If you’re playing with black ($100) chips, a 1/4% increase in your win rate may be worth the trouble, if you can play an advanced strategy with speed and accuracy. If not, you may be wasting your time, or even lowering your win rate.

Consider a game that would net the Red Seven Count about 1%, and would net a more advanced system, like the Zen Count, about 1 1/4%. Whereas the Red Seven Count would win at a rate of $8 per hour, the advanced system would win only about $10 per hour, even if you played with equal speed and accuracy.

$10 x .0125 x 80 = $10 per hour

So, if it’s $20 per hour you’re shooting for, the advanced techniques alone won’t accomplish your goal. By all means, go for the greater win if you can, but don’t delude yourself if you’re struggling with decisions at the table. Your mental efforts are unlikely to pay off in dollars and cents.

For the average card counter, there is little to gain from an advanced counting strategy. Most players would either slow down so dramatically, or play so inaccurately, that they would gain nothing. Many would actually decrease their win rates.

The last factor in the Profit Formula is hands per hour. Most blackjack authors estimate that a player gets about 75 to 100 hands per hour. Full tables may cut this down to 60 hands per hour, or even fewer if the other players act slowly. Head-on play, when you can find it, will get you about 200 hands per hour. Many players do not believe they can find head-on games, and when they can, they do not believe they can play that fast. Actually, this is a pretty normal rate of play in a head-on game—if you don’t waste time making your decisions.

Playing faster is more challenging, and is also excellent cover. Dealers and pit bosses expect card counters to play slowly and thoughtfully. Also, in hand-held games, dealers will sometimes deal deeper into the deck for fast players, which is another advantage. After all, the faster you play, the more often the dealer must shuffle. If you’re accomplished enough as a counter to carry on some semblance of small talk while playing your hands at a good clip, you will more likely be judged as no threat to the house.

To find head-on games (also often called heads-up, or head-to-head), especially at low stakes, you must play at off hours. Mornings and early afternoons on weekdays are often excellent times to go hunting for dealers who are standing behind empty tables twiddling their thumbs. The best times are often different for different casinos; scout and you’ll find out. There are, to be sure, other arguments—pro and con—with regards to playing under various crowd conditions for purposes of camouflage, team/partner attacks, and the like. I will attempt to cover all of these considerations later. For now, it’s important that you understand the basic math of how a card counter estimates his win rate in dollars and cents.

In a game where 80 hands per hour nets you $10 per hour, 200 hands per hour, assuming the same average bet size, and the same % advantage from your card counting efforts, will raise your expectation to:

$10 x .01 x 200 = $20 per hour

One question that many new counters ask is, “How much money can I make?” The answer, as you can see, is not so cut and dried. Every one of the factors in the Profit Formula is a variable, and every one has a big effect on the answer.

Stem-sellers who claim that using their blackjack system will net you $XXX per hour, per day, per week, or per year, are generally hawking nonsense. Unless they fill in all the variables of the Profit Formula—which will differ for every player, and change according to the table conditions you face—any such claim is pure speculation. In the meantime, to best apply the Red Seven Count, or any other card counting system, you’ll need to learn much more about table conditions, betting strategies, camouflage, toking, and every other aspect of casino blackjack that is important to a professional player.

But how do you figure out your average bet size? You don’t just pick a number out of thin air and decide to bet that much per hand. Any pro will tell you that the most important factor in bet-sizing is the size of your playing bankroll, and even if you don’t see yourself as a pro player, you must take into account the same factors that professionals do when sizing your bets.

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Average Bet x Advantage x Hands Per Hour = Hourly Profit

The formula is simple, yet it provides a good approximation of what a card counter might expect to win per hour in the long run. Say that you are making average bets of $10 with a 1% advantage over the house from card counting. You estimate you're playing about 80 hands per hour. To calculate your expected hourly win:

$10x.01 x80 = $8 per hour

(Note that your 1% advantage is expressed decimally as .01, for use in the formula. A 2% advantage would be .02, etc. How about 2 1/2%? That would be .025, while 1 3/4% would be .0175. You might find it helpful to follow this math with a pocket calculator, and you must familiarize yourself with expressing percentages as decimals if you are at all serious about making money from gambling, as most books on gambling use this notation.)

Let's also say that you want to increase your expectation above $8 per hour. That's simple enough to do, keeping the Profit Formula in mind. Simply raise the value of one or more of the three vital factors in the formula.

Start with the first: average bet. Obviously, if you made an average bet of $25, assuming the same 1% advantage over the house, and the same 80 hands per hour, your expectation would immediately rise to $20 per hour:

$25 x .01 x 80 = $20 per hour

It's a simple solution, but it's problematic if you have a limited bankroll, as increasing your bet size leads to greater fluctuation. Although your long-run win rate may rise to $20 per hour, you may never see the long run. Do you have a big enough bankroll to increase your average bet size to this level? Don't guess! Instead, keep reading…
The next variable in the Profit Formula is advantage. It's simple enough to see how to raise your expectation to $20 per hour by altering this factor; just raise your advantage to 2 1/2%. Thus:

$10 x .025 x 80 = $20 per hour
This is the tactic most card counters employ—they start using an "advanced," higher-level, system, and keep side counts of aces, and sometimes fives or sevens, and memorize more extensive strategy tables.

Unfortunately, this tactic does not pay as well as most counters would like. Even the most advanced counting system will rarely raise your advantage by more than 1/4% to 1/2% over your advantage with a simpler system, and that's only if you can deploy the more complicated system without errors.

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• Blackjack – Kelly Betting (0)

And what if the table minimum bet allowed is $5? That means I have to have a 5% advantage over the house, based on my count, before I can even place a single table-minimum $5 bet! This may sound extreme, but the fact is that betting full out according to the Kelly Criterion causes huge fluctuations. There's wisdom in raising and lowering bets based on current bankroll, but betting full-Kelly is too risky in a game like blackjack.

How do the pros handle bet-sizing? Most employ some form of fractional Kelly betting. After determining the size of their bank—that is the total amount they have available to risk at playing blackjack they devise a chart of bet sizes based on one-third, one-quarter, or even smaller fractions of the ideal Kelly bets. By doing this, they hope to reduce fluctuations to a tolerable level, compensate for the increased fluctuations caused by placing bets when the house has the edge, bets placed for purposes of camouflage, and occasional errors in the application of their playing and betting strategies. (Many other methods used by professional players to limit fluctuations will be discussed in Chapter Fourteen.)

However, for a solo card counter, starting out on a limited bankroll, it's often all but impossible to stick to fractional Kelly betting. If you've got a total playing bankroll of $2,000, and you want to bet at the one-quarter Kelly level, with a 1% advantage you would place a bet of only $5, and at a 2% advantage your bet would be only $10.

With the rare 3% advantages that occur in shoe games, you could place $15 bets, and these would be your high bets! If you could actually find a game that allowed minimum bets of $1, then you could use a betting spread of 1 to 15, and beat these games handily. Unfortunately, $1 minimum tables are pretty much a thing of the past. If you can find a $5 minimum table, you'd have to bet from $5 to $75 to employ this 1-15 unit betting spread, but you'd need a bankroll of $10,000 to afford it if you were determined to minimize your risk by betting at the one-quarter Kelly level.

All of this may sound very discouraging if your hopes and dreams have been centered on making a living by playing blackjack, and you're currently looking at a total playing bank of only a few thousand dollars. But stick with me…

Most pros that I know started small, and if you are cut out for it, you can do it too. By the same token, card counting still has a lot to offer players who are not cut out to be pros. If you always play with an edge over the house, at a level that you can afford, in the long run you will come out ahead—which puts you way ahead of the rest of the gambling public who are all a bunch of sure losers. If you follow the advice provided in this chapter, you should be able to keep yourself from getting in over your head, and you should be able to beat the casinos over time so that you can pay for your vacations at the table, maybe even bank a few thousand bucks per year, and have a lot of fun doing it.

For those of you crazy enough to still entertain notions of playing this game professionally, or with any serious amount of money, there is one simple mathematical formula you should learn, which I call the Profit Formula. You may use this formula to get a handle on what your expectation from the blackjack tables might be, based on your average bet size.

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It's very important that you understand the logic of what statisticians call the Kelly Criterion, another mathematical concept discussed to death in many other blackjack texts. With Kelly betting, you cannot lose your entire bankroll. Never. Or, at least, that's how it works in theory. The basic premise is that you always bet a percentage of your bankroll based on your percentage advantage over the house.

Though somewhat oversimplified, a good example would be that if I have a 2% advantage on a blackjack hand based on my count, then I bet 2% of my bankroll. If I had a $10,000 bankroll, then I would make a $200 bet. The reason I would never go broke is because I can never place a final bet in which I put more than a small percentage of my bankroll at risk. If my bankroll gets smaller due to negative fluctuations, my bets will likewise get smaller in proportion. If I lose $5,000 of my original $10,000, then my Kelly bet with a 2% advantage becomes $100 instead of $200.

The theory behind Kelly betting is that not only does it prevent me from ever losing my whole bank, but since I increase my bets as my bankroll grows, I also maximize its growth by betting more when I can afford more risk. For instance, if my bankroll grows to $15,000,1 can bet $300 with a 2% advantage over the house.

This description of Kelly betting is oversimplified in order to clearly show its logic. But I do want you to understand the pitfalls of Kelly betting in a game like casino blackjack. First, consider what your ideal Kelly bet is on hands where the house has the edge…it's zero. You shouldn't bet at all on hands where the house has the edge over you or you violate the Kelly betting system—even in a game like the single-deck version in our example that would simply be impossible. In virtually all casino blackjack games, the house has the edge more than 50% of the time over card counters.

Second, the Kelly betting system is based on a theoretical fact that you can never go broke, since you always bet only a percentage of your current bankroll. But what if my $10,000 bankroll fluctuates downward to $100?

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Years ago, a mathematician determined that it was possible to figure out the likelihood of a gambler either doubling his bankroll or going broke trying to do so. The formula is just a simple algebraic equation that takes into account the size of the gambler's bankroll in units, the size of his bets, and the advantage or disadvantage in the specific game being played. This concept has traditionally been called the Gambler's Ruin Formula.

Professional card counters more commonly call a variation of this formula specifically devised for blackjack games the "risk of ruin" (or RoR); it was discussed by Ed Thorp in Beat the Dealer, Allan Wilson wrote about it in his 1965 Casino Gambler's Guide, and it was further described by Ken Uston in Million Dollar Blackjack. Since then, the concept of risk has been analyzed to the nth degree by many of the major authors.

Personally, I'm not crazy about the idea of individual players determining their bet sizes solely based on Risk of Ruin. Uston discussed how some of the teams he was involved in based their bets on a 5% element of ruin. This sounds pretty good to most players; if you double your bank 95% of the time (19 out of 20 banks double) that's a huge win-expectation in the long run.

But Uston was involved in big teams of players, with multiple investors, and if the team went broke on a play, the investors could simply put together another bank and do it again. That's not an option easily available to a solo player. If you have a bank of $10,000, and you lose the whole bank on your first play, can you simply put together another $10,000 and do it again? You might argue that it's unlikely that you'll lose your bank on your first attempt to double it, but consider it from my perspective as an author whose advice is being followed by thousands of individual players: For every ten thousand players who go out and plays to a 5% RoR, 500 of them will go broke! How many of these players can quickly put together another bank? How many have lost their life savings? How many will write nasty letters to me blaming me for their new poverty?

Basing your bet sizes on a 5% (or any!) risk of ruin should be left to those who can afford to put together another bank easily if the first one fails. This is for big teams supported by investors, and solo players who have the capability of forming another playing bank through easily accessible outside sources of funding. A better method for bet-sizing for most players is…

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High rollers rate casinos according to the action tolerated. Sawdust joints. Carpet joints. Most amateurs, on the other hand, are rule freaks. They see everything in terms of being able to split up to four hands, re-split aces, double after splits, double any two and surrender. (Sounds okay to me…) But the point is that after you analyze the table conditions, you've got to analyze the casino itself.

The rarest type of casino is one where you hardly feel the current at all. The games are just so delectable you forget you're even in the river. You look around—good rules, deep penetration. There's a lot of money on the felt, but nobody in the pit seems to be guzzling Maalox. It's not a river; it's fish heaven. All the worms you can eat, and no hooks! Or, at least, you don't see them—provided you don't try to take the entire can of worms back home with you on any one visit, you can nibble away at the feast indefinitely. Places like this pop up now and then, but they don't often last long.

More commonly, when you think you're in fish heaven, there are unseen hooks, nets, and harpoons aimed right at you. You walk in, you see these unbelievable table conditions, you notice that the dealer has dealt out almost the entire two decks, and he's still not starting the shuffle. You decide to make small talk with the dealer, test his friendliness. "So, how long have you been offering this two-deck game with double after splits and surrender? Whoops! You ran out of cards!"

Unfortunately, if you sit down at the table, you'll often get that ominous tap on the shoulder just after you make that first black chip bet on a high count, or maybe a few minutes later, after they've got a good close-up photo of your mug. By the time you hit the street, your picture is already being faxed to casinos you've never heard of.

Of course, it's possible that you misjudged this casino in the first place. It only looked like fish heaven. In actuality, it was, first and foremost, a fish bowl. Some salmon may be a bit large for your average fish bowl, and big fish won't last in a small bowl.

Many casinos in Las Vegas, even big casinos that can take table limit action, offer one or two hand-held games that really are nothing more than counter bait. These juicy tables are always under extra surveillance from the sky, and the casinos use these games simply to identify and weed out counters. So, if you see that a casino has 25 six-deck shoe games with mediocre penetration, and one hand-held two-decker with great rules and good penetration, you're probably best off to leave that two-decker alone.

To further confuse matters, even if the conditions look great on every table, you may have to leave the casino entirely if your bet level attracts too much attention. Look around—how much are the other players in this joint betting? Many casino table-limit signs are mislabeled; the signs may say $1,000 or even $5000, but that's just what the signs say. Nobody in the pit takes those things seriously. Ignore the signs. If all you see are tourists betting a red chip or two, and if a couple of black chip bets lead to a suit convention in the pit, then those limit signs are just for show.

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In Ed Thorp's Beat the Dealer we were introduced to a character who was known in the Puerto Rican casinos as the "Salmon." The nickname was pinned on him by one of the casino pit bosses, as a reference to his "swimming upstream." He was winning steadily, which was going against the current in this boss's view. The pit boss also believed that this current, the house edge, was so strong that it would inevitably pull even the Salmon downstream.

This analogy to beating the house has always appealed to me. The current is so strong in most casinos that if you really spend much time at any of the games, you inevitably see player after player just floating down that mighty river…

From the perspective of a card counter, you are a salmon. You can and do swim upstream, watching all the other little fishies going the opposite direction. It's fun to fight a mighty river and win, but you have to pick a current you personally can overcome—not one that just looks good on paper, or may be right for some other salmon, maybe one with bigger fins than yours. Most importantly, since salmon are always in season in the casinos, you've got to watch out for bait.

I've seen dozens of players' casino rating systems over the years. Some players use standard "report card" ratings, with grades running from "A" to "F." I've seen "star" systems, kind of like movie ratings. Four stars: Don't miss it! One star: Don't even rent the video.
Many card counters today are penetration fanatics; they rate games according to the percentage of the cards dealt. They can drive down the Strip, pointing at the casinos as they go: "70%, 60%, 67%, 55% yuck, 79.8%—Hmm.. .valet parking's full…" It's not a bad way to rate casinos, but there's more to it than that.

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