Discount Gambling

Updated Ultimate Texas Hold’Em Practice Game

Posted in ultimate texas hold'em by stephenhow on February 27, 2011

I’ve re-written the Ultimate Texas Hold’Em practice game in Flash to make it more presentable and enjoyable. I’ll be improving it over the next few days, so most of the features will be added soon. I’ll link this game into my main Ultimate Texas Hold’Em Page, and it’ll eventually replace the old Java game. Enjoy!

Click on the screenshot below to play:

New Card Craps Practice Game

Posted in +EV, card craps, csm by stephenhow on February 21, 2011

The best way to understand counting for card craps is to see it in action. I wrote a new practice game to demonstrate counting against the point, and when it’s correct to lay odds with your Don’t Pass bet. The game is configured with the Viejas parameters (10x odds, 312 cards in a ShuffleMaster 128 CSM) so if you’re planning to check out the game, practice here first! Sometimes I just like watching the rolls, so I also included an “Auto” mode to continuously play by itself. This might give you an idea of session variance, and what to expect if you actually decide to play 10x odds.

Click on the screenshot below to play:

I like watching all the animation and highlighting. It’s a lot more fun to run the game in a browser window, and occasionally see how it’s doing, than it is to sit and grind it out at Viejas all day 🙂

Practical Collusion For Rabbit Hunter Stud

Posted in collusion, rabbit hunter stud by stephenhow on February 14, 2011

I played Rabbit Hunter Stud all day Sunday @Pala with my friend (2 spots x 8 hours) and we came out even. I received a few mis-pays, totaling about $30, which helped overcome the expected $72 house edge (40 hands/hr * 8 hrs * 2 players * 2.25% house edge/hand * $5 Ante) + tokes. Overall, it was a very enjoyable experience, and everyone had a good time. Several of us discussed how the game is “too easy”, and that they’ll soon figure out the house hold is way too low to keep it around. As I’ve said before, the 2.25% house edge is less than half of comparable poker-based carnival games, because there’s no “optional” bonus bet (additional 2-4% house edge).

The floorman told me the story of how the original version of the game required a 2x Play bet, and there was no dealer qualifier on the Ante. They told ShuffleMaster no one was playing the new game “in this economy”. So they re-designed it to be easier, with a 1x Play bet, and an Ace-high dealer qualifier on the Ante. It only took a few months for the re-design and Gaming Commission approval to put the new version on the floor. It was popular yesterday, and full all day. Newbies watched the game, then joined in and played the simple optimal strategy. There were quite a few full houses (30:1), and a girl playing for the first time made a straight flush (100:1) when nobody held either of her 2 outs.

With only a 1x Play bet and a dealer qualifier on the Ante, the variance is very low. Paying for a 6th card (“rabbit hunting”) is very enjoyable, and you actually look forward to doing it (47% of hands). The only “crying call” in the game is when you have Ace-high and no draw. Folding is obviously no fun, but it only happens 22% of the time.

The players at the table share information about their hands, and occasionally, it’s helpful. At a full table, you can ask for info at the following decision points:

6-Player Collusion Modifications for Rabbit Hunter Stud
Hand Collusion Modification Frequency Hand EV
Overall EV
low pair only don’t hunt if no trip outs 6.56% +13% +0.86%
two pair don’t hunt if no full house outs 0.34% +100% +0.34%
K-high call if 4 aces out 0.73% +27% +0.20%
gutshot w/o high cards fold if no straight outs 0.51% +22% +0.11%
high pair w/ gutshot don’t hunt if 1 or less straight outs 0.22% +26% +0.06%
KQ-high call if 3 aces out 0.56% +4.5% +0.05%
total 8.92% +1.62%

This simple collusion reduces the house edge from 2.25% down to 0.63%. Of course, there are probably a whole bunch of other optimal decisions you can make with knowledge of all your outs. However, it’s too awkward to ask for info on more than just one card. Notice that you make modified decisions on almost 9% of your hands. That’s a very high percentage, and requires a lot of info sharing at a table. The game is naturally chatty, but you’ll need to keep it low-key. You’ll need to develop a good rapport with everyone, and minimize your queries.


You have a pair of 2’s with no flush or straight draws. You ask if anyone has any deuces, and the other players tell you they have both of them. You don’t pay to hunt, you just call. If there was still a deuce left, you’d go ahead and pay for your 6th card.

Your hand is King high. You ask if all the Aces are out. The other players have all 4 Aces. You go ahead and Play 1x (call).

Your hand is King-Queen high. You ask if all the Aces are out. The other players have 3 Aces. You go ahead and Play 1x (call).

Your hand is JJKT9. You ask if anyone has a Queen. The other players have two of your Queens, so there are two left. You pay for a 6th card. (If there was only one left, you would not pay to hunt.)

Your hand is 97652. You ask if anyone has an Eight. The other players have three Eights, so there’s one left. You pay for a 6th card. (If there weren’t any Eights left, you’d fold.)

+EV Mississippi Stud: Why The House Doesn’t Worry

Posted in +EV, mississippi stud by stephenhow on February 12, 2011

Lately, I’ve been playing more full exposure Mississippi Stud at my local Barona Casino. I’ve called it “the least enjoyable +EV game” around, because of it’s high variance. Generally, it’s an “expensive game”, played by an older crowd that can afford it. Even though the full exposure game is +EV (around +1.5% of the Ante) using a simple strategy, the game is only full (exploitable) on weekends. The way I think, people should be all over this game, keeping it full, betting $25 Antes, and grinding out $0.37/hand. But the game is usually empty for good reasons: it would take months of full-time grinding and a huge bankroll to take advantage of it. And you’d need a full team of 6 players.

Even when the game is full, the house’s hold (EV) is huge. Because there is no way on earth that people are going to play correctly, no matter what. I play with my cheat sheet, which tells me the approximate return of hands on 3rd and 4th street, and their exact returns on 5th street. Other players wouldn’t be caught dead following this advice, because it tells them to fold more than they like to (and occasionally, it tells them to raise more than they like to). Most players don’t like folding their hands, especially at 2nd street (first two cards), and at the river. They acknowledge that they shouldn’t “chase”, but they don’t know how bad (-EV) it is, and they get caught up in it.

The cheat sheet points out the cost of each mistake, and even the smallest mistake is usually in double digit territory. For example, if you’re on 2nd street, and you have only 1 high out and 2 mid outs, you’re giving up about a 31% house edge (of the Ante) to 1x call and see 3rd street. The return of this call is -1.31 Antes. Folding would be a better choice, costing only 1 Ante (-1.0 return). Calling will return -1.31 on average, or an additional 0.31 Ante loss to see a card. At a $5 Ante, this is an additional $1.55 cost over folding.

When you “chase” a hand, you often pick up just enough outs to “force” you to call again. In our 1/2/0 (high/mid/low outs) example, we called to see 3rd street, making our hand worth -1.31. If we pick up 2 more high outs on 3rd street, we now have a 3/2/0 hand, and we should 1x call again to see 4th street, since folding has a value of -2.0, while calling has a value of -1.75. Notice that we now have a hand that is 0.75 Antes worse than folding on 2nd street (-1.0 Antes), and we’re forced into investing 3 Antes. Chasing could get worse. If we pick up another 2 mid outs on 4th street, we’re again forced into another 1x call, to “protect” our 3/4/0 hand and 3 Ante investment to extract out its -2.94 Ante value (would be -3.0 to fold on 5th street). So that’s how a 31% mistake escalates to a -300% cost. Of course, if we paired up our hand, we could win big. That’s why it’s only a 31% mistake on average.

“Chasing” is horrible, because you should just fold and wait for the next hand, instead of forking out -EV to the house. If you don’t hit, EV just gets worse. Often at the table I hear, “I always see the first card”, meaning they’ll play any two cards to 3rd street. I simulated this “call anything” 3rd street strategy combined with perfect strategy on 4th and 5th street, and the result was a 13.5% house edge. Notice that’s worse than having no other information and playing basic strategy (4.91% house edge). It’s no wonder that most people lose a tremendous amount of money at the game. It’s hard to say, but I’d guess the average player is giving up about a 20% (of an Ante) edge to the house. At a $5 Ante, that’s $1 a hand.

Of course, that $1/hand cost might be the marginal utility of “not folding” + “getting lucky” + “playing hunches” – “bleeding off” to that player. I’m kind of the exception. To me, giving up a 5% edge to the house on a mistaken call feels a lot worse than its $0.25 average cost 🙂

Card Craps Source Code

Posted in +EV, card craps by stephenhow on February 3, 2011

If anyone is interested in verifying the CSM card craps edge (e.g., @ Viejas), I’m making the Java source code for the simulator/analyzer available here. You just need the Java SDK installed to compile and run the program. If your Unix environment is already set up for Java development, just follow these steps to get up and running:

>curl | tar zx
  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current
                                 Dload  Upload   Total   Spent    Left  Speed
100 24576  100 24576    0     0  67205      0 --:--:-- --:--:-- --:--:--  105k
>cd card_craps
javac -Xlint warning: [unchecked] unchecked conversion
2 warnings
>java Analyzer
don't pass, 10x odds, 14 card min buffer depth, 6-roll window
0 rolls: net +1.0, EV/roll +Infinity%, EV/game +100.00%
1000000 rolls: net +2828.0, EV/roll +0.28%, EV/game +0.95%
2000000 rolls: net +9921.0, EV/roll +0.50%, EV/game +1.67%
3000000 rolls: net +12754.0, EV/roll +0.43%, EV/game +1.43%
4000000 rolls: net +24592.0, EV/roll +0.61%, EV/game +2.07%
5000000 rolls: net +36467.0, EV/roll +0.73%, EV/game +2.46%
6000000 rolls: net +47067.0, EV/roll +0.78%, EV/game +2.65%

There are several options to the program, so you can experiment with the different CSM model parameters:

>java Analyzer -h
usage: Analyzer <options>
where options include:
 -n <number of rolls>             specifies number of rolls to simulate (default 100 million)
 -d                               play Don't Pass line (default)
 -p                               play Pass line
 -o <max odds>                    specifies odds to take/lay for good count
 -b <buffer depth>                specifies minimum reservoir depth (default 14)
 -w <window depth>                specifies count window depth (default 6)
 -a                               print per-point statistics
 -h, --help                       display this usage
Place a space between the option and parameter value.

The program shows the game is +EV, but it’ll also show you the huge variance for any given session. You can use the -n 1000 option to simulate a session (1000 rolls is possible in a few hours, heads up).