Counting Cards

Counting Cards :

How to Beat The Game of Blackjack

Counting cards is a technique to gain an advantage while playing the game of blackjack. It was originally discovered by a mathematician named Edward Thorpe, who used it gain an advantage against the casinos in Las Vegas.

On the surface, blackjack appears to be a relatively simple game.You are dealt two cards, and must make hit or stand decisions based upon the total of your two cards. If you go over 21 you lose. And yet beneath this illusion of simplicity there exist deep rivers of complexity.

Basic Strategy

The first tool in making blackjack decisions you should familiarize yourself with is a basic strategy chart like the following :

 

Now what this chart does is list the expectation maximizing decision for any player holding vs any dealer upcard. Most of the entries are self explanatory. When it says Ds or Dh, that means double if you are able to do, and stand or hit respectively if you are not. This is because you can only double on your first two cards, so you can make a soft eighteen with for example A43, in which case you could not double against a 5, so you would choose to stay instead. 

By faithfully following the correct basic strategy chart for the game you are playing, you will reduce the house edge to around 0.5%. This is extremely low relative to most gambling opportunities. Furthermore, because asymmetries between the house hand and the player hand, the odds in blackjack change. 

Specifically, the house favours small cards, like 2-7, and the player prefers big cards, like 9, T, J, Q, K, and A. Why?

One simple reason is because of the 3:2 payoff on blackjack. If you get AQ or any other form of two card 21, you are paid a 50% premium on your wager. Conversely, if the house gets blackjack, they win but they do not get paid a premium. 

Also, a deck rich in high cards allow you to complete your double downs more successfully. 

Effects of Removal

Wizard of Odds lists the effect of removal of various cards in a six deck game:

https://wizardofodds.com/games/blackjack/effect-of-removal/

You'll note the profound effect of removing fives. This is because a five can never bust a hit, unlike a six which can bust a 16. Fives and fours are also good at "spiking" high values (like if the dealer hits on 15 and gets 20), something which a 2 cannot do. 

So if the house edge is just 0.5%, then remove two fours and two fives and already the odds are even.

Counting Cards

We can see the EOR for eights and nines is negligible, so we can ignore them. We also ignore the 7 for simplicity and balance. See, if we take 2, 3, 4, 5, and 6 and contrast that with T, J, Q, K, and A we have 5 and 5 ranks. 

This is the essence of the hi lo system, which counts

+1 for 2, 3, 4, 5, and 6 

and - 1 for T, J, Q, K, and A

So every time a low card is dealt you add +1 to the running count, and every time a high card is dealt, you subtract 1 from the running count.

7s, 8s, and 9s are treated as neutral and not counted.

This enables you to keep track of when the deck is rich in high cards or low cards. 

The True Count

However, there is a problem. What we are really concerned with is the density of high cards and low cards throughout the entire remaining shoe. A +8 running count is more meaningful if there is 1 deck left than if there are 4 decks left, as that represents a 4x higher concentration of high cards.

So we must convert from the running count to the true count.

So what you do is you look at the discard tray. You see how many decks have been dealt. You then subtract that amount from the initial number of decks to return the number of decks remaining. So if there is 1.5 decks dealt out of 6, then there are 4.5 decks remaining.

You then divide the running count by the number of decks remaining to get the true count.

For example, if the running count is 8, and the number of decks remaining, you divide by 4.5 and get just under 2. However, we're going to truncate all our results, so 1.85 or whatever just becomes 1. Truncating means you cut off anything after the decimal place. You could also round, that works fine too. There are different methods. You could even try employing fractional true counts. It's a free society, you can do whatever you want. I truncate.

Betting Based on the Count

Once you can convert to the true count, you can now capitalize on your main source of advantage in the modern blackjack shoe game, betting based on the count. Usually card counters use a ladder approach for example in a $5 game they might bet :

TC 1 or below $5 
TC 2                $20

TC 3                $40

TC 4+              $60

This is a healthy 12-1 spread, but does require a bankroll of at least $6000 to have limited risk of ruin or ROR.

You want to have at least 100 max bets in your bankroll. In the above spread you cap out at 1 hand of $60, so $60 is your 'max bet'. The reason why you want 100 max bets is because there is substantial variance associated with card counting blackjack. You might have a 1.5% or 2% edge, but every hand is still essentially a coin flip as to whether or not you will win or lose. And when you factor in doubles and splits, it is pretty easy to lose 10 or 20 or even 30 max bets in a single session. So you want a decent sized bankroll to be able to absorb the swings.

The other thing you can do is increase or decrease your bets as your bankroll increases or decreases. This enables you to earn incrementally more, while also decreasing your ROR during downswings.

Index Plays

Index plays are deviations from basic strategy based on the count.

 Here are the top 18 most profitable deviations from basic strategy for Hi Lo. There are a lot more, but they occur so infrequently that they aren't as important. Deviating from basic strategy based on the count can increase your winnings, although in the modern shoe game the bulk of your expectation is generated simply from betting based on the count.

Please note these are indexes for a game where the dealer stands on S17. If you are playing a game where the dealer hits on soft seventeen, both basic strategy and the index plays will be slightly different. You always need to look up exactly the correct basic strategy and rules for your game.

So there you have it. Card counting isn't really that hard after all, now is it? The main thing is that you practice until you get it perfect.