Discount Gambling

ShuffleMaster’s Dealer Bluff Six Card Poker @ Pala Casino

Posted in dealer bluff by stephenhow on November 15, 2009

I just tried out ShuffleMaster’s new Dealer Bluff Six Card Poker game at Pala Casino, just north of San Diego. It’s a new idea in poker-based table games, where the dealing machine knows the value of its hand, and bets against you. When I first saw this game last week, I was really puzzled. How would you play your hand? Would it cost a lot of money to figure out how aggressive the machine was? How was I supposed to analyze this game?

I looked into the details of the game, and its actually pretty simple how it all works. By its stated math, its not a bad game at around 0.5% house edge (element of risk). The player first bets an equal Ante and Blind bet. All players and the dealer are dealt six cards, from which to make a five card hand. The dealer acts first, and either checks (0x), or bets 1x ,2x, or 3x the Ante, based on its hand strength, and simple randomization. This simple randomization is stateless (independent from hand-to-hand), and uses a published wager matrix (“house-way”). The player may either fold (or check if no dealer bet), call, or raise (double the dealer bet). The dealer calls all player bets/raises. The hand is resolved just like their Ultimate Texas Hold’em game, where the Ante plays only if the dealer qualifies with a pair or better, the Play bet always gets even-money action, and the Blind bet pays only if the player wins, and according to a paytable. The game is easy to analyze, because of the simple, stateless, and published dealer betting strategy (“house-way”). Given house-way, a player basic strategy is determined, and the house edge is calculated.

The game is kind of fun, because the dealer acts first, and you benefit from this position. If you raise the dealer, it must always call (it can’t come over the top, and re-raise you). Sometimes you have easy folds, or easy raises. However, basic strategy requires you to call or raise a lot of hands, even when the dealer is betting 3x, since it bluffs a lot. This of course adds to your variance, and sometimes you’ll wonder why you had to call 3x “to keep the dealer honest”.

As usual in these ShuffleMaster games, the Ante bet is -EV because of the pair qualifier needed to pay, and the Blind bet is -EV because of the paytable. The Play bet is +EV, because you’re acting last, and the dealer must call your bets/raises, and cannot re-raise. However, the dealer may bluff, so you need to know (exactly) how the betting logic works. If you have this info (or can learn it), then the Play bet will always be +EV. The game is designed so that the sum of these 3 EVs yield a reasonable house edge.

This is why I have reservations about the game. Player basic strategy is completely dependent upon how the dealer bets his hand. ShuffleMaster goes out of its way to provide all the data on this process, and even provides the players with basic strategy and percentage tables in their literature. At Pala, there are ample supplies of this literature at the table. The dealer house-way is provided. However, if house-way should change for any reason, the player using an out-of-sync basic strategy may be severely penalized.

ShuffleMaster Published House-Way Wager Matrix (Version 3B?)
dealer hand 0x (Check) Bet 1x Bet 2x Bet 3x
Royal Flush 1% 1% 5% 93%
Straight Flush 1% 1% 5% 93%
Four-of-a-Kind 1% 2% 5% 92%
Full House 3% 6% 10% 81%
Flush 3% 6% 15% 76%
Straight 3% 6% 10% 81%
Trips 1% 7% 20% 72%
Two Pair 3% 8% 40% 49%
High Pair (Tens – Aces) 6% 12% 52% 30%
Mid Pair (6’s – 9’s) 16% 40% 35% 9%
Low Pair (2’s – 5’s) 26% 50% 15% 9%
Nothing 35% 51% 6% 8%

This table provides the percentages of the way the dealer will bet his hand, using a random number generator. No previous knowledge of the player’s history, bet amount, or anything else is used to determine the dealer’s bet.

Based on this house-way wager matrix, basic player strategy is optimized as follows:

Dealer Bet Fold Call Raise
0x AK or better
1x KJ6 or worse in between any pair or better
2x pair 7’s or worse,
pair 8’s w/o kickers
in between pair J’s w/ kicker, or better
3x pair J’s or worse in between two pairs, 5’s and 3’s, w/ kicker, or better

If everything operates exactly per these assumptions, then the house edge is only 0.5% (element-of-risk), or about 2% of the Ante bet. This is only $.10 per $5 Ante bet, and is very reasonable. However, if the dealer strategy is not exactly as described by the stateless house-way table above, the player return could be much worse. For example, the dealer cannot sub-divide the last “Nothing” row, into various sub-percentages based on A-high, K-high, etc. It’s assumed that it treats all no-pair hands the same, and applies an equal bluff probabilities to them, regardless of high card value.

What’s worse, if the dealer behaves significantly differently from the house-way table, the effect on the player using a basic strategy optimized for it could be disastrous. As an experiment, I tweaked the wager matrix to make the dealer more honest (bluff less) in a few rows, to see the effect.

First, I made the dealer more conservative with its high pairs. I shifted the majority of these bets to 1x, thereby giving the player less opportunities to come over the top with a raise to 2x, or even 6x. I modified the following single table row to

dealer hand 0x (Check) Bet 1x Bet 2x Bet 3x
High Pair (Tens – Aces) 0% 80% 15% 5%

and the results were very significant, increasing the house edge to about 5.2% (element-of-risk), or -17.8% of the Ante bet! This really surprised me. The house could (not intentionally, of course) change a few small settings, and really hurt the player relying on the published basic strategy. Unless the player could look at the stats maintained by the betting mechanism, it’s a real leap of faith to get involved with this game for any period of time.

Next, I looked at the effect of making the dealer more conservative with its nothing hand, making it check the vast majority (80%) of the time, and betting 1x the rest of the time (20%). Again, this reduces the ability of the player to just call and win with a reasonable hand, or come over the top with a big raise.

dealer hand 0x (Check) Bet 1x Bet 2x Bet 3x
Nothing 80% 20% 0% 0%

The effect of this row change was less significant, increasing the house edge to about 2.0% (element-of-risk), or -6.6% of the Ante bet. If both these row changes are applied together, the effects are additive. Of course, if the player knows about these changes, then he can modify his basic strategy to again be +EV on the Play bet. Again, since the dealer acts first, must call all player raises and cannot come over the top, the Play bet will always be +EV, given knowledge of how the dealer behaves. The above house edge effects for the wager matrix changes are based on a player using the published basic strategy.

I stopped after looking at these two simple, but significant effects. That’s all I needed to see.

Usually, I’m very naive, and always assume the casino is operating according to fair rules, and everything is on the up-and-up. However, with the advent of this new type of game, where the shuffler actually reads all hands it deals (it must, as the dealer hand is the last out of the shuffler, and the operator hits the ‘stop’ button to tell the betting logic use the last hand), I’m getting a little nervous. Also, the nature of a heads-up poker game requires knowledge of your opponent. Although ShuffleMaster provides a complete model of this opponent, its always possible that something gets lost in the process, a transcription error occurs, and/or something changes, and basic strategy gets out of sync with the actual dealer behaviour.

I think the game could be fun and safe, provided that ShuffleMaster provides a few assurances to the players. First, they need to make it extremely clear, and verify, that there’s only one version of the wager matrix. Furthermore, this can never change. Additionally, they could provide assurances to the players that the betting logic is audited by built-in stats collection in the shuffler, and periodically checked against the published, unchanging house-way. If they can provide these assurances, you can feel safe walking up to the game for the first time, and betting following basic strategy. Otherwise, while possible, it’s a pretty big task for people to figure out the dealer betting strategy, and to devise the appropriate counter-strategy. I’m just there to have fun, not to play Big Blue (that can see your cards).

ShuffleMaster Ultimate Draw Poker Machine @ Viejas

Posted in Uncategorized by stephenhow on November 13, 2009

Table-Master_cutout_3There’s a new multi-player video “table” game at Viejas from ShuffleMaster, called Ultimate Draw Poker. (This game is different from the cards and table version of the game, which uses community draw cards.) The new Ultimate Draw machine seats up to five players, who play against a dealer hand. The game is “virtual single deck”, meaning that as far as any one player is concerned, you’re playing heads up against the dealer using a single deck. I’ll explain how they do this below.

The minimum bet (Ante) for this game is $3, and the maximum is $100. The video table is very nice, a single horizontal display for all player and the dealer hands, with nice visual effects (card animations, etc.). A vertical display is used to show a life-size dealer from the waist up, which is close enough to soft-core pornography to make you feel slightly uncomfortable. The dealer is dealt five cards face down, and also 5 replacement cards (not shown) from which she may draw. The remaining 42-card deck is then cloned for each seated player. Each player is dealt a five card hand of out a shuffled, 42-card cloned deck. The player decides what to discard, then draws from his cloned deck.

Once all players have discarded and drawn to their final hand, the dealer turns up her hand. The dealer applies a simple house-way discard policy:

  1. hold a pair or better, ELSE
  2. hold a four-card flush draw, ELSE
  3. hold an open-ended straight draw, ELSE
  4. hold all high cards (>= Jack), ELSE
  5. discard everything.

The dealer needs to make a pair or better to qualify. If she doesn’t qualify, you win 70% of your Ante bet. If she qualifies, then your Ante bet plays for even money against her hand.

Fortunately, “house-way” is a little weak, and a better player strategy exists (0.32% better than “house-way” vs. “house-way”):

  1. hold a pair of 3’s or better, ELSE
  2. hold a pair of 2’s unless flush draw w/ Jack or better, or unless kicker is King or better, ELSE
  3. hold a four-card flush draw (unless offsuit kicker better*), ELSE
  4. hold an open-ended straight (unless kicker better**), ELSE
  5. hold two highest cards >= Jack, ELSE
  6. hold JTs, ELSE
  7. hold highest card >= Ten, ELSE
  8. discard everything.

*Ace is better than four-card flush draw, unless draw contains Queen or bettter
*King is better than four-card flush draw, unless draw contains Jack or better
**the following table shows kickers better than open-ended straight draws

draw min kicker to hold
2345 Ten
3456 Ten
4567 Jack
5678 Queen
6789 King
789T Ace
89TJ Ace

The house edge is very small for this game, only 0.61% for the above player strategy. However, the bonus bet is really bad, since it pays something like a Jacks-or-better video poker game, but you’re playing a strategy to beat the dealer hand, not to win a bonus. For the following table, and above player strategy, the bonus bet has about a 14% house edge. If you want to play the bonus bet, go find a video poker machine, it’s faster and pays more.

Hand Win
Royal Flush 1000
Straight Flush 150
Four Of A Kind 25
Full House 8
Flush 7
Straight 5
Three of A Kind 3
Two Pairs 1
all others -1

There’s a small “collusion” opportunity in this game. Because the game is played with cloned decks, and each player acts in turn, a player acting last gets to see a lot of the 42-card cloned deck. For example, if you look at all the dealt player hands, you can see what’s available in the cloned deck (any card you see is in the cloned deck). And, when you see what’s drawn, you get more info of what’s available. There’s a few cases where this info would help you make a borderline discard decision. There’s probably aren’t enough situations like this to make it worthwhile, but I could be wrong.

Practice Viejas Card Craps Game

Posted in +EV, card craps by stephenhow on November 9, 2009

The best way to get the feel of the Viejas craps game is to actually play it. I wrote a Java applet to show the way you record rolls, and to model the 18-slot CSM with 44 sets of dice. You can look at the last 6 rolls or so, and figure out if you want to lay 10x odds on your Don’t Pass bet. I wrote this game because I wanted to try out laying 10x odds with a CSM model before I did it in real life. The best thing about writing down the rolls is that it gives you a better view on the key cards (e.g., Aces when the point is 6) than a mechanical 6 roll window.

Click on the screenshot below to play the game. I couldn’t embed it in this hosted blog, because they don’t allow Java applets here 😦

Card craps practice game.

Try out the game. You can start with a basic 6-roll window strategy, and go from there. I think the human is more capable of determining the risk from the key cards in the roll history, than a simple fixed 6 roll window (+1.8% player edge on the flat bet). If it plays well for you, then come on out to San Diego.

Card Craps Counting With Pen & Paper @ Viejas

Posted in +EV, card craps by stephenhow on November 5, 2009

I just figured out the perfect way to play card craps at Viejas Casino. I always see Baccarat and Roulette players recording and studying the hand history right at the table, so I figured I’d make real use out of the right to pen & paper at the craps table. I sat down at the CSM craps game tonight, and recorded each roll on paper. That allowed me to look over the last 5-6 rolls, and see if the count was positive for laying odds on my Don’t Pass bet. This took all the guesswork out of counting, and was quite fun and relaxing. Before, I’d have to think back and guess if I saw the key cards for the point. It was inaccurate, and I probably made a lot of mistakes. Now, it’s smooth sailing, and I know exactly when to lay odds.

I had a good winning session (my 3rd in 3 consecutive nights), and played for about an hour or so. The play is pretty fast out of the CSM, and I recorded about 300 rolls (all of them). I played Don’t Pass on 62 points, laying odds on 24 of them (39%). It was really easy to see when the count was good. (Of course, any time the count is positive, I should be laying 10x odds.) When I change my odds, I note it to the right of the roll. I also use exclamation marks (!) to indicate the outcome when I’m laying odds. For example, “win!!!” means I won when laying 3x odds; “lose!” means I lost when laying 1x odds. I use a horizontal line to indicate the come-out roll.

I played with two other semi-regulars tonight (compared to me, everyone else is semi-regular). One guy was playing $5 pass line with 5x-10x odds, and got killed. He watched me vary me odds bet during the roll, and saw I usually won when laying odds, and I usually didn’t have odds when I lost. After he busted out, he brought out another $200, but decided not to play. Instead, he watched what I was doing with the notation. I’m sure he knows that card craps is not normal, and that its possible to count the cards in some way. Of course, you’re not really going to figure it out unless you have a lot of time and energy on your hands. Or find this site. I really hope someone reads this, and understands how good the game is. For crying out loud … you can count with pen and paper right at the table! This is completely and absolutely classic.

Below are photos of my session (I don’t have a scanner). Take a look, and you should see exactly how to play. I highly recommend taking advantage of this method of playing. It’s the only way I’m going to play the game in the future.

card craps rolls 1,2

Card craps session notation, pages 1 & 2


Card craps session notation, pages 3 & 4.

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!