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Hitting Soft 17

Basic strategy instructs a player to hit a soft seventeen in every situation, yet most players are hesitant to do so, assuming their chances of winning are better if they stand on 17 than if they risk decreasing the value of the hand with subsequent hits. A closer examination of the math behind the advice can be helpful in understanding why it makes sense always to hit a soft 17.

Standing

Seventeen is a weak hand from the very start. The following table shows the odds for the outcome of the dealer's hand, regardless of what cards are originally dealt:

As you can see, a player who stands on a 17 of any kind has only a 33.15% chance of winning, because the dealer must bust in order for the player to win at all. Even if you count the 14.61% chance of a push as being in the player's favor, there remains a 52.24% chance the player will lose. Given this level of risk, and an even-money payoff if the player comes out on top, the house has roughly a 20% edge over a player when he stands on seventeen.

Hitting

Naturally, it doesn't make sense to hit a hard seventeen. Since there are only four of thirteen cards, there's a mere 30.76% chance of improving the hand, and a much greater chance (69.23%) of busting.

However, since the ace in a soft 17 can revert to a value of one, the four ten-value cards pose no risk—drawing a ten will leave the player no worse than he was to begin with. This mans that, with the first hit alone, the chances of drawing a tenable hand with a value between 17 and 21 are eight in thirteen—or 61.53%.

In the remaining 38.47% of all possibilities, the immediate outcome of the player's hand will vary between twelve and sixteen. If the player stands pat, his chances of winning are the same as if he'd stood on the soft 17, because the dealer will still need to bust in order for the player to win, regardless of the total of the player's hand. Even if the situation calls for the player to take additional hits, there remains a 44.85% chance the player will hit to a tenable hand.

In the end, the probable outcomes of hitting a soft seventeen are:

While the player who hits a soft 17 does run the risk of busting (21.21% as compared to 0% if he'd stood), he has a much greater chance of improving the hand (44.56% as compared to 0%).

Final Comparison

When compared to the possible outcomes of the dealer's hands, the chances of winning after hitting soft 17 are considerably better than if he'd have stood:

This trims the house's edge over the player from 20% to less than 5%—which makes hitting the soft 17 the smart play in every situation.

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