Buster Blackjack @ Sycuan, CA
At my nearby Sycuan Casino, they offer a sidebet on some of their games called “Buster Blackjack”. It’s an optional “bonus” bet the player can place, up to the amount of his blackjack bet, and limited to $100. It’s a bet that the dealer will bust, and its paytable is based on the number of cards the dealer busts with.
I wrote a little recursive program to calculate the distribution of dealer busts for a 6-decks shoe, and worked in their paytable.
| Dealer Bust Cards | Payout | Probability | Return |
|---|---|---|---|
| 3 | 2:1 | 1.73032e-01 | 0.346064 |
| 4 | 2:1 | 8.93918e-02 | 0.178784 |
| 5 | 4:1 | 2.04726e-02 | 0.081890 |
| 6 | 12:1 | 2.63760e-03 | 0.031651 |
| 7 | 50:1 | 2.14444e-04 | 0.010722 |
| 8 | 250:1 | 1.15280e-05 | 0.002882 |
| no bust | -1 | 0.714240 | -0.714240 |
| total | 1.000000 | -0.062247 |
So the bet has a typical bonus bet edge of 6.2%. It’s a lot better than I thought it’d be.
Spanish21 @ Sycuan Casino, CA
One of the best games in San Diego is Spanish 21 at the Sycuan Casino. The dealer hits on soft 17, but the player can double a hand up to 3 times. This comes in handy with a game that allows doubling on any number of cards, even after splits. I wrote my own program to find the basic strategy for this game, and verified it through simulation. The game at Sycuan yields a small 0.4% edge for the house. That’s really good, considering normal blackjack yields at least 0.6% house edge, and the carnival games and “bonus” bets yield anywhere from 2%-8%. As far as discount gambling goes, this is as good as it gets … it costs you only $.02 per $5 bet. This level of action will hardly pay for the casino lights ($.02/hand @ 60 hands/hr = $1.20/hr).
Here’s the results I obtained from my program. The table almost exactly with The Wizard Of Odds, except for a few cases like 8-8 vs. a dealer 10 (you should just hit), A-3 vs. dealer 3 (you should just hit), and a three card 10 (e.g., 2-3-5) against a dealer 8 (you should just hit). There’s an inconsequential difference on the after doubling table too.
Basic strategy for Spanish21.
I wrote the program in C++, and used a recursive algorithm to walk all possible player options and their outcomes against a given dealer upcard. The code is very compact, because of its recursive nature, but it’s a little slow. I speeded up the algorithm a bit by saving intermediate decision EVs, and using them to automatically prune off improbable option branches. For example, it took my Intel-based Mac Mini over 6 minutes to solve the basic strategy play for player 5 6 vs a dealer 2 upcard:
Macintosh:Debug show$ time ./spanish_21 -u 2 5 6 dealerHand: 2 playerHand: 5 6 EV +0.348048 double real 6m15.242s user 6m10.942s sys 0m0.799s
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