimum for this system.

This time, instead of betting the pass line, you’re betting don’t pass. To use this system, you watch the game until there have been four successful pass line bets in a row. Then you bet $10 on don’t pass, because surely by now the dice are bound to lose, right?

This system is flawed because it doesn’t take into account the fact that each roll of the dice is an independent event. The probability on the upcoming roll doesn’t change just because of the four rolls prior.

People who like this system like to point out that the odds of the dice winning five successive passes are 31 to 1. So the idea is that you’ll win $10 31 out of 32 times. The advice this system promotes is also to quit playing for the day once you’ve won.

What if you do lose, though? The system has a plan for that, too. You double your bet on don’t pass. The odds of six successive passes are 63 to 1, and if you win this time, you win your money back and then some. And if you lose again, you double your bet again, because the odds of seven successive passes are 127 to 1.

Every progressive betting system faces the same problem. Eventually you’ll wind up with a long enough losing streak that you won’t be able to make your next bet in the progression because it’s over the house maximum bet.

Also, you’re not betting that five (or six, or seven) successive passes will be made. You’re only betting on the next pass. The odds of winning are slightly less than 50%, regardless of what happened on the previous rolls.


Hot and Cold Betting Systems

The idea behind these kinds of systems is to bet the pass line when the shooter is hot, and to bet the pass line when the shooter is cold. One common way to approach this system is to bet the pass line.

If the shooter wins, you continue to bet the pass line. As soon as the shooter loses, you switch to betting on the don’t pass line. You switch back as soon as the shooter wins again. The goal is to eventually catch someone on a winning streak (or a losing streak) and win lots of money during that streak.

This would work great if the house didn’t have a total on the don’t come bets that don’t win or lose. The percentage of those will eventually eat up any edge you might have gained using this system.


The Best System Is No System at All

Going with the best odds is the best craps system you can use. That’s easy enough to do. Just bet the pass line (or the don’t pass line), and whenever you’re able to take or lay odds, take or lay the maximum you can. This reduces the house edge dramatically. It doesn’t eliminate it, but your entertainment dollar will stretch a lot farther.