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Of blind men, elephants, and pairs of eights against 10s at blackjack

25 June 2012

Everybody knows the parable of the blind men and the elephant. One held the tail and thought the elephant was like a rope, another the ear and said it resembled a fan, and so on ... imagining a snake, a wall, a tree, and a spear. The upshot, as told by John Godfrey Saxe, was “Each in his own opinion,/Exceeding stiff and strong,/... was partly in the right,/And all were in the wrong!”

Everybody who’s played more than a shoe or two of casino blackjack knows they’re always supposed to split pairs of eights. This, even when the dealer’s upcard is a 10 and splitting seems like jumping from the frying pan into the fire. The blind men who met the elephant and blackjack players with pairs of eights against a 10 are somewhat analogous. The blind part because solid citizens are usually aware of the rule but rarely of its rationale. And being simultaneously right and wrong because a single decision may not be best in all conceivable cases.

The dictum to split eights against 10 is based on a statistic the math mavens call “expectation.” This isn’t what’s really expected to happen. It’s the average fraction of a gross wager that will be won or lost after enough action that frequencies of results home in on theoretical probabilities.

Expectation for eights versus 10 is highly negative, however the combination is handled. The whack is just over $0.54 per dollar bet by standing, slightly under $0.54 on the dollar by hitting, exactly $0.50 per dollar by surrendering, and a bit below $0.49 per dollar splitting when doubling down is allowed on hands formed with the separated eights. Basic Strategy is predicated on the option with the expectation for the most profit in favorable situations and the least loss under adverse conditions. Expectations are that splitting saves about a nickel per dollar relative to hitting or standing and a penny in contrast to surrendering. It’s therefore the Basic Strategy rule. However, a blackjack buff’s personal preferences might suggest criteria other than expectation for this particular hand, such that splitting would not be the optimum tactic.

An alternate criterion might be the greatest chance of a net win or the least of a net loss in a particular round. The probabilities for the eights versus a 10 are as follows.

• Standing: 23 percent of wining and 77 percent of losing one unit.
• Hitting: 20 percent of winning and 74 percent of losing one unit, with 6 percent of pushing.
• Surrendering: 100 percent of losing half a unit.
• Splitting with subsequent doubling permitted: 27.6 percent of winning (7.5 percent for one unit, 16.5 percent for two, 3.4 percent for three, and 0.2 percent for four), 53.4 percent of losing (11.2 percent for one unit, 37.7 percent for two, 4.4 percent for three, and 0.1 percent for four), and 19.0 percent of pushing.

The probability standard therefore tends to reinforce the “always split” rule. Ignoring the amounts, it also supports hitting over standing as second best.

Risk of ruin considerations offer other criteria for eights-versus-10 decisions. This combination only occurs on the average of once in 560 or so hands. So it’s reasonable frame risk of ruin in terms of the likelihood of achieving some goal before losing a stated amount in the short term.

One risk of ruin question is the chance of earning some stated profit before losing a given sum on pairs of eights versus dealer 10s. Specific answers depend on the amounts involved, of course. Say a player wants to earn $20 before losing $100 making $10 bets on this hand alone. The probability of success is about 9 percent by hitting and roughly 8 percent by standing. It soars to 72 percent by splitting. Obviously, splitting is best if earnings are the primary concern.

The other risk of ruin question is the chance of playing this hand some number of times and not losing over a stated amount, starting rounds with bets of a specified size. Pretend a person wants to go at least 10 times without losing $100 on $10 initial bets. Prospects of success are 94 percent standing, 95 percent hitting, and only 55 percent splitting. Here, hitting becomes the best choice, closely followed by standing and trailed significantly by splitting. This explains the sinking feeling folks often get when they put 100 percent more at risk under adverse circumstances in the here and now, hoping to save what turns out to average only 5 percent over the long term.

Not all gamblers have the same criteria. Distinctions arise from person to person, or in the priorities of single individuals at different times and in disparate contexts. So it helps to know not only how the gurus say to play, but the basis for this rule or that. Something akin to the adage that not all sponges fit every mop. Or, as the bettors’ bard, Sumner A Ingmark, cleverly quilled:
Before you start to do or die,
Be sure you know the reasons why.

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.