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Best of Alan Krigman

Gaming Guru

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What's the Advantage of Card Counting in Blackjack?

17 December 1996

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



 

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.