Discount Gambling

Buster Blackjack @ Sycuan, CA

Posted in blackjack sidebets by stephenhow on February 18, 2009

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.

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Spanish21 @ Sycuan Casino, CA

Posted in spanish21 by stephenhow on February 18, 2009

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.

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

real    6m15.242s
user    6m10.942s
sys     0m0.799s
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