How Edge at Blackjack Is Trimmed to the Bone

10 May 2004

By Alan Krigman

If blackjack players stuck to the same strategy used by dealers, hitting anything below 17 and standing above, chances of reaching various totals would be the same on both sides of the table. The casino's edge in the game would be based entirely on the rule that players lose immediately if they bust, regardless of what subsequently happens to the dealer's hand.

The chance of busting with the "house strategy" is roughly 28 percent. The chance of both the dealer and the player busting on the same round is 28 percent multiplied by itself, or about 7.84 percent. The 3-to-2 payoffs that dealers award for uncontested blackjacks, which aren't reciprocated by the bettors, trim the unbalance inherent in the "who goes first" feature by 2.26 percent. The resulting house advantage would accordingly be 7.84 - 2.26 or 5.58 percent.

Notwithstanding the spectacle of solid citizens swarming over the slots or making bets at tables which give the bosses bigger bites than this from their bankrolls, blackjack would be a footnote to gambling history were it a 5.58 percent game. The edge hobbling the hopes of reasonably proficient players is actually a tenth this high, about half a percent. Great enough to take a toll on persistent punters, but hardly noticeable in the statistically short span of a single session or casino visit. Half a percent amounts to a fee of one bet every 200 hands. At a table with three other players, that'd represent about two hours of action.

The lion's share of the tenfold reduction in edge comes from standing on totals between 12 than 17 when the dealer shows an appropriately low upcard. The gain to the player is approximately 3.2 percent. Alone, this brings the edge down to 2.38 percent.

Doubling down represents the next most substantial weapon in the player's arsenal. The accompanying table shows the drop in house advantage achieved by properly doubling under each of the "standard" conditions in multi-deck games. The total with no resplitting is 1.49 percent. Resplitting raises this to 1.51 percent. Edge falls to 0.89 or 0.87 percent for the cases of doubling without and with resplitting, respectively. If, in a moment of inspired generosity, a casino allowed doubling down on three or more cards, it would sacrifice another 0.22 percent of its take. Don't waste too much time looking for this option.

The reduction in house advantage obtained by
properly doubling down under various conditions

doubling condition	reduction in edge
2-card 11	0.74%
2-card 10	0.46%
2-card 9	0.08%
soft hands	0.09%
after split with no resplitting	0.12%
after split with resplitting	0.14%

The remaining decrease players can get in edge because of what they can do that dealers can't involves splitting pairs. With no resplitting and only one card dealt to a split ace, the boon is 0.39 percent. Resplitting non-aces jumps this to 0.43 percent. When aces can be resplit, the total is 0.50 percent. The overall edge against a strict Basic Strategy player is therefore 0.50 percent with no resplitting, 0.44 percent with resplitting of paired non-aces, and 0.37 percent with full resplitting.

The number of decks in the shoe also makes a slight difference. For instance, doubling is more powerful with six decks while splitting is stronger with eight. Overall, fewer decks mean lower house advantage. A favorable enough set of rules, including doubles on any two cards, doubles after splits, and resplits on non-aces, gives the house virtually no edge in single deck games.

It should, but doesn't, go without saying that to get the available benefits, blackjack buffs must learn Basic Strategy. And adhere to it rigorously, realizing it has a firm statistical footing predicated on minimizing the house edge, as opposed to being one expert's say-so over another's. There's room for opinion, to be sure. But at the level of an individual's gambling goals, not at how best to achieve them once established. For, as the sharpster's Shakespeare, Sumner A Ingmark, cleverly quilled: