Discount Gambling

Welcome Wizard of Odds Readers!

Posted in Uncategorized by stephenhow on November 2, 2009

I got a mention on the universally-known “last word on gambling” Wizard of Odds site. Needless to say, its nice to suddenly get much more page hits in a day then I used to get in a month. So welcome, especially if you’re here for the +EV angles I’m working to find. Well, if you’re in San Diego, there are two +EV games right now, Mississippi Stud @ Barona, and CSM (card) craps at Viejas. These games have been spread for a while, and the casino isn’t afraid of any advantage players. They’re making plenty of money with these games. No one is going to get rich from these small edges. Its a lot like card-counting in blackjack, but without all the hard work. I just re-wrote the page on the Viejas craps game, to make it easier to see the edge, and how to play it. Hopefully someone will actually try it. Welcome!

PlayCraps Example Session with Counting

Posted in Uncategorized by stephenhow on August 27, 2009

I thought I’d post a thorough description of how to play the PlayCraps game at Viejas, including how to account for the shuffle, using a fair-weighted counts for all the points.

First, here’s the value of each roll, and how it contributes to the counts for each point.

Point ΔCount
4 +4 if both cards ≤ 3, -4 if both cards ≥ 4, else 0
5 +2 if no Fives or Sixes, -1 if one Five or Six, -4 if two Fives/Sixes
6 +1 if no Sixes, -2 if one Six, -4 if boxcars
8 +1 if no Aces, -2 if one Ace, -4 if snake-eyes
9 +2 if no Ace or Deuce, -1 if one Ace or Deuce, -4 if two Aces/Deuces
10 +4 if both cards ≥ 4, -4 if both cards ≤ 3, else 0

Ideally, you’ll keep a count for each point. Of course, this is hard to do. I just wait for the point to come out, then I try to guess if I saw any key cards lately, and make up an initial count for the point. Then I adjust the count for each roll as in the above table. It’s very easy while the muck accumulates. Then, when the dealer shuffles the muck into the CSM, I keep counting as normal, for about 5 rolls (approx. buffer depth). After these five rolls, I start the count again, based on a guess of what’s in the muck.

simulated session with annotations after the jump! (more…)

Triple-Down BJ @ Texas Station, Las Vegas

Posted in Uncategorized by stephenhow on August 8, 2009

I’m finally getting to a reader’s request about a triple-down blackjack game at the Texas Station casino in North Las Vegas. Here are the relevant rules:

  • triple-down on first two cards totals of 9, 10, 11 (including soft totals)
  • blackjack pays even money (1:1)
  • blackjack is an automatic winner, if you stay
  • normal double-down rules
  • no triple after split
  • double-deck

The overall house edge for this game is 0.83%. The triple-down rule gives the player a +1.62% boost, but it’s not enough to overcome the even money blackjacks. The basic strategy is the same as double-deck, except that doubles on hard 9, 10, 11 are replaced by triples. Also, 9 vs a 7 upcard, and A-9 vs 4/5/6 are triples.

Interestingly, tripling a blackjack against a dealer 6 upcard isn’t too bad of an option. The EV is .998, instead of the 1.0 automatic winner for staying. It’s worth a gamble, if you feel like it. Tripling a blackjack against a dealer 5 upcard isn’t as good, as the EV here is only .946. That’s giving up 5.4% of your original bet, on average.

Someone should petition Texas Station to allow triple-down on any two cards. This still leaves the house edge at 0.59%, which is about equal to a liberal shoe game.

Easy Way To Beat PlayCraps™ @ Viejas Casino

Posted in Uncategorized by stephenhow on August 1, 2009

Ok, I just got straightened out on what the actual lay 4/10 vig is. You put up $41 to win $20, so this is better than I previously thought. So I fixed the OpenOffice spreadsheet, and my simulations:

Macintosh:Debug show$ ./laycraps -n 100000000000 -r -t 2 -m 15
max muck depth: 15, CSM buffer depth: 10, threshold: 2, seed: 1249092576
...  ...
roll: 61970000, net: 40131.900, return: +0.15%
roll: 61980000, net: 40184.350, return: +0.15%
roll: 61990000, net: 40218.950, return: +0.15%
roll: 62000000, net: 40254.550, return: +0.15%
roll: 62010000, net: 40231.850, return: +0.15%
roll: 62020000, net: 40243.700, return: +0.15%

Where the 0.15% edge is on the total action, which includes $41 for each roll the lay is ON. This is a pretty conservative way to state the return.

Another way to look at it is the edge for any given roll:

Running Count Lay 10 Player Edge
0 -0.29%
1 -0.04%
2 +0.23%
3 +0.48%
4 +0.76%
5 +1.01%

So, the easy way to play this is to lay the 4 and 10 when the count is good (at Viejas, you pay the vig up front). Then, while the count is good (i.e., RC >= 2 for the lay 10, and RC <= -2 for the lay 4), you leave the lay bet ON. When the count isn't good, you turn the appropriate lay bet OFF. Usually, this means both the lay bets are OFF, then when one of the counts gets good, that bet goes ON. When the count goes bad, both bet OFF. When the count is neutral (0), the distribution shows the odds are greater then 2:1 to hit the 4/10. However, the odds aren't good enough to overcome the vig. But, you can gamble, and turn both bets ON, and if 7 comes up, you win both bets.

It’s a little strange to have both lay bets up there, and turning them ON/OFF with every roll. The dealers might get a little irritated, and you’re only picking up a small edge. (While a lay bet is ON, you’re picking up from approx. 0.25 – 1.0% edge.) Too bad it’s not an electronic game 😦

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PlayCraps™ @ Viejas Casino, CA

Posted in Uncategorized by stephenhow on July 31, 2009

There’s a new craps game at Viejas Casino, that I’ve been playing lately. It’s definitely my new favorite game, since it’s dealt to players seated at a table, and it provides the best odds in the casino. In fact, it’s a winning game for a player using basic strategy (yes, I know, sounds impossible, but read my full analysis). Although the game is beatable, you can only make a killing the normal way, by gambling and getting lucky. However, it’s always good to know the odds are in your favor.



If you haven’t read my full analysis yet, you’ll first need to know the player edge is on the don’t pass / don’t come side, and the house’s edge on the pass odds are higher than usual. So don’t rush out here and start betting the pass line and taking odds like you normally do. Switch over to the Dark Side first, if you’re not already over there.

If you like taking a shot a craps, come on out to Viejas, and have some fun. The layout of the game is really enjoyable, because it promotes fast action, and you get to sit while you play. It’s very relaxing, and there’s no stress of rolling the dice in front of a bunch of angry players. It’s just you watching the cards that come out, and deciding to increase/decrease your don’t pass or don’t come odds. Even for the best counts, you’re not really justified in buying any No-4’s or No-10’s, but at times, the odds overcome the vig.

If you like advantage play, and can enjoy playing the Don’ts, read up on this game, and come on out. It’s not every day that a game is beatable by basic strategy.

No-Bust Blackjack @ Ocean’s 11, CA

Posted in Uncategorized by stephenhow on March 3, 2009

By chance, I learned that the Ocean’s 11 cardroom offers a no-bust version of 21. As usual, I got myself worked up on the slim possibility that the game was better than intended, and set off to crack it. You can probably guess how the story ended. On the positive side, I improved my C++ programs to include a general BlackjackAnalyzer class, where you just subclass the Hand and DealerHand classes for any blackjack variation (just a few lines per rule). I also cleaned up some small bugs, and improved performance tremendously by making some small approximations. The analyzer returns the EV for the game in seconds, without simulation. Yay!

The bottom line is the No-Bust Blackjack yields a -0.18% edge for the bank, that is, before 1% house collection. So including collection, it has about twice the house edge as a typical 6-deck shoe game. See my O11 No-Bust BJ page for details and a basic strategy table. The game is characterized by a few different rules:

Rule ΔEV
Blackjack pays 6:5 -1.39%
3-card lower bust pushes +1.22%
surrender at any time +0.29%
double on any number of cards +0.24%

I spent a few days on the programs, but it was worth it. I’ll post them one day, to save others the effort of re-coding this common tool.

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Three Card Poker @ Ocean’s 11, CA

Posted in Uncategorized by stephenhow on February 27, 2009

At the Ocean’s 11 Cardroom in Oceanside, CA, they play a version of Three Card Poker, where you get to see one of the dealer’s up cards.  It’s also a little different than the licensed casino game, which pays an ante bonus for 3-of-a-kind or better.  The Ocean’s 11 version just pays even money on the ante for all winners, and when the dealer doesn’t qualify.  And they pay off 200:1 on the Pair Plus bonus bet for royal flushes, whereas the licensed game only pays 40:1 for all straight flushes.  I wanted to see how this game compared to the licensed version, so I wrote some programs to analyze basic strategy.  I then simulated the game to verify my results. (The Wizard Of Odds doesn’t provide a strategy for the Ocean’s 11 version of California Three Card Poker.)

Overall, the game is actually better than the licensed version, even though you have to pay collection on each bet (at the least, collection costs 1% of your bet).  The basic strategy is very simple, fold on any of the following:

  • the dealer’s upcard is at least a Q, AND it beats your entire hand
  • the dealer’s upcard is a Q, AND your hand is less than Q-9-garbage
  • the dealer’s upcard is a K, AND your hand is less than K-9-garbage
  • the dealer’s upcard is a A, AND your hand is less than A-9-garbage

This strategy yields a 1.8% house edge, which is less than the casino version of the game (3.38%). Even with the 1% house collection (by law, these California games are player-banked), the game is still better than the casino.

Even more surprising, the Pair Plus bonus bet is 3.00% better than the casino version.

Hand Probability Paytable Improvement ΔEV
Royal Flush 4/C(52,3) +160 0.028959

So if you play the Pair Plus bonus bet, the Three Card Poker game at Ocean’s 11 is by far better than the licensed version at the casino.

Hello world!

Posted in Uncategorized by stephenhow on February 18, 2009

Welcome to my gambling presence on the web!