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What Do Deviations from Basic Strategy in Blackjack Cost?

4 January 1999

Many experienced blackjack buffs follow basic strategy closely. But not completely. Sometimes, they deviate from dogma because they're mistaken about certain marginal decisions. For example, bettors may double rather than hit ace-three versus four, or hit instead of split four-four against six. Alternately, they may know what "the book says," but trust their own instinct more than the laws of mathematics. Illustrations are hitting rather than splitting eight-eight against 10, or insuring their blackjacks.

Violating basic strategy may, but doesn't necessarily, affect the outcome of a hand. When it does, consequences may be good, bad, or indifferent. There's no way to know in advance. Further, specific results are tempered by chance, so they aren't valid as rating criteria, either. The only tenable means of evaluating decision quality is to eliminate the influence of randomness -- the luck factor -- and examine the likelihood of winning or losing different amounts, playing hands in various ways. This is done by comparing "expected" win or loss for the alternatives.

Blatant basic strategy violations can be costly. For instance, 18 against a nine is vulnerable. Standing, the optimum play, is expected to lose \$18 for every \$100 bet. But bezonians who figure they might as well hit and go down fighting boost expected loss to \$61 per \$100. Splitting 10s rather than standing on 20 against six-up cuts expected win from \$70 to \$57 per \$100. Against a 10-up, such a play would slash expected win from \$56 to \$5 per \$100.

Conversely, proficient players may be surprised to learn how small the penalties are for many common "incorrect" decisions. As examples, basic strategy deviations involving soft doubles and non-10 splits against low dealer upcards typically cost no more than a few dollars per \$100 bet. Similarly, bettors who stand on an underdog soft 18 versus a non-blackjack ace face an additional expected loss of less than \$1 per \$100 bet relative to hitting.

Here's the data for two such moves I noticed this past weekend.

Philip followed basic strategy almost to the letter. The single exception I observed was to hit, not double, 11 versus 10. He explained, "I never double into 10s. They're too dangerous."

How much did Philip sacrifice? In a six-deck game, neglecting cases when the dealer has a blackjack, the expected win on every \$100 bet with 11 versus 10 is \$18 when the hand is doubled and \$12 when hit. The difference is \$6 per \$100. The probability of getting 11 versus non-blackjack 10 is 1.36 percent. The overall impact of this decision on house edge in the game is therefore equivalent to 1.36 percent of \$6 -- roughly \$0.80 per \$100 bet. Phyllis made an inverse shift from basic strategy, doubling on 11 versus ace-up. This error is common in multi-deck games. The reason is that doubling is correct with one deck, and many older or copy-cat sources give this rule without qualification.

Again, assume six decks and neglect hands with dealer blackjacks. The expected win per \$100 bet with 11 versus ace is \$15 when hit and \$13 when doubled. The difference is only \$2 per \$100. The probability of receiving 11 versus non-blackjack ace is 0.25 percent. The impact of this decision on house edge is therefore equivalent to 0.25 percent of \$2 -- half a cent per \$100 bet.

Another thing. Many solid citizens think that players who make incorrect decisions "change the flow of the cards" and ruin the game for everyone else. 'Tain't true! One person's decisions may affect the distribution of cards at a table in the current and later rounds. This may, of course, cause others at a table to win or lose. But, at the instant the decision is made, it can't affect the likelihood of any such result because it has no impact on the expectation of any hand other than the one in question.

Sumner A Ingmark, who often diverges from the doctrines of basic poetry, thought of such departures from orthodoxy this way:

Some people make their fortunes breaking rules,
While those who follow custom look like fools.
But lacking deeper insight it seems wise,
To heed the cautions specialists advise.
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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.