Discount Gambling

When 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.

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.