Systems That Don't Work
Over the last few months I’ve talked about various aspects of card counting, and in particular I’ve introduced some of the elements of the powerful “complete point count” system of Harvey Dubner, Julian Braun, and Edward Thorp that I play.
Card counting works. Outside of Space-Time Warping (to be discussed in a future column … a VERY future column), no other systems work. Here I’m going to compare the complete point count system to two of the most popular “systems” that people have used through the ages.
The “Do Not Bust” system is known to just about every blackjack player and the “Small Martingale” system is known to just about every blackjack and roulette player. I’m going to compare these two systems to the complete point count system. You’ll be amazed, I’m sure, and will acquire more faith in card counting systems and decide to abandon once and for all the “Do Not Bust” and “Small Martingale” strategies. I have faith and I’ve been able to learn the complete point count because I nourish my body and brain with a healthy lifestyle. After all, my body is my temple. Unfortunately, few come to worship. You may come to worship after you read this month’s column.
Do Not Bust
The “Do Not Bust” strategy is self-explanatory. If you have a total of 12 or more, stand.
Here’s one example of how the strategy decisions made under the “Do Not Bust” system and complete point count differ. Let’s say you are playing a 52-card deck, and 24 cards remain with a point count of -6. Say you are dealt a Jack and a 2, for a hard 12, and the dealer has a 5 showing. After the deal, 20 cards remain, and the updated point count is -5.
That means that of the 20 remaining cards, five more 2s through 6s are present than ten-value cards and Aces, and the rest are the neutral 7s, 8s, and 9s. For the sake of being concrete, say we have two 3s, two 4s, three 5s, and two 6s, four 10-value cards, and seven 7s, 8s, and 9s. The high-low index would be (–5/20 * 100) = -25. The complete point count decision would be to take a hit. The “Do Not Bust” strategy, in contrast, would say “stand.”
You, however, have an 80% chance of improving your hand if you ignore the “Do Not Bust” strategy. Here’s the figuring. You only have a 4 in 20, or 20%, chance of busting on the first card drawn, if you were given one of the 10-value cards. You have a 12 in 20, or 60% chance of being dealt any of the 5s through 9s, giving you a pat hand of 17 through 21. Finally, you have a 4 in 20, or 20%, chance of being dealt a 3 or 4. With the resulting 15 or 16 against the dealer’s 5, you would stand according to the complete point count system. As I said, in this example you have an 80% chance of improving your hand if you ignore the “Do Not Bust” strategy.
In general, whenever you have a negative high-low index, following the “Do Not Bust” strategy is a bad decision. We simply have too many 2s through 6s left in the deck and you are giving up the chance to most likely improve your hand.
The Small Martingale
The “Small Martingale” system is the strategy in which you double your bet every time you lose a hand, and reduce your bet to your minimum every time you win a hand.
One reason it can’t work in the long run is that the tables have a limit. Say you bet $5 and lose. You double your bet to $10 and lose. You double your bet to $20, $40, $80, $160, and $320 in succession and lose every time. If the table limit is $500, you have lost a total of $635 and you can’t increase your bet. Seven losses in a row essentially wipes you out, and it does happen. Of course, if your initial bet is $10, you only need 6 losses in a row to amass losses greater than that table limit, and if your initial bet is $25 then you’re saying bye-bye if you lose only 5 times in a row.
Worse than that, it’s a bad strategy for determining your bet size. We’ve learned enough about card counting to realize that sometimes the deck is in your favour and sometimes it’s against you. Generally speaking, when the deck is in your favour you will win more frequently, and the counting systems tell you to increase your bet. When the deck is against you, you will lose more frequently, and the counting systems tell you to decrease your bet to its minimum.
Now, if you are on a winning streak, it would seem to anyone who I would consider allowing into my temple that the deck is in your favour. You should, according to card counting systems, increase your bet. The Small Martingale system says, to the contrary, bet your minimum!
On the other hand, if you have lost 2, 3, 4 or more hands in a row, it would seem to anyone who I would consider allowing into my temple that the deck may be against you. You should, according to card counting systems, decrease your bet. The Small Martingale system says, to the contrary, increase your bet! Dumb, dumber, dumbest. Yes, the “Small Martingale” system tells you to increase your bet when the deck is against you!
Okay, now that you are getting to understand why counting cards is better than these two famous prehistoric systems, I’m going to compare them to the complete point count system by playing some hands.
Get the Point
First, let’s play a bunch of hands comparing the complete point count strategy to the Small Martingale system. You’ll see the poor betting decisions that result from using the Small Martingale system. I dealt a deck to myself. (I did not fix the order of the cards, as they do in some casinos. Trust me. You can trust me, can’t you?)
After burying one card, I dealt 8 hands out of a 52-card deck. In the table (guaranteed to be headache proof), the first two columns show the bet based on the complete point count and Small Martingale systems. The “1” can stand for your minimum bet, be it $1 or $10 or whatever. Then I show the hand I was dealt and the dealer’s up-card.
My bet depends on which system I’m using. In the complete point system, the high-low index calculated at the end of a hand determines the bet for the hand that follows (the bet is 1/2 of the high-low index, or 1 if the index is zero or negative). Under the Small Martingale, of course, I double my bet after a losing hand and reduce it to my minimum bet after a winning hand.
At the end of 8 hands, with only 9 cards left, I “shuffled” the deck and stopped the experiment. “SM” and “CPC” in the table refer to “Small Martingale” and “complete point count.”
Based on the high-low index and complete point count decision tables, I made the strategy decisions noted and played out the rest of the hand. The results are shown for both systems.
As you can see, when the deck got hot and I hit a blackjack I had increased my bet. Also, when the deck got cold and I lost 4 hands in a row, the Small Martingale strategy led to hurt and pain because we were increasing our bet. Under the complete point count, you could tell the deck was cold and so the minimum bet was placed.
In the two “Results” columns, we see that as the deck got colder, according to the high-low Index column, my losses under the complete point count system decreased while my losses under the Small Martingale increased. Indeed, as I talked about earlier, if your minimum bet was $25 and the table maximum was $500 you were only 1 losing hand away from not being able to double your Small Martingale bet again!
Of course, every experiment won’t work out this way. It showed my point, that increasing the bet when playing against a poor deck, and keeping the bet at its minimum when playing against a favourable deck, will not work in the long run to your advantage. It’s also interesting that I won two of the three hands with the largest bet, based on the complete point count system. Of course, this doesn’t always happen either.
It’s not as easy to compare a card counting system against the “Do Not Bust” strategy because you can’t use the same deck of cards to show the comparison. It’s best done referring to the strategy table for standing and drawing with a hard hand. That’s where we’ll continue next time.
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