Blackjack card counting! Words that panic the pits and exasperate the executive suite. Cautious casinos even have count teams. Members, fronting as friendly floorpeople, monitor blackjack tables and thwart suspected counters - usually by shuffling after half or fewer of the cards have been dealt.
Card counting is simple in concept. Practitioners tally low minus high cards dealt. The net is the "running count." Dividing by the number of decks left in the shoe yields the "true count." This serves as an index, indicating how rich the rest of the shoe is in high or low cards. The information is applied two ways.
1) When what remains in the shoe is high-end rich, players following basic strategy have an inherent edge over the house; card counters then enter a game, or raise their bets if they're already playing. When what's yet to be dealt is neutral or low-end rich, the house is favored; counters then cut their wagers or drop out entirely.
2) Basic strategy gives bettors the statistically best decisions for a neutral pool of unseen cards. Highly sophisticated card counters deviate from basic strategy, optimizing their decisions according to whether and how much the remaining cards are biased high or low. For instance, with excess high cards to be drawn, it's better to stand on 16 versus a dealer's 10 than to surrender or hit.
How great is the incentive to count cards? Benefits depend on whether or not player changes decision strategy, the bet "spread," and factors such as shoe size, penetration point at which cards are shuffled, and rules for options like resplitting, doubling, and surrender. The accompanying tables show how advantage changes with count for solid citizens who alter their bets but not their decision strategies in two common situations.
Here's an example of interpreting the tables. In the liberal six-deck game shown, the probability of the count being +2 is roughly 8.4 percent; at this stage, the player can expect to win 50.35 percent - just over half - of all hands. Considering probability of occurrence and expectation of winning, counts of +2 boost the player's overall edge by about 0.06 percent.
The tables show the impact of card counting to be real but small. As counts rise, fractions of hands players expect to win slowly increase over 50 percent. However, chances are low of a count ever rising to the point where the expectation is significant relative to the game's characteristic short-term fluctuations.
Here's another hitch. Consider what normally happens before a count goes to the moon, say +10. It would first be at favorable values such as +2, +5, and +6. Counters would have raised their bets at these levels. But, the count continuing to rise means low cards kept appearing. So bets were big while cards favoring the house were coming. And, if the high cards are concentrated past the shuffle point, the anticipated edge is never realized.
Is counting worth the effort? For players, who gain a small advantage a modest fraction of the time? For casinos, who pay monitors and institute time-consuming and therefore costly safeguards to minimize the threat? Look at the figures and decide for yourself - remembering, of course, the rhyme written by blackjack bard Sumner A Ingmark for such dilemmas.
It's tough to find valid implications,
In averages dwarfed by fluctuations
| Six decks, penetration to 100 cards,
resplit pairs including aces to four hands,
double on any initial two cards,
double after splitting, surrender. |
| count | probability
this count
will occur
(%) | percent of
hands player
will win at
this count
(%) | contribution
to overall
player's
edge
(%) |
| -12 & lower | 0.00651 | 45.00769 | -0.00065 |
| -10 & -11 | 0.03936 | 46.70811 | -0.00259 |
| -8 & -9 | 0.21663 | 47.26244 | -0.01099 |
| -6 & -7 | 0.99421 | 48.18825 | -0.03603 |
| -5 | 1.32619 | 48.50711 | -0.03960 |
| -4 | 2.54299 | 48.80397 | -0.06056 |
| -3 | 4.80756 | 49.13494 | -0.08318 |
| -2 | 8.96917 | 49.38183 | -0.11089 |
| -1 | 17.10224 | 49.63908 | -0.12345 |
| 0 | 30.50491 | 49.89495 | -0.06409 |
| +1 | 15.99062 | 50.13644 | +0.04363 |
| +2 | 8.39897 | 50.35427 | +0.05951 |
| +3 | 4.45245 | 50.58596 | +0.05236 |
| +4 | 2.32937 | 50.81990 | +0.03820 |
| +5 | 1.20291 | 51.07643 | +0.02590 |
| +6 & +7 | 0.88885 | 51.35732 | +0.02413 |
| +8 & +9 | 0.18861 | 51.75938 | +0.00664 |
| +10& over | 0.03847 | 51.70262 | +0.00131 |
| Eight decks, penetration to 160 cards,
no resplitting, no surrender
double on any initial two cards,
double after splitting. |
| count | probability
this count
will occur
(%) | percent of
hands player
will win at
this count
(%) | contribution
to overall
player's
edge
(%) |
| -12 & lower | 0.00009 | 46.17347 | -0.00001 |
| -10 & -11 | 0.00227 | 46.12086 | -0.00018 |
| -8 & -9 | 0.03233 | 47.59601 | -0.00155 |
| -6 & -7 | 0.31712 | 48.31871 | -0.01066 |
| -5 | 0.63943 | 48.49303 | -0.01927 |
| -4 | 1.60902 | 48.86714 | -0.03646 |
| -3 | 3.76320 | 49.11298 | -0.06676 |
| -2 | 8.44174 | 49.32598 | -0.11380 |
| -1 | 18.76623 | 49.58336 | -0.15638 |
| 0 | 34.81398 | 49.78000 | -0.15319 |
| +1 | 17.75710 | 49.99304 | -0.00247 |
| +2 | 7.95774 | 50.20688 | +0.03293 |
| +3 | 3.51559 | 50.42675 | +0.01748 |
| +4 | 1.48645 | 50.58782 | +0.01748 |
| +5 | 0.58337 | 50.78573 | +0.00917 |
| +6 & +7 | 0.28442 | 51.06765 | +0.00607 |
| +8 & +9 | 0.02795 | 51.33248 | +0.0074 |
| +10& over | 0.00197 | 52.03045 | +0.00008 |
