Discount Gambling

Dealer Bluff Collusion Strategy (+EV)

Posted in +EV, dealer bluff by stephenhow on January 28, 2013

dealerBluffWhen you play ShuffleEntertainment’s Dealer Bluff 6-Card Poker, you can feel at a disadvantage. The dealer makes the first bet (1x to 3x the Ante), and of course, you don’t know what he has. He might be bluffing. It’s easy enough to fold your weak hand to a strong bet, or to raise your strong hand against a weak bet. But the in-between decisions aren’t obvious, and you’re left blindly following basic strategy.

Interestingly, full-table collusion (6 players) makes this game +EV against the dealer. After all, the confederates’ 36 cards give some indication of what the dealer holds. (E.g., the dealer can’t have a pair of Aces when the confederates hold three of them.) So, you can get better idea of when to call, raise, or fold your hand. I worked out the collusion strategy details, hoping for a big edge (some games, ahem, yield near double-digit edges with collusion; you never know). Alas, I only came up with a +0.66% +EV 6-way collusion strategy 😦

The full rules and game details are available from the WoO. Briefly, you post the familiar ShuffleEntertainment Ante = Blind bets before the hand starts, and each player and the dealer receives 6 cards. The shuffler reads the dealer hand, and bets 1x to 3x against the players. The player, in turn, must either call (wager a Play bet equal to the dealer bet), raise (wager a Play bet twice the amount of the dealer bet), or fold his Ante and Blind. The dealer will always call any raise. The hands are then turned over, and the bets are resolved. The remaining Antes push if the dealer doesn’t qualify with a pair or better. The Play bets always receives even-money action against the dealer hand. The Blind bets only pay for winning player hands of trips or better, according to a paytable.

The dealer follows a simple table that dictates the 1x, 2x, and 3x betting frequencies for each type of hand (nothing, low pair (2-5), mid pair (6-9), high pair (T-A), two pairs, etc.). This betting table completely describes “how the dealer plays”, and basic strategy is a nearly optimal counter-strategy (based on your hand only).

My collusion strategy tracks the “strong ranks” available to the dealer. Strong ranks are defined as card ranks (2 thru A) that the confederates only hold 0 or 1 copies of. These ranks are “strong”, because of the dealer’s chance of holding a pair of them. For example, the Seven is a strong rank for the dealer if the 6 confederates hold 1 or less Seven’s in total. But if the confederates hold 2 Aces, then the Ace is not a strong rank for the dealer. When you hold a pair, you’re usually interested in the number of strong ranks that are higher than your pair. When you hold 22’s or less, you’re interested in the total number of strong ranks.

Dealer Bluff 6-Way Collusion Strategy
Dealer Bet Basic Strategy Collusion Strategy
1x 2x pair 3’s or better 2x two pairs or better
2x pair 7’s thru A’s when 0-2 higher strong ranks
2x pair 3’s thru 6’s when 0-1 higher strong ranks
2x pair 2’s when 0 strong ranks
1x pair when 3 or less higher strong ranks
fold pair when 4+ higher strong ranks
1x KJ8 or higher 2x AK when 0 strong ranks
1x A-high when 0-2 strong ranks
1x K-high when all Aces seen and 0-2 strong ranks
1x K-high when 3 Aces seen and 0-1 strong ranks
fold others fold others
2x 4x pair J’s or better
4x pair T’s w/ 0-2 cards under T
4x two pairs or better
4x pair 9’s thru A’s when 0 higher strong ranks
2x pair 7’s thru T’s
2x pair 6’s w/ 0 cards under 6
2x pair 8’s thru K’s when 1 higher strong ranks
2x pair 5’s thru 7’s when 0 higher strong ranks
fold other pairs fold other pairs
3x 6x with pair K’s with A-kicker, or better 6x two pairs or better
6x pair A’s or K’s when 0 higher strong ranks
3x with pair T’s thru K’s 3x pair 8’s thru Q’s when 0 higher strong ranks
fold pair of 9’s or less fold others

For each dealer bet (1x-3x), the strategy is listed in priority from the top down. Yes, the strategy says to fold a pair of K’s against a 3x dealer bet if 1 or less Aces are held among the 6 confederates. There are undoubtedly better collusion strategies out there. As I said, I was hoping for a big edge, especially since you have 6x, 4x, and 2x raise opportunities. But I couldn’t find much more than the above +0.66% strategy, so I kept it simple and published it for reference’s sake.

How would you use this strategy in practise? Well, I guess you’d find a table full of friendly, helpful players. Then you start betting black ($100 Antes), and start asking questions when you need help. Say you’re holding AK, and the dealer bet is 1x. You start asking around if anyone has any deuces, treys, fours, etc. You count the dealer strong ranks (when the players have 1 or less cards of the rank), and play accordingly. When the floorman asks you not to discuss your hands during play, just tell him it’s not going to help much. You should be able to play for an hour before they ask you to leave.

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).