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Best of Alan Krigman

Gaming Guru

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Should You Sacrifice Long-Term Edge for Short-Term Prospects?

15 August 2000

Basic strategy in blackjack indicates the decisions for various combinations of player hands and dealer upcards which minimize house edge and maximize expected bettor returns. In the long run, this should be the optimum way to play. But sagacious gamblers sometimes ask whether alternate decisions are better suited for short runs such as sessions, weekends, or adult human life spans.

On certain hands, expectations differ little between the best and next best decisions. Then, the theoretical short-term penalty for violating basic strategy is correspondingly small. As examples, "the book" says hit 16 versus 10 and A-7 versus ace, but standing in these cases only gives up a projected $0.05 on a $10 bet. Under conditions like these, however, when the same money is involved either way the hand is played, there's no motivation except hunch or superstition to flout the laws of probability.

When the choice involves doubling or splitting rather than standing or hitting, the short-term wicket gets stickier. This, because more or less money goes up for grabs. On these types of close calls, aggressive bettors may knowingly trade a small amount of edge for greater possible return, perhaps doubling when Basic Strategy is to hit. Or, conservative players may swap a bit of edge for smaller potential loss, maybe hitting when Basic Strategy decrees a split.

An example is A-7 versus 2-up. Basic Strategy gives the best play as standing, next best as doubling. But both are favorable. And expectations are nearly equal ?? projected average wins per $100 bet being only $0.30 off, at $12.10 standing and $11.80 doubling. Chances of rounds having various results are as follows. Stand: win 49.3 percent, lose 37.2 percent, push 13.5 percent. Double: win 48.9 percent, lose 43.0 percent, push 8.1 percent.

Despite similar expectations, the extra money associated with doubling causes short-term characteristics to diverge. To illustrate how, I simulated 2 million solid citizens playing this hand 10 times each at $1 a shot. Half hit, half doubled. The accompanying table shows how many finished where.

Adding up the columns verifies the long-term averages. The standers, together, earned $29,990 more than the doublers. Since the total amount bet by each group was $10 million, this rounds off to the predicted $0.30 per $100 wagered.

Individually, 596,791 standers won an average of $3.13 each, 126,224 broke even, and 276,985 lost an average of $2.38 each. Obviously, none went over or under $10. Conversely, 503,982 doublers won an average of $6.03 each, 145,608 broke even, and 350,411 lost an average of $5.31 each. More, 23,505 doublers ended worse than $10 behind, including 219 who dropped $20; 54,785 closed over $10 ahead, including 777 who won $20.

Should you violate Basic Strategy because of the extra money on hands like these? As usual in gambling, the answer involves a trade-off. Doubling rather than hitting A-7 vs 2 wins less often, but the take is twice as much. It loses more often, but the hit is twice as great. For the session in the example, chance of being between $10 up or down would still exceed 92 percent by doubling, and those who pass these limits have odds of nearly 7?to-3 they'll be over the top and not in the sewer.

If you know that differences are really small, you can weigh the costs and benefits of close calls like these against your personal preferences. It's usually a matter of a better shot at a small win versus a lower probability of a bigger score. But, consider this caveat of Sumner A Ingmark, the Chaucer of choice:

Go challenge fortune if you please,
By throwing caution to the breeze.
But only if you are insane,
Go try it in a hurricane.

Number of a million bettors finishing at various levels
after 10 instances of A-7 vs 2-up, at $1 per hand,
by standing and by doubling

loss or
number of bettors
profit ($)
stand
double
-20
--
219
-19
--
--
-18
--
402
-17
--
--
-16
--
2,782
-15
--
--
-14
--
4,375
-13
--
--
-12
--
15,728
-11
--
--
-10
52
20,342
-9
185
--
-8
966
51,009
-7
2,492
--
-6
7,327
55,038
-5
14,476
--
-4
30,450
105,581
-3
47,357
--
-2
77,008
94,936
-1
96,674
--
0
126,224
145,608
1
128,108
--
2
135,361
107,842
3
110,144
--
4
94,040
136,431
5
58,805
--
6
39,978
81,013
7
17,903
--
8
9,300
85,349
9
2,309
--
10
842
38,563
11
--
--
12
--
34,175
13
--
--
14
--
10,719
15
--
--
16
--
7,815
17
--
--
18
--
1,298
19
--
--
20
--
777

 

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.