There is simply not enough information available to overcome the house edge. I note that perfect five-player collusion gives a house edge of about 0.61%. The standard deviation from perfect six-player collusion is 1.598. The player edge from perfect six-player collusion is 7.327%. My program computed optimal strategy on-the-fly for each hand. This strategy is unknowable in any practical sense.

The following table is based on a simulation of two billion (2,000,000,000) rounds of HCF, where the players use perfect collusion strategy. I will call these 10 cards the “remainder.” The small size of the remainder is what gives collusion its power in HCF. This leaves only ten (10) unknown cards from which the dealer will select seven for his hand. Because seven cards are dealt to each hand, a full table will require 42 cards for the player hands. The HCF tables I have seen have spots for six players.

If the player and dealer push, then the Ante and Play bets push. If the player loses, he forfeits his Ante and Play bets. If the player wins, his Ante and Play bets are paid even money. If the dealer qualifies then the player and dealer compete. If the dealer does not qualify, the Ante bet wins even money and the Play bet pushes. The dealer needs at least a nine-high three card flush or better to qualify. The dealer then turns over his cards and makes his best flush. The Play bet amount depends on the number of cards in the players flush. The player can then fold and surrender his Ante or can make a Play bet to compete against the dealer. Flushes with the same number of cards are ranked by their highest card(s). Flushes are first ranked by the number of cards used in the flush. To rank flushes, the following two criteria are used. The player makes the highest ranking flush from his seven cards. The player and the dealer receive seven cards, face-down. They use the familiar Ante/Raise structure. The rules for HCF are fairly easy to understand. This post presents my analysis of collusion advantage play against HCF. He gave a practical strategy that yielded a 3.1% player edge. With six players at the table sharing full information about their hands (colluding), he stated that these players could each get a 7.3% edge over the house. High Card Flush (HCF) is a relatively new game that distinguished itself by winning “Best Game” at the Cutting Edge Table Games Conference in 2012. Recently Stephen How demonstrated that HCF has a significant collusion issue (see this post at his blog, ).

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