Compare bbjd with other counting methods
We have seen that in order to win you must remember which cards have gone. This gives you the number of cards which are still in the shoe. This isn't a simple task, specially if you have to do that in your head. Therefore some people have invented simplifications. If you look at the shoe calculator and reduce certain card values, you will see that the total Expectation varies, so as some other expectations. Therefore you must alter your decision making if the distribution in the shoe changes. The table shown here tells you how much the total Expectation ΔtE varies, if one card is taken out of a shoe with two decks of cards. The value N is the number of cards in the shoe.| Card value | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | X | A |
|---|---|---|---|---|---|---|---|---|---|---|
| A shoe with two complete decks. For this shoe the total Expectation is -0.79 | ||||||||||
| N | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 32 | 8 |
| ΔtE | +0.18 | +0.22 | +0.28 | +0.38 | +0.24 | +0.17 | 0.0 | -0.07 | -0.21 | -0.28 |
| A shoe with two decks, where many low valued cards are gone. For this shoe the total Expectation is +7.10 |
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| N | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 32 | 8 |
| ΔtE | +0.29 | +0.37 | +0.42 | +0.43 | +0.19 | +0.24 | +0.15 | +0.07 | -0.17 | -0.31 |
| A shoe with two decks, where many high valued cards are gone. For this shoe the total Expectation is -7.20 |
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| N | 8 | 7 | 7 | 6 | 6 | 5 | 5 | 4 | 12 | 1 |
| ΔtE | -0.01 | -0.03 | -0.04 | -0.06 | +0.02 | -0.03 | +0.02 | +0.16 | +0.23 | -0.96 |
Interpreting this table
Calculations of the total Expectation have been done for three representative distributions of cards in the shoe. The first one is a shoe with all cards, in the second the low values cards are gone, in the third one the high valued cards are gone. As you can see, removing a card from the show does not change the total Expectation linearly.Generally speaking low valued cards (ie. 2, 3, 4, 5 and 6) help the player whereas high valued cards (ie. X and A) help the dealer. This is quite logical because the Five helps the dealer bringing a stiff to a final score of 17 to 21. A stiff is a score of 12 to 16 and here the dealer is risking to bust his hand. This statical table also shows, that the more high valued cards are in the shoe, the better it is for the player, whereas the more low valued cards are in the shoe, the better it is for the dealer. Depending on which cards are gone in the previous rounds, the total Expectation varies between about -8 and +8.
Many more and less complicated counting methods have been invented. Lets have a look at one of the simplest ones: The "High-Low" counting method assigns +1 to the low valued cards (2 to 6), -1 to the high valued cards (X and A) and 0 to the rest (7, 8 and 9). A player can easily remember these counter-values and remember the sum. Now he has to divide this sum through a certain factor depending on the number of decks during reshuffle. With this method the player can compute the total Expectation upon which he shall place his stake.
However the "High-Low" counting method is a very simplistic approach. It assumes that the total Expectation is a number which can be computed by a linear equation. But computing the total Expectation is a far more complicated task and bbjd has been written to find out the total Expectation through algorithmic analysis.
For example, take out all cards with a value of 10. The linear equation says that this should give a total Expectation of -6.72 but bbjd tells you that the total Expectation is +0.05. Here you can see, using a linear equation to compute the total Expectation does not give you exact results.
Nevertheless, counting methods may be used and have been used with success to beat the Blackjack dealer. But always keep in mind that they don't give exact numbers, so be aware that in some cases you will get misleading results.
Please also note that the playing strategy varies from the basic strategy if cards of a certain value are gone. The effects here are not as dramatic as with the total Expectation, however it is important to adopt the basic strategy accordingly.