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# How Different are Blackjack Totals of 16 and 17?

1 December 1997

Blackjack buffs occasionally wonder whether totals of 16 and 17 are really as different as the experts insist. When a dealer's upcard is seven or greater, the gurus say hit 16 and stand on 17. With exceptions, of course. If surrender is offered, they favor this option with 16 against nine, ten, or ace. And if the 16 is a pair of eights, they advocate splitting it in all instances.

But some bettors hesitate to hit 16. They know eight of the thirteen possible draws will cause them to bust, and the five that will improve their hands still don't assure a win. "You stand on 17, when nine cards are automatic losers and only four can help," one solid citizen explained. "It's almost the same for 16. Since it's right to stand on one, why not the other?"

Less often, a player who realizes 17 is weak will draw, especially against 10 or ace. "You're supposed to hit 16 even though you'll probably bust, so you might as well risk it on 17. If not, the dealer's bound to win anyway," another deep thinker told me.

This dilemma illustrates why qualitative reasoning can be costly in gambling. Examining the numbers quantitatively emphasizes the contrast between hands of 16 and 17.

First, consider the chances of losing by standing. The dealer must draw to 16 or below and will therefore either bust or finish with 17 or above. As a result, a player's 16 loses unless the dealer busts. A player's 17 pushes if the dealer finishes with 17 and loses otherwise. The difference is accordingly in the pushes. A dealer will finish with 17 about 37 percent of the time starting with seven, and between 11 and 13 percent otherwise.

Next, evaluate the chances of breaking when a card is drawn. Starting with 16, the likelihood of exceeding 21 is 8/13 or 61.5 percent. With 17, the prospect rises to 9/13 or 69.2 percent. These probabilities aren't "almost the same." Divergences of 7.7 percent can be devastating over extended play, even though they may not be readily apparent from hand to hand.

Last, combine these factors with the chances that non-breaking draws will push or win. The final results can be expressed as expectations - expected profits or losses for every dollar placed at risk at the beginning of a round. Expectations serve to compare the effectiveness of alternate strategies.

Expectations for playing 16 or 17 against a dealer's upcard of seven through ace are shown in the accompanying table, assuming a six-deck game and no dealer blackjack. As an example of interpreting the data, standing on 16 versus dealer seven presents an expected loss of \$0.48 per dollar bet. Hitting reduces the expected loss to \$0.41. If the 16 is a pair of eights, splitting offers an expected net profit of \$0.22.

The tabulated expectations are negative, confirming that 16 and 17 are underdogs for dealer upcards of seven and above, other than for splitting eights against a seven. But the values also show the extent to which hitting 16 outperforms standing - and splitting, when possible, is better yet. Similarly, the entries indicate how much less onerous standing on 17 is than hitting.

Hardly anyone would hit 19 against a dealer's six, hoping for a two, figuring the dealer might have four in the hole and draw a 10. Why not? Because it flagrantly flouts the odds. Misplaying hands of 16 or 17 also flouts fate. How do these cases differ? Sumner A Ingmark, the bettor's Browning, counted the ways:

Distinctions that prove the toughest to see,
Are matters of kind and not of degree.

 Table Expectations for Alternate Decisions with Hands of 16 and 17 for High Dealer Upcards dealer hit 16 stand 16 split 8-8 hit 17 stand 17 7 -0.41 -0.48 +0.22 -0.48 -0.11 8 -0.45 -0.51 -0.08 -0.50 -0.39 9 -0.51 -0.54 -0.40 -0.55 -0.42 10 -0.53 -0.54 -0.48 -0.58 -0.42 A -0.52 -0.66 -0.39 -0.56 -0.48

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Best of Alan Krigman
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.