HiLo Card Counting

The system explained here is HiLo, which is the most productive of the simple systems. Many books have been written on other systems that have more predictive accuracy, but are more detailed in what they ask you to keep track of in your head. It is also possible to keep side counts for special purposes. This will be taken up later.

For purposes of this explanation, the card counting system is a single one, with one parameter: the current “count per deck” of the pack of cards in use. The count will be either negative, positive or zero in accordance with whether small cards outnumber big ones, or vice versa, or if they are balanced.
The use of the count is to influence the size of bets and the use of basic strategy (and insurance) by telling the player what to do in reaction to the count. The count is a way of predicting more accurately whether small cards or high cards are more likely to have been dealt to the dealer or to be dealt to the player or the dealer.

Thus, there are two components to card counting: (1) being able to keep the count, and (2) knowing how to use the count to alter bets and plays.

Keeping the Count

In the discussion of basic strategy, the deuce through the six was referred to as a “low card.” Well, in counting, low cards are worth a +1. “High” cards in counting are considered to be tens and aces. Each of them is worth a -1. The three cards in the middle (7, 8 & 9) are disregarded. Thus, the 52-card deck will have 20 high cards and 20 low cards. Running through a complete deck and keeping the count should wind up at the end with a count of zero. Everything is balanced. At any moment, if the count is positive, it means that there is a preponderance of high cards in the deck as compared to low cards. The higher the count, the more lopsided the distribution is. Likewise, a negative count means that low cards prevail when compared to a uniform distribution of highs and lows.

Why does it matter whether the remaining deck is richer in low cards or high cards? In general, low cards favor the dealer, as the dealer is less likely to bust. High cards are said to favor the player, as it makes naturals more likely (paying 3:2) and it more readily makes pat hands. A high positive count will inform the decision whether to buy insurance when the dealer shows an ace. A low count is helpful in deciding whether to hit a fifteen or sixteen against a dealer’s ten.

To keep the count, the player simply has to keep a running total while the cards are exposed. All exposed cards are relevant to the count – those in the player’s hand, those in the other players’ hand, and the dealer’s. Even the card at the bottom of a hand held deck, if it has been exposed. It is usually most efficient to make a group count for a group of cards, and then sum the groups. For example, a table of three players may have the following at the conclusion of play:

The net is +1 after this hand

Now there is an evident complication: In a six deck game, the net count is zero at the end, just as in a one-deck game. But there are six times as many high cards and low cards as in a one-deck game. More to the point, when there are 17 cards left in the deck and the count is +5, it means a whole lot more than if there were 102 cards left in a six-deck shoe and the count is +5.

This reality leads to two key points about card counting. The first is that the count has to be converted into a “count per deck” to standardize the effect of the count and hence formulate sensible decision rules based on it. The second point gets at why card counting is always more productive the deeper into the deck the dealer goes. This is called “penetration.”

Count Per Deck

The concept is fairly simple: If the count is four and there’s only half a deck left to deal out, the effect is the same as if the count were eight and a full deck were left. Likewise, if the count is 4 and there are four decks left to deal out, the concentration would be the same as a count of 1 when just one deck were left. Thus, “the count” can not be used until it is converted into a count-per-deck. To do so, estimate the number of decks left to be dealt out, and multiply the running count by that number. The result should be truncated (not rounded) to a whole number.

Penetration

A newly shuffled deck has a count of zero. As it is dealt out, the count might eventually become lopsided in one direction or the other, but the first few hands out of a fresh deck are unlikely to push the count too far in a positive or negative direction. Card counting is most profitable, of course, when the counts are high in either direction, since that is when deviations from “normal” betting and basic strategy are most called for. As a deck gets down towards the bottom, if there is an uneven distribution of low and high cards, the predictive value of card counting goes up. (Remember that a raw count of 4 is really an 8 if only 26 cards are left.) Card counters like it when dealers allow the cards to go close to the end before re-shuffling. Pit bosses like to have frequent shuffles if there’s a suspected card counter, as it resets the count before it can get to high in one direction or another.

If You Lose the Count

Questions will arise in counting about starting over. If you join a game in progress and did not start counting from the last shuffle, just start counting from the next deal. Your count may not be “the count” but is will probably be close. Remember that the expected value of the count is zero, so assuming that the count was zero when you started to count is like estimating the count so far by taking its average. The same is also true if something distracts you and you forget to count a card or perhaps lose track of the count altogether. Just do the best you can. It may not be a perfect recovery, but it will at least help chart the way from that point to the next shuffle.

Sidecounts in HiLo

The main inaccuracy of the HiLo system is that it counts aces as high cards when in fact they can serve as low cards. One might think that by keeping a separate count of aces, it would then be possible to take that flaw into account whenever the presence of an ace is really important. Experience shows, however, that keeping track of aces does not perceptively increase the profitability of counting with Hi-Lo. What does pay off is keeping a second count of just the tens. This may seem daunting at first, but remember that the main count will have to be so ingrained that it will not be hard eventually to add a second one. The key is long hours of relentless practice.

The reason for knowing the count on just tens is that it will be more accurate than the HiLo count when it comes to buying insurance. Specifically, if the dealer shows an ace, when does it make sense to buy insurance against a ten underneath? The “normal” count rule is to insure with a count of +3 or more. Part of the time the concentration of tens in the cards to be dealt will be lower than the count would have you believe because of aces. Also, the count does not keep track of the middle cards, so if they are greatly depleted, the count will not reflect the increase in concentration of both high and low cards. (The count will be unaffected).

But suppose you had also been keeping a parallel count of tens? This count would be a +1 or any card other than a ten, and a -2 for any ten. The count is a running count, not divided for a count-per-deck. It does not sum to zero. (It sums to 4 times the number of decks in use.) The rule is that whenever the count is more than 4 times the number of decks in use, it makes sense to insure. The reasoning relates to why the insurance bet is not a good buy if one is not counting. The pay-off is two to one, so it is only a good bet when the chances of winning it are better than 2 to 1, i.e., when the concentration of tens in the deck is greater than 331/3%. When the count is positive by more than 4 (in the case of a single deck), it means that the ratio of tens to all cards is greater than 1 in 3. (Of 52 cards in a deck, 36 are +1 cards and 16 are -2 cards (31% tens). A count of 5, for example, indicates that the concentration of tens is greater than an even distribution. (It is 34% for example, after one hand in which 8 cards were played, one of them a ten, with a tens count of +5.)

Counting tens should add about $0.65 to the hourly winnings of a person whose average bet is $10.

Other Blackjack Card Counting Systems

You may see references to the “Einstein Count,” also known as High-Opt I. (It is named after Charles Einstein, not Albert Einstein, and you do not need to be an Einstein to use it. But it is tricky). This count keeps track of tens (-1) and low cards – the three through the six (+1). Sevens, eights, nines, aces and deuces are ignored. Sometimes there is a side count of aces with High-Opt I, as the main count ignores them. Many authors have described other counting systems (like High-Opt II and Omega). For so long as the counting system keeps track of the concentration of high cards and low cards in the deck or pack, they will offer results. According to some, the only complex system that can beat Hi-Lo, in spite of its simplicity, is the Halves Count. This system is more complex (8 is zero. 9 is -½. Tens and aces are -1. 2 & 7 are +½. 3, 4 & 6 are +1, and 5 is +1½). Sticking with Hi-Lo for starters is a good idea. Once you have won enough money to buy the gambling books, it will be appropriate to invest the time and effort in alternative systems.