Stand or hit on soft 17?

Blackjack buffs are better off when dealers must stand on rather than hit "soft 17s" hands like ace-six or ace-four-two where ace is valued at 11. Many players find this hard to believe.

Dealers are clearly more likely to bust when they must hit soft 17s than when they stand, a factor that seems to favor players. Moreover, solid citizens typically think of this question by picturing themselves stopping with totals of 16 or less against a six-up. They reason they'll get beaten straight away if the dealer flips over an ace and can stand; they still have a shot, even with the ace in the hole, if the dealer must hit the 17.

This logic is, in fact, valid when a dealer shows a "stiff" and a player stands with under 17. The accompanying table highlights the effect for six-up. The data show the probabilities of various dealer final results for the alternate ways of handling soft 17.

Probability of dealer ending with various
totals, starting with six-up, standing on
and hitting soft 17 in eight-deck games

final hand	stand on soft 17	hit soft 17
17	16.56%	11.50%
18	10.62%	11.46%
19	10.64%	11.50%
20	10.16%	11.02%
21	9.72%	10.58%
bust	42.29%	43.93%

The figures indicate that players with totals under 17 against sixes have 43.93 percent chance of winning when dealers hit soft 17, as opposed to 42.29 percent when they stand. The difference, 1.64 percent, is worth $1.64 for every $100 bet on this hand. The distribution of the other dealer final results doesn't matter because any of them will beat a player under these circumstances.

The phenomenon is similar although less pronounced when players properly stop below 17 against upcards from two through five. For instance, pretend the dealer has a two-up. The chances of dealers busting are 35.67 when they hit soft 17 and 35.35 percent when they stand. With five-up the probabilities are 41.91 percent hitting and 41.79 percent standing.

The rule is irrelevant with upcards from seven through 10. In these situations, dealers have no way to arrive at soft 17.

The balance tips toward the higher desirability of dealers standing on, not hitting, soft 17 in all other situations. That is, when players stop at or over 17 against ace or two through six. Here, the increased chance of dealers busting by hitting is offset by the lesser likelihood of their besting players' totals above 17 when they do. Essentially because 17 is a weak dealer total, pushing a player's 17 and beating nothing higher.

To illustrate the impact, say a player has 17 against a dealer's five. The player wins if the dealer busts, pushes if the dealer gets 17, and loses on a dealer's 18 through 21. If the dealer hits soft 17, the probabilities for players are 41.91 percent to win, 11.81 percent to push, and 46.28 percent to lose. The net of losses over wins is 4.37 percent, an average of $4.37 per $100 bet. When the dealers stand, the values for players are 41.79 percent to win, 12.20 percent to push, and 46.01 percent to lose. The net is 4.22 percent losing, an average of $4.22 per $100 bet. Players are underdogs either way, but less so when dealers stand.

Ace-up is more extreme. When dealers hit soft 17, their prospects of busting are 13.91 percent. Say a player has a 19 in this situation. The chance of a dealer winning with a 20 or 21, including a blackjack, is 51.77 percent. The chance of the player winning against a dealer's 17, 18, or bust is 33.93 percent. The net expected loss is 17.84 percent, $17.84 per $100 bet. When dealers stand, the figures are 37.64 percent for players to win and 49.29 percent to lose, yielding a net expected loss of 11.65 percent, $11.65 per $100 bet. Again, not a joyous outlook but far less gloomy when the dealer must stand on than hit soft 17.

All of which warrants the wisdom of the wily wordsmith, Sumner A Ingmark, in his troublesomely telling triplet:

Reliance on your intuition,
May sap your fortune by attrition,
And leave you in a weak position.

Is Blackjack Better When Dealers Must Stand on or Hit Soft 17?