No Bust Strategy

One strategy that appeals to the squeamish player is the “no bust” strategy, which advises a player never to take a hit on any stiff hand. In many cases, this turns out to be the technique used by “gut instinct” players who, when looking at a sixteen against any upcard, get butterflies in their stomach and decide to stand pat, hoping for the dealer to bust.

The folly of this approach is fairly evident when you consider the dealer’s chances of making a hand of 17 or greater out of anything he happens to deal himself:

1718192021BUST
34.22%11.44%11.14%11.14%11.1421.21%

By following the no-bust strategy, a player who consistently refuses to risk busting a fifteen is relying on the probability (33.15%) that the dealer will bust—and will lose in 66.85% of all such instances. If he were to hit that fifteen, he runs a 58.58% chance of busting the hand anyway. The odds are against him regardless of what he decides to do, but he improves his chances by almost 10% by leathering up and taking the hit.

The no-bust strategy is clearly foolish when facing a high upcard, when the dealer has a high probability of having a pat hand. It fares no better when you consider the chances across the spectrum of all possible situations:

First, a player will be dealt a bust hand (one he will not hit by the no-bust rule) in 38.46% of all situations—and as probability goes, he will lost 66.85% of them. This guarantees the house a 25.71% advantage over the player in these situations.

Second, a no-bust player will only hit a hand of eleven or less, or a soft (hence unbreakable) hand of 12 to 16. This counts for only 26.63% of all possible two-card hands. What’s more, the chances are still 44.96% that the first hit will result in a bust hand—less than 17, but still breakable—and the player will also lose 66.85% of these.

Finally, the probability that a player will be dealt a pat hand (17 or greater) at the onset is only 34.91%, and the chance of bringing an unbreakable hand to a tenable total only 14.65%. This gives the no-bust player a 49.56% chance of making a tenable hand at all—and there is no guarantee that these hands will win: the dealer has a 52.24% chance of beating a pat 17, a 38.37% chance of beating a pat 18, and so on.

In the end, the odds a no-bust player faces are even worse than if he had played his hand according to house rules—which makes the no-bust strategy a clear loser.