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What price do you pay for not doubling down or splitting pairs in blackjack?

15 August 2011

Experienced blackjack buffs, and lots of novices as well, know that “the Book” says to double down in some situations and split pairs in others. When appropriate, these tactics lower the house edge in the game – improving solid citizens’ long-term prospects. In doubling, players match their original bets and receive single additional cards. In splitting, they also match their original bets then play each half of the pair as the first card of a separate hand.

Not everyone is comfortable doubling or splitting, chiefly because of the extra money which must be put at risk. Some players wonder whether the lower house advantage justifies exposure to the possibility of steep bankroll downswings if these moves go awry.

In principal, the probability of receiving a hand calling for doubling is 9.5 percent in an eight-deck game. On average, that’s roughly once every 10 or 11 hands – twice per shoe at a table with four spots in action. Splits are less common, with probability of 2.5 percent. Again on average, that’s approximately once every 40 hands – once every two shoes under the same conditions.

Averages are meaningful over large numbers of trials. During one or a few sessions or casino visits, though, encountering doubles twice per shoe or splits once every two shoes is pure happenstance. You might run into stretches featuring none at all, and others where they occur far more often. Getting fewer than the predicted number, or ignoring those that come along, boosts the effective house edge, a change only the bosses can like; it also holds the volatility of the game down – which you may regard as good or bad. Conversely, receiving and acting properly on more than the average can give you an edge. Further, if you succeed or fail more than anticipated on these hands, especially when they present themselves frequently, the volatility can boost you into the big buck bracket or wreak havoc with your finances, as the respective cases may be.

Naturally, enquiring minds want to know the actual effect doubling and splitting have on edge and volatility. As a baseline, take an eight-deck game with doubling on any two cards, doubling after splitting, resplitting any pairs except aces, and dealer standing on soft 17. Perfect Basic Strategy in this environment keeps the house edge at a slim 0.43 percent and volatility, measured by “standard deviation,” at approximately 1.15 times the amount bet at the start of each round.

Without splits or doubles, standing or hitting – whichever is the next best choice – adds 2.15 percent to house advantage for 2.58 percent in all. With doubles but no splits, edge jumps 1.58 percent to 2.01 percent. With splits but no doubles, the increment would be 0.79 percent to 1.22 percent. Volatility-wise, avoiding splits or doubles cuts the bet multiplier per hand from 1.15 to 0.98. With doubles but no splits, standard deviation is 1.12; with splits but no doubles, it’s 1.02.

Over enough decisions, edge overwhelms volatility in casino gambling. It’s how the bosses make their moolah. The volatility of individuals’ wins and losses cancel out and leave a small fraction of a large gross wager in the casino coffers. Particular players rarely reach a point where edge dominates, certainly not in a single session or visit. Depending on the extent of their action, a balance of edge and volatility defines prospects for ecstasy or agony. Exploiting or skirting doubles and splits influences both parameters simultaneously. To appreciate how this affects projected performance, consider the impact of alternate modes of play on the chances of doubling a stake before going bust, and of staying in a game on a given budget for a specified period.

With perfect Basic Strategy, $10 bets on a $200 bankroll at the outset of every round yield approximately 47 percent chance of doubling a bankroll before going broke. At blackjack tables with four spots in play, chance is roughly 65 percent of remaining in the fray – up or down but not out – after four hours.

With neither doubles nor splits, prospects drop to 25 percent chance of doubling the bankroll and 59 percent of being in action for four hours. Doubling but not splitting, the outlook is 34 percent of doubling the stake and 57 percent of surviving for four hours, Splitting but not doubling, the likelihoods are 38 percent of doubling the poke and 66 percent of enduring for four hours.

Overall , hope of doing well is brightest by adhering to Basic Strategy, keeping edge low and volatility at 1.15. Obtaining more than the statistically-correct instances of splits and doubles, and succeeding at more than the theoretical rate, would be a bonus. There may be circumstances under which a proficient player holds back on these options. But bettors who do so as a general rule would be well advised to ponder whether they’re overbetting their fanny packs or their proclivities, and to weigh this wisdom of the wordster, Sumner A Ingmark:
Not everybody can afford,
To gamble for a big reward.

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.