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# If 17 in blackjack isn't much better than 16, why treat them differently?

25 April 2011

Some folks play blackjack by guess and by gosh. Others learn and follow Basic Strategy but do it by rote and haven’t a clue why hands call for the treatments they do. Solid citizens of the latter ilk don’t guess but do exhibit lots of gosh when bets go bad even through they abide by the rules.

The differences in treating 16s and 17s offer a case in point. Experienced players know they’re in a pickle with hard 16. They may not be thrilled but aren’t overly worried with hard 17. After all, Basic Strategy says to stand on either against those safe twos through sixes, but to hit 16 and stay at 17 against those dangerous sevens through aces. So, 17 must be pretty good.

Must be? Pretty good? Hard 17 is actually a dog. It only wins if the dealer busts, just as is true of 16. The distinction between these totals mainly lies in the fact that 16 loses to any pat dealer’s hand while 17 pushes to a dealer’s 17 but loses to 18 through 21. The accompanying table gives the probabilities of all possible dealer final hands. The data can be used to illustrate how 16 and 17 differ in practice.

Probability of various dealer finishing totals for all, low, and high upcards

```upcards                17      18      19      20       21      bj      bust
all                 14.5%   13.9%   13.4%   18.0%     7.3%    4.7%     28.2%
2- through 6-up     13.8%   12.4%   12.0%   11.5%    11.0%    0.0%     39.3%
7- through ace-up   14.9%   14.9%   14.2%   22.0%     5.0%    7.7%     21.2%```

The first row of the table shows that for all upcards, dealers are expected to bust – so 16s win – 28.8 percent of the time and lose the remaining 71.8 percent. The net average cost per \$100 bet is therefore \$71.80 - \$28.20 or \$43.60. A 17 is also projected to win 28.8% of all rounds but to push 14.5 percent and lose the other 57.3 percent. This makes the net average cost per \$100 bet \$57.30 - \$28.20 or \$29.10. They’re both losers, but 16 is \$43.60 - \$29.10 or \$14.50 worse.

The second row of the table shows that against two- through six-up, 16 wins 39.3 percent and loses the other 60.7 percent. The net average cost per \$100 bet is \$60.70 - \$39.30 or \$21.40. Final 17 also wins 39.3 percent but pushes 13.8 percent and only loses 46.9 percent. The net average cost per \$100 bet is \$46.90 - \$39.30 or \$7.60. Both lose money, on the average, but 16 is \$21.40 - \$7.60 or \$13.80 per \$100 worse. Enquiring minds might want to know why Basic Strategy says stand on 16, since it’s unfavorable as-is and any improvement will either slash the expected penalty or break through to the projected winners’ column. The answer involves the fact that, while five out of the13 ranks strengthen the 16, eight out of the 13 result in an immediate bust. Coupled with the degree of enhancement from each of the five strengthening cards, hitting will result in a larger average net loss than standing.

The third row of the table shows that against seven through ace, final 16 wins 21.2 percent and loses the remaining 78.8 percent. The net average cost per \$100 bet is \$78.80 - \$21.20 or \$57.60. Final 17 also wins 21.2 percent but pushes 14.9 percent and loses only on the other 42.6 percent. The net average cost per \$100 bet is \$63.80 - \$21.20 or \$42.60. Basic Strategy is to hit 16 under these conditions. The expected \$57.60 per \$100 net loss by standing is enough to warrant taking the five out of 13 shot of improving versus the eight out of 13 prospect at busting on the spot.

For hard 17 against seven through ace, however, the projected loss by standing is \$42.60 per \$100 bet, still high but less so than the \$57.60 for a 16. Coupled with the shift of one rank – the five – from the improvement to the bust regime, hitting ends up worsening the situation.

Circumstances change when the player’s 16s or 17s are soft. Soft 16 is always a hit because the hand can’t get any worse. A nine, for instance, drops the total to 15 – which still can’t push and only wins if the dealer busts – just like a 16. And, against a high upcard, lowering the total with a hit affords the opportunity for another draw – which may then yield an improvement.

Soft 17 is more complex. Basic Strategy says never to stand. Hits are the order of the day against two or seven through ace and doubles are prescribed against three through six. Soft 17 is projected to lose money, on the average, against eight through ace whether you hit or stand. The expected cost is less by hitting, remembering that if taking one card lowers the total, you can draw again. Against a two or a seven, hitting moves the hand from the negative to the positive category. Against three through six, the total of 17 is projected to yield an average loss. Combining the likelihood of the dealer busting with the prospect of staying at 17 or improving with a single draw, the probabilities and returns yield positive expectation by hitting and a yet greater average profit by doubling.

All of this illustrates a key feature of Basic Strategy. It isn’t an open secret that always gives players a better chance of winning than losing. Sometimes, it’s only a way to lose less. A dilemma described thusly by the beloved bard, Sumner A Ingmark:

A person who makes key decisions judicious,
Can lessen the impact of spots unpropitious.