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Bust: A Dealer Busting Hand Bet
Introduction
At casinos in Spain, Liechtenstein, Switzerland, and Austria I noticed a side bet on the dealer busting. It simply pays 5 to 2 if the dealer goes over 21. According to the rule booklet of Swiss Casinos Zurich, the title of the bet is simply "Bust."
The following table shows the probability of the dealer busting by number of decks and whether the dealer hits or stands on a soft 17. I also assume the dealer always plays out his hand, even if every player at the table busted.
Probability of Dealer Busting
| Decks | Stand Soft 17 |
Hit Soft 17 |
|---|---|---|
| 1 | 0.283585 | 0.287485 |
| 2 | 0.282582 | 0.286446 |
| 4 | 0.282086 | 0.285931 |
| 6 | 0.281921 | 0.285760 |
| 8 | 0.281839 | 0.285675 |
The next table shows the player expected value if a win pays 5 to 2. For example, in a six-deck game where the dealer stands on soft 17, which are the usual rules in Europe, the player can expect to lose 1.3% of every bet made. That makes this one of the best side bets I've ever seen. Note how if the dealer hits a soft 17 the bet offers a player advantage with six or fewer decks.
Player Expected Value
| Decks | Stand Soft 17 |
Hit Soft 17 |
|---|---|---|
| 1 | -0.007451 | 0.006198 |
| 2 | -0.010962 | 0.002561 |
| 4 | -0.012699 | 0.000759 |
| 6 | -0.013275 | 0.000161 |
| 8 | -0.013563 | -0.000138 |