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.

7 Responses

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  1. Tom said, on January 29, 2013 at 9:35 am

    Thanks for your analysis; I too am surprised a larger edge can’t be obtained with so many known cards and the ability to raise 6x.

    Would you have any interest in analyzing the 5 Card Hi-Lo game? It is rather new and I can’t find any numbers on it anywhere. Details of the game are located here: http://www.nj.gov/oag/ge/docs/TempRegs/5cardhi-lotextrevised112712.pdf

    Thanks!

    • stephenhow said, on January 29, 2013 at 9:38 am

      Thanks for the tip on the new game. Sure, I’ll look at it to see if there’s a collusion edge. If I find a big one, we’ll keep it secret 🙂

      I could run a Monte Carlo analysis to see what the upper limit on Dealer Bluff 6-way collusion is. (I probably should have done it before looking for any collusion strategy!) I’m pretty sure I didn’t miss any big edge, but you never know …

    • stephenhow said, on February 2, 2013 at 11:45 am

      Tom,

      I just ran a Monte Carlo analysis of the 5-Card Hi-Lo game, and even with perfect collusion among 6 confederates, the house edge is still 1.0%. So there’s no collusion advantage play here 😦

  2. Tom said, on February 4, 2013 at 9:59 am

    Ah, bummer. Thanks again for trying, though! What is the HE in this game? Just trying to gauge how much improvement the optimal collusion helped.

    • stephenhow said, on February 4, 2013 at 3:48 pm

      I didn’t bother calculating the house edge for the game; that’s the beauty of a Monte Carlo collusion analysis. The game didn’t seem very fun or challenging, so I didn’t bother with the full analysis.

  3. James said, on February 4, 2013 at 6:10 pm

    Steve,

    Any interest in analyzing the collusion strategy on top of the sort(card sorting) for caribbean stud ?

    Sometime(you never know!) the AP can sorts the cards into these two groups:

    High cards = {K, A}
    Low cards = {2, 3, 4, 5, 6, 7, 8, 9, T, J, Q}.

    The AP looks at the dealer’s cards and counts the number of high cards, which will be one of the numbers: 0, 1, 2, 3, 4, or 5. This total includes the dealer’s up-card, which may be an Ace/King as well(no perfect information !).

    Again, The AP looks at other players hand and count the number of high card, he should able to differentiate the Aces or King(with perfect information)

    Based on the number of APs’ high cards and the number of dealer high cards, the AP decides to raise or fold.

    Double digit player edge ? 🙂

    James

    • stephenhow said, on February 9, 2013 at 2:50 pm

      If it was easy to edge sort the cards in a carnival game, then you should attack Mississippi Stud. You’d beat the game silly …


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