The Effect of a Side Count on Your Card Counting Win Rate
FROM ET FAN:
Can Side Counting Make You a Super Card Counter?By Arnold Snyder
(From Blackjack Forum Volume IV #3, September 1984)
© Blackjack Forum 1984
I've spent the past four years advising blackjack players to streamline their card counting strategies.
In 1980, in The Blackjack Formula, I showed that the most important factor in a card counter's win rate is penetration. Since then, computer tests and mathematical analyses have shown time and again that the most important factors affecting the card counter's win rate are indeed the blackjack game conditions -- shuffle-point, the number of decks in play, hands per hour, etc.
Given like conditions, the more complex systems, such as those with side-counts, rarely significantly outperform the simpler systems. This is especially true in multi-deck games, where side-counts have even less value. My angle on beating the tables has been to exploit those games that are the easiest to beat, rather than struggle to get an edge in a tough game.
Most card counters, because they are not full-time professional gamblers, do not have enough time to dedicate to the memorization and practice required for the more difficult card counting systems. Yet, casual players who can recognize which games are more exploitable, can do quite well as blackjack players if they can accurately apply a simple count strategy.
One of the major simplifications a player can employ, with little effect on his win rate, is to quit attempting to side-count aces. Many card-counting systems provide ace adjustment advice, but maintaining two separate counts, and then utilizing this information with precision, is not an easy task for most players. In multi-deck games, a side-count of aces will rarely increase a card counter's win rate by more than 1/20 of 1%. Even in a deeply dealt single-deck game, a side-count of aces is not worth more than 1/5 of 1% to a counter's win rate.
Players who follow some sort of Kelly betting scheme, however, will find that any percentage increase in win rate will be worth more, in dollars and cents, than is immediately apparent. A Kelly betting scheme is loosely one in which the player attempts to bet a proportion of his bankroll equal to his percentage expectation. For instance, a player with a 2% advantage would bet roughly 2% of his bankroll (actually, slightly less, to account for the increased fluctuation from double downs and pair splits).
Side Counts and Kelly Betting
Let's look at a simple example of the effect of Kelly betting on the value of a side count.. Forget for the moment that the game is blackjack, and ignore the intricacies of the game. Assume that two players, each with a $1000 bankroll, are betting in a game where one player has an advantage of 1% over the house; the other player, due to a superior strategy, has an advantage of 2% over the house.
If both of these players placed equal sized bets, then the player with the 2% advantage would expect to win twice as much money as the player with the 1% advantage. If both players were using a Kelly-type betting scheme, however, the player with the 2% advantage would expect to win 4 times the expectation of the player with the 1% advantage.
Here's why: With a Kelly betting scheme, the player with the 1% advantage would bet 1% of his bankroll, or $10. His expectation on this bet would be 1% of $10, or 10¢. The player with the 2% advantage, however, would make a bet of $20 (2% of his bankroll). His expectation on his bet would be 2% of $20, or 40¢. So, with twice the advantage, he'd expect 4 times the return in $.
Simply side-counting aces would not double anyone's advantage, so you couldn't expect to quadruple your return. But the same effect as illustrated above would occur, albeit less dramatically, with smaller increases in advantage.
For instance, if one player had a 1.5% advantage, and another had a 1.7% advantage, you might quickly estimate that the player with the greater advantage would expect to win $17 for every $15 expected by the player with the lesser advantage. But this would only be true if both players were betting equal amounts of money. Using a Kelly method of bet sizing, the player with the 1.7% advantage would expect to win more than $19 for every $15 won by the player with the 1.5% advantage.
Mathematicians have been arguing for some years now about the long run effect of Kelly betting. Far be it from me to proclaim that in the long run doubling your advantage would quadruple your dollar expectation. But on any one given bet this is so.
Since a Kelly bettor sizes his bets according to the size of his bankroll, he will also find that a small increase in win rate could have a significant long run effect on his dollar return. One tenth of a percent may look like nothing on paper, but when you consider it might be the difference between a 1% win rate and a 1.1% win rate, it's actually a rate of return 10% higher. When you're thinking seriously about how many hundreds of hours it might take you to double a bankroll, small differences like this look much more significant.
When a Side Count May Be Worth the Trouble
So, the first players I might advise to side-count aces would be those who are serious players who play primarily in single-deck games, who have the talent to side-count easily and accurately. This does not mean I'd advise most serious players to side-count aces. Most of the blackjack pros I've asked about this do not side-count aces. They feel their time at the tables is more profitably spent maintaining a friendlier camouflage than would be possible for them with a multi-parameter counting system.
There are also many serious players who do not employ any type of Kelly betting scheme. There are nickel chip players who have been playing with nickels for years, who may profit up to a few thousand dollars per year at the blackjack tables. They play frequently and are talented counters dedicated to winning.
But these players don't think in terms of "bankroll." If they win $500 in a week, they do not increase the size of their bets the following week. And if they lose $500, they do not decrease their bets. Winnings are simply treated as income, and losses are absorbed.
These players, though serious about winning at the game, are not trying to get rich or become high stakes pros. They generally hold jobs and play blackjack for enjoyment. There are also high stakes players who pay no attention to the Kelly criterion. They are often junketeers who always play at a certain level to maintain their comp ratings. Though they may be excellent and consistently winning card counters, they have little use for Kelly betting.
Most of the card counters I know who have really made a fortune playing blackjack have used some form of Kelly betting. But this isn't for everyone. Some players will side-count aces regardless of how small the dollar return might be, simply to play more accurately for the sake of playing more accurately. This type of player enjoys the challenge of playing a mathematically precise game more than any other aspect of card counting, including profit potential.
One such player said to me: "I like counting cards and I do it well. I'm not going to eliminate my ace count just because it's only worth two dollars per week. Neither am I going to throw two dollars out the window every week, just because it's only two dollars."
For those players who want to count aces, for whatever reason, I will present the best ace-counting methods I know.
The Best Ace Side Counts
In Blackjack Forum II #3, I reviewed a book by C. Ionescu Tulcea titled A Book on Casino Blackjack (1982). In my review, I mentioned that although Tulcea's counting systems were presented impractically for non-mathematicians, I liked his method of side-counting aces. What he proposed was to keep the ace count as a balanced count, balancing the aces vs. specified low cards, then adjusting the primary running count by adding the two counts together.
Tulcea advises using this method with my Zen Count (which he calls the "Main Count"). I would never advise side-counting aces with the Zen Count, which already has a high betting correlation.
The simplest count system that would lend itself well to this approach is the Hi-Opt I count: Tens = -1; 3s, 4s, 5s, and 6s = +1. For your ace side-count, you would count aces as -1, and deuces as +1.
For example, your count starts at 0/0. The first "0" is your Hi-Opt I running count; the second "0" your ace-deuce running count. Let's say the first hand uses 2 tens, a 7, a 5 and an 8. Your running count is now -1/0. The second hand uses 2 tens, a 5, a 2, and a 9. Your running count now becomes -2/+1. In order to make an ace-adjustment, you would simply add together the two running counts. -2 + 1 = -1 (your ace-adjusted running count).
This ace-adjusted running count, in fact, is exactly what your running count would be if you were keeping the Hi-Lo Count only. The ace-deuce count does not measure the proportion of aces left in the remaining deck(s); it measures only the proportion of aces to deuces. But by adding the ace-deuce count to your primary count (Hi-Opt I), you would raise your betting correlation from .88 to .97, as high as you could hope to raise it with a perfect side-count of the proportion of aces to the remaining deck(s).
To use this count in play, you would use the Hi-Opt I count alone for all insurance and playing strategy decisions, except doubling down on hard 9 and 10 and splitting 10's. You would use your ace adjusted count for all betting decisions, doubling down on hard 9 and 10, and splitting tens. The reason you would use the ace-adjusted count for these few doubling and splitting decisions is that the Hi-Lo Count has a slightly higher playing strategy correlation than the Hi-Opt I Count for these decisions.
Your true count adjustment should be made after your ace adjustment. If you play in single-deck games, you could use Armand Seri's Optimal Running Count strategy tables (see Blackjack Forum III #4), and eliminate the necessity of true counting entirely.
The most cumbersome thing about keeping a double-parameter count like this, is that you could become confused with the slash (/) separating your two counts in your head, especially when one count is positive and the other negative, with one count going up while the other is going down, etc.
One method of eliminating some of this confusion is to remove the +/- sign from your ace-deuce count. Start your count at 0/50. Your Hi-Opt I Count would still go back and forth between positive and negative, but the ace-deuce count would always be a positive number. In single-deck games, it would only run from 46 to 54, and even in multi-deck games, it would rarely go below 40 or above 60 (possible, but highly unlikely). You would adjust your count by adding or subtracting the number above or below 50 to your primary (Hi-Opt 1) count. Example: -2/47 = -5 (ace adjusted running count).
My Side Count Method
One method I taught myself for keeping a double-parameter count some years back was to keep the secondary count with letters, instead of numbers. I started my secondary count at the letter "M," and added or subtracted letters instead of numbers. A running count of -1P would adjust to a running count of +2, since "P" is 3 letters higher than "M." This method totally eliminates the number confusion of maintaining two separate numbers in your head. It does require that you train yourself to count with letters. This is not difficult but takes practice.
First, learn to recite the alphabet backwards as quickly as forwards. Second learn to count letters by twos and threes, backwards and forwards quickly and effortlessly.
For example, you should be able to recite an "even" alphabet and an "odd" alphabet, these being: ACEGIKMOQSUWY; and BDFHJLNPRTVXZ. You must be able to recite these fragmented alphabets with the same ease with which you could count 2, 4, 6, 8, 10, 12, etc., or 1, 3, 5, 7, 9, etc.
Most people can count by 2s and 3s automatically, backwards and forwards, with numbers. Try it with letters, however, and most people are incapable, simply because they've never had any need to practice this. It's easy if you make an effort to learn it. The third step to counting with letters is learning to associate each letter with a specific number:
I = -4
J = -3
K = -2
L = -I
M = 0
N = I
0 = 2
P = 3
Q = 4
This is simply the memorization of a chart, which will allow you to make your ace-adjustment quickly and accurately.
What I like most about side counting aces with a balanced running count, rather than by comparing the number of remaining aces to an estimated number of quarter decks, is that it reduces the degree of error inherent in the approximation method. But is it worth it to make an accurate ace adjustment to a level one count, such as Hi-Opt?
You might consider the fact that a higher level count system such as Hi-Opt II or the Zen Count would perform as well with no ace side count as Hi-Opt I with an ace side count. It seems to me that it would be easier for most players to learn and use Hi-Opt II than to learn and use Hi-Opt I with an accurate side count of aces.
Some counters disagree with this and have told me so. Apparently, multi-level counting, i.e., assigning point values higher than + or -1, is more difficult for some players than multi-parameter counting, i.e., keeping more than one tally of numbers. We all have different capabilities when it comes to math, so you have to consider your own talents when choosing a system.
But what if you are capable of using a multi-level counting system, and maintaining a secondary count. Okay, blackjack fiends, this is how to ace-adjust the Hi-Opt II Count system. Your primary count is Hi-Opt II: 10s = -2; 2s, 3s, 6s and 7s = +1; 4s and 5s = +2. Your secondary count is: Aces = -2; 3s and 6s = + 1.
The difficulty here is that not only are you maintaining two level two running counts, but that the 3s and 6s are counted as + I in both counts. The nice thing about this counting system is that when you make your ace-adjustment, which is done exactly as with the Hi-Opt I Count, by adding your two running counts together, your ace-adjusted Hi-Opt II Count becomes Revere's Level II Point Count, with a betting correlation of .99. This is as accurate a counting system as is possible with only two parameters.
Adding Additional Side Counts
If you want to play more accurately than this, you'll have to add more parameters. The major problem with adding parameters even if you are capable of keeping many separate tallies in your head is in utilizing the information properly for strategy decisions. Optimally, all of your separate counts would be cross-referenced, and you would have to memorize myriad strategy charts to accurately make your decisions.
Probably the most ambitious multi-parameter counting system readily available is the complete Hi-Opt I system with multi-parameter charts developed by Peter Griffin. To use this system you would keep Hi-Opt I as a primary count with 5 separate side-counts of the aces, deuces, 7s, 8s and 9s.
At the 1981 Conference on Gambling and Risk-Taking, Dr. John Gwynn, Jr. and Jeffrey Tsai presented computer simulation results which showed that, considering the difficulty of using this approach in the 4-deck game, the gains from employing this count system are not significantly greater than those of the Hi-Opt I with no side-counts.
More recently, Dr. Gwynn has run some single-deck simulations of this system. In single-deck games, especially when deeply dealt, the complete Hi-Opt I system does significantly outperform the simple Hi-Opt 1. The complete Hi-Opt I performs a few tenths of a percent poorer than "perfect" computer play, a variation of which Gwynn also tested. The results of these simulations will be in a paper Gwynn will present at the Sixth Gambling Conference in Atlantic City in December of this year. (See his abstract for this paper elsewhere in this issue).
Some time back, I developed a counting system, which I humbly dubbed "Snyder's Folly," based on a combination of numbers, subtle body postures, and code words, which allowed me to keep perfect track of the exact number of every denomination of card remaining in a single-deck. I practiced with it for awhile, got pretty quick at counting down a deck, then gave a demonstration to Sam Case. He dealt about half a dozen hands to me, which I played out, then he asked me what my count was.
"It's 5 duckboy 3," I answered.
"What does that mean to you?" he asked.
"It means there are seven l0s remaining, one ace, no twos, one 3, two 4s, no 5s, three 6s, no 7s, no 8s and one 9."
Sam spread out the cards, put them in order, and, as I expected, my count was 100% accurate. "That's incredible," he said. "Do it again."
We ran through a few more decks with him dealing, and at various points he would ask me for my deck analysis, which always proved accurate. Then the inevitable happened. He dealt himself an ace up and asked me if I wanted to take insurance. Five seconds later, with no response from me, he said, "What's wrong? You can't take this long to decide on the insurance bet."
"Well," I explained, "I know you've got eleven tens, three aces, four deuces, one 3, four 4s, two 5s, two 6s, two 7s, one 8, and three 9s remaining. I know this because my count is 9 Farley 3 and I'm sitting with my weight on my right cheek. But I can't make my insurance decision till I tally up all these damn numbers and figure out the ten ratio."
Sam laughed. "Your incredible new counting system sucks, Snyder. If you can't even make an insurance decision, how do you make your other strategy decisions?"
"Well," I admitted. "I can't use this count for strategy decisions. It's too complicated. I have to play basic strategy when I keep this count." Sam laughed harder. "What the hell good is this counting system? Can't you even devise a set of strategy tables for it?"
"I could come up with a great set of strategy table for it using Griffin's book," I explained. "But it would take me too long to make my decisions at the tables. And it would also be too much to memorize."
"Then what good is Snyder's Folly?" Sam asked. "It's a waste of time. You're side counting for no reason. You're not using the count data!"
"It's good for one thing," I confessed. "Impressing other card counters. You know I'm not in this game for the money, Sam. I just enjoy being a big shot. Wait'll I demonstrate this count to Stanford Wong, or Ken Uston, or Peter Griffin . . . Why, they'll go nuts over it!"
"Just pray you don't have to make an insurance decision," Sam said. ♠
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