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Best of Alan Krigman

Gaming Guru

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Splitting Eights against a 10: The Whole Story

8 September 1997

Blackjack buffs who otherwise "play by the book" often have trouble with pairs of eights against a dealer's a 10-up. Just this past weekend, I heard all of the following:
o You're supposed to assume the unknown card is a 10. If I stand, I lose to the dealer's 20. If I hit, I bust and lose, too. But if I split and end up with two 18s, I lose twice. I'll hit. Maybe I'll get lucky. At least I'll cut my losses.
o I heard you should split 'em except when you can surrender.
o The "book" says split. But who says the "book" is right?

Pick what's best for yourself. But not based on blather like the above. Rather, guided by rules derived from the statistics of the game, as ascertained by meticulous computer analysis.

Statistically optimum play, manifest in basic strategy, is a big part of the story. Forget the foolishness about all unseen cards being 10s. Basic strategy is a way to maximize profit. It's determined by examining all possible card combinations or automatically "playing" each hand millions of times, calculating "expectations" - projected net wins minus losses per round for $1 bets, then finding which decisions yield the highest values.

Results of such an analysis for eight-eight versus 10 are shown in the first row of the accompanying table. These expectations are for multi-deck games in which pairs can be split only once, for cases when the dealer doesn't have blackjack.

All values are negative; the hand is weak no matter what you do. But the penalty is least for splitting with doubling, so this is what the "book" decrees. As an example of interpreting expectation, hitting anticipates a setback of 53.98 cents per dollar initial bet, while splitting with doubling costs an average of 48.95 cents. That's a nickel difference per dollar bet, folks.

But there's more to the statistical story than expectation alone. The win/loss section of the table is another chapter. It shows computer-derived probabilities you'll win or lose multiples of the initial bet by following the various playing tactics.

These probabilities indicate that splitting slightly raises your chance of winning a round while greatly lowering the likelihood you'll lose - the divergence arising from an increase in pushes. The table further shows you're almost as likely to collect multiple units by splitting as to win a single bet by hitting.


The win/loss probabilities also reveal the downside of splitting - the risk of multi-bet losses. Hitting yields 74.04 percent chance of losing one unit. Splitting with doubling cuts total probability of a loss back to 53.42 percent. However, this includes 37.75 percent chance of sacrificing two units, 4.37 percent chance of three bets biting the dust, and a small but non-negligible 0.14 percent chance of a four-wager wipeout.

To solid citizens especially sensitive to multi-unit losses, this disadvantage may outweigh possible benefits. Such a group might include bettors with small bankrolls, players who've progressed their wagers and have exceptionally big bets on the layout when the eight-eight versus 10 appears, and neophytes too nervous to push out the extra chips needed to split and possibly double down thereafter. If you're vulnerable, for whatever reason, knowing the numbers can help you choose a rational fallback position.

Whatever you decide, make your moves and don't look back when you see the cards that happen to come along next. It was Sumner A Ingmark, the prominent punting poet, who thus warned the wagering world against relying on hindsight:


All gamblers face this mystery:
When to learn from history,
Or when are certain incidents,
No more than coincidence.

Table
Expectations and Probabilities
for Alternate Ways to Play
Eight-Eight versus Dealer 10-up
 
stand
hit
surrender
split
without
doubling
split
with
doubling
expectation
-0.5404
-0.5398
-0.5000
-0.4955
-0.4895
win/loss
 
 
 
 
 
+4
--
--
--
--
0.21%
+3
--
--
--
--
3.38
+2
--
--
--
19.18%
16.51
+1
22.98%
20.04%
--
5.08
7.46
0
--
5.92
--
23.66
19.02
-0.5
--
--
100.00%
--
--
-1
77.02
74.04
--
11.18
11.16
-2
--
--
--
40.90
37.75
-3
--
--
--
--
4.37
-4
--
--
--
--
0.14
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.