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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