Assigning the Values in Counting Cards

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by , 10-15-2015 at 04:04 PM (7662 Views)
To take the value of a card-counting system further, we need to know exactly how much each card is worth. To determine this, we simulate a benchmark single-deck game using the basic strategy. As mentioned in Chapter 2, we come up with an expectation of -0.02%.
We then simulate the same basic strategy in a single-deck game that has one card removed, for example a 2, and note the resulting expectation of +0.38%. Comparing the expectation of the two games gives us a measure of how valuable the 2 is. For this particular example, we find that removing the 2 is "worth" 0.40% to us.
We then repeat the process for each other card rank. In so doing, we can construct a table of the relative values of each card. All values are changes in the expectation for the benchmark single-deck blackjack game, assuming we are playing by the fixed generic basic strategy and these values were derived from simulations of the benchmark game assuming a fixed generic basic strategy.
The table below gives the change in player's expectation that arises from removing a card of a certain denomination.
For example, if we remove just one 5 from a single deck, the change in player's expectation is +0.67%. For our benchmark single-deck game (with an initial expectation of-0.02%), the "new" expectation, after removing the 5, is now +0.65%. On the other hand, removing a single ace changes the expectation by -0.59%.
What happens if, for example, both an Ace and a 5 are removed? To a very good approximation, we simply add the resulting effects. So the total change in expectation is -0.59% (for the Ace) + 0.67% (for the 5) for a total change of +0.08%. Thus removing these two cards leaves us almost where we started; they've nearly cancelled each other out.
Relative value of cards in single-deck blackjack (assuming a fixed generic basic strategy):
Removed Card Change in Player's Expectation
2 +0.40%
3 +0.43%
4 +0.52%
5 +0.67%
6 +0.45%
7 +0.30%
8 +0.01%
9 -0.15%
Ten -0.51%
Ace -0.59%
A deficit of high-valued cards, mainly aces and tens is bad for the player. As players, we want the pack to contain an excess of these high-valued cards. We will label tens and aces as good cards.
In this same vein, removing low cards (namely 2s through 7s) from the deck increases our expectation. In removing these cards, we are in effect creating an excess of high-valued cards, which gives us an advantage. These are the cards we'd like to see out of the deck. We will label 2s through 7s as bad cards.
We can now summarize the crux of card counting. We keep track of cards played in order to ascertain which cards remain unplayed. As the deck composition changes, the excess or deficit of good and bad cards shifts the advantage back and forth between the player and the house.
The key, then, is to identify when we have the advantage and when we don't. We make big bets when we do and small bets when we don't. In so doing, the gains from the big bets will more than make up for the losses from the small bets.
We will come out ahead in the long run.
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