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Best of Alan Krigman

Gaming Guru

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What Is Resplitting in Blackjack Worth to You?

16 November 1998

Blackjack buffs who believe that gambling is more than just dumb luck - the right place at the right time with the right bet - look for favorable rules. When there's a choice among nearby casinos, the two options that most often distinguish one game from another are numbers of decks per shoe and maximum number of hands that can be created by splitting pairs.

Assuming other parameters remain the same, the fewer the decks shuffled together, the lower the house advantage. However, in most casinos, opportunity to play games with under eight decks per shoe is more commonly a matter of bigger bankroll than enlightened management. And, in joints where one- and two-deck games are offered, factors such as limitations on hands which can be doubled or rules like "dealer hits soft 17" confuse the issue.

Provision to resplit - to branch into three, even four, hands when a new pair is formed after an initial split - also lets proficient players improve their prospects. Logically, if proper splits are desirable, proper resplits must be more so. The bad news is this feature is increasingly being restricted to high-limit pits. The good news is sedulous solid citizens can still find casinos where it's available at every table.

Does resplitting matter enough to warrant using it to decide where to wager? Factors beyond mathematical expectation may influence your choice. For instance, perhaps you dabble at $5 or $10 blackjack a few times a year, but have a platinum Pampered Player pass to the posh Eaton Drinkup Club at one casino. Then resplitting may not justify jumping to a joint where they treat you like an ordinary tourist with a 2-for-1 buffet coupon.

The following list shows the house edge when splits are permitted to two, three, and four hands in eight-deck games. Figures assume perfect Basic Strategy with doubling allowed on any two-card hands including those formed by splits; split aces draw only one card and cannot be resplit.

maximum
number
of hands
house
edge
(%)
two 0.50793
three 0.45620
four 0.43760

 

Theoretical savings achieved by proper resplitting, based on house edge, are small. In fact, on learning how small, folks often wonder what's the fuss. From two to three hands, the gain is 0.052 percent of the initial bet. From two to four hands, the improvement is 0.070 percent. Say you're a $10 bettor, pressing up to $25 when you get sufficiently cocky. In a two-hour session, you might play 200 hands and bet a total of $3,000. Considering edge alone, ability to resplit is worth $1.56 and $2.10 for maxima of three and four hands, respectively. Hardly spectacular.

Edge reliably measures long-term effects. But even marathon sessions are statistically short, so the positively-skewed fluctuations accompanying splits may be more important than edge to individual bettors. Some splits, of course, are more beneficial than others. And, the potential gain is greatest when one or more sides are subsequently doubled. Many's the profitable session in which the entire net earnings can be traced to multiple wins after splitting and doubling a single hand.

The following are probabilities of making these favorable moves following Basic Strategy in the cited eight-deck game. Likelihood of premium situations grows slowly. Splits to four rather than two spots add an average of one shot in a two- to three-hour sitting. But a single extra golden opportunity may be enough, especially since the result is magnified by the amounts players are favored to win when multiple splits and doubles do occur.

maximum
number
of hands
probability
of splitting
(%)
probability
of doubling
(%)
two
2.505
10.033
three
2.779
10.108
four
2.824
10.120

 

You decide! What are a slightly better edge and an occasional promising try at a multi-unit payoff worth? If not over-riding, they're surely factors in choosing games. The parabolic poet, Sumner A Ingmark, lauded the effect as light but relentless:

It was no brick that hit it blindside,
The last straw broke the camel's hindside.

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.