Mathematical Foundations of Card Counting Part 2
Driving Average Bet
We have already discussed the role of betting in specific hands. Basically a card counter would want to bet as much as they can when the count is good, and nothing at all when the count is negative. Average bet will be a function of how close you can get to this ideal situation, as well as what your maximum and minimum bets are set at. Average bet itself is a simple concept, but understanding it could make a huge difference as your black jack career progresses.
Looking back to the formula for expected profit, it seems like a counter would simply want their average bet to be as high as possible. Mathematically this is true, but there are subtleties when you include the prospect of risk (see lesson ten). Once you understand standard deviation and risk you will be in a much better position to contemplate what effects increasing your average bet will have on your bankroll. Until then lets simply try and approximate what your average bet will be so you can find your expected profit.
To find what your average bet will actually be takes an extremely solid understanding of many different aspects of blackjack and a lot of math. Fortunately you can get a fairly close approximation knowing only your spread (lesson five) and your minimum bet (a betting "unit"). You will probably also need a calculator.
To find your average bet simply take your spread to the power of 0.4. The outcome will be in betting units, so multiply the result by how many dollars each betting unit is worth.
For example. If you are using a good spread of 1 to 10 with one unit equaling $10 then the equation would look like this:
(10 ^ 0.4 ) x $10 = avB
In this common situation, the average bet would be approximately $25.
As you can tell from the formula the easiest way to increase your average bet would be to increase your spread. This also lowers risk and has a very positive effect on your play. However, as mentioned in the lesson on spread, the larger your spread is the more obvious your counting may be.
If you paid close attention to the formula you may have noticed another way to increase your average bet, increase the amount of money in a unit. This will be covered in the section on exponential growth but will usually occur naturally as your bankroll increases.
Other than increasing your spread and unit amount, there are ways outside of this formula to increase your average bet (remember the formula is just an approximation). All of these issues are covered in Lesson Seven. Specifically the methods for effectively increasing your average bet include - better penetration (longer good counts means more high bets), better casino rules (which allow for more doubles and splits), and wonging (which reduces the number of hands played at the minimum bet).
Use the formula above to figure out about what your average bet should be. Write down this number as well so you can recall it quickly when we get to the end of this lesson on expected profit. Now you should know both your hands per hour and your average bet. This leads us to the final section, the section on the statistics of average advantage.
Average Advantage in Card Counting
From a mathematical point of view, blackjack is all about advantage, it is indeed the only reason you will make money playing blackjack. When we talk about average advantage I am not trying to re-explain everything that advantage is, nor are we talking about all the ways of increasing your advantage, we are just trying to establish an understanding of how your average advantage will affect your profit.
Average advantage is the only one of the three variable in the profit equation that can be negative. You will never play a negative amount of hands, and the casino probably wont let you bet a negative amount of money. This means advantage is the single most important factor, because it is the only one which can result in a negative expected profit. The good news is that your average advantage is totally under your control. The bad news is... that your average advantage is totally under your control. If you don't practice, or get in a situation where you are making decisions instead of knowing which move is the correct move, you can easily loose your advantage.
Lesson five was essentially about ways to increase your advantage, so we won't re-explain these methods. Instead lets try and get a good idea of what your advantage actually is so that you can form a realistic picture of your expected profit. First, do you know perfect basic strategy? If so then you would have about a 0.5% disadvantage against the casino. Do you have the counting system down to a science? Then you are probably sitting at about a 1.2% advantage. Finally do you know the 20 basic strategy variations? If so, you have about a 1.8% average advantage. You can go ahead and use these numbers if you want, but I would suggest taking a look at the next couple of graphs to get a more accurate number.
Many of the things that affect your average bet will also affect your advantage. After perfect card counting, penetration is the most important, then there is wonging, the casino's rules, and finally spread. Besides penetration and rules, these factors are mostly under your control. You will probably want to wong more and increase your spread if you feel like you are doing an exceptional job staying under the radar, while you will want to lower your spread if you feel like you are getting heat ( in many cases, wonging can actually be less suspicious than min betting. Re-read the lesson on wonging for details).
Keep reading these lessons for a deeper understanding of card counting and it's mathematical foundations.
To learn more about card counting and the mathematical formulas involved, check out Modern Card Counting here: http://www.amazon.com/Modern-Card-Counting-ebook/dp/B0058TU2O2
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