# Six Card Poker

## Rules

1. Six Card Poker is a house-banked poker game played heads up against the dealer. The object of the game is to win by having a better five card poker hand than the dealer using six cards.
2. The game is played using one standard 52-card deck. The game uses standard poker rules for scoring and comparing hands.
3. To begin, the player makes an Ante Bet.
4. The dealer deals six cards face down to the player. The dealer deals to himself, three cards face up and three cards face down.
5. The player examines his cards and must either fold the hand, losing his Ante, or raise by making an additional wager that is equal to his ante. Players may not share information about their cards with other players.
6. The dealer reveals his hole cards and compares his best five card hand to the player’s best five card hand. The dealer must qualify with ace-king or higher.
7. If the dealer does not qualify, the player’s Ante bet is a push. The raise bet is resolved as follows:
• If the dealer’s hand beats the player’s hand, the player loses his raise bet.
• If the player’s hand beats the dealer’s hand, the player is paid 1 to 1 on his raise bet.
• Otherwise, the player’s raise bet is a push.
If the dealer does qualify:
• If the dealer’s hand beats the player’s hand, the player loses his Ante and raise bets.
• If the player’s hand beats the dealer’s hand, the player is paid 1 to 1 on his Ante and raise bets.
• Otherwise, the player’s Ante and raise bets push.
Analysis
The game was analyzed through brute force, combinatorial analysis. The following table summarizes the analysis results. The bottom left cell shows the house edge of 1.2717%. With an average bet size of 1.6987, the element of risk is 0.7486%.

### Ante Bet Analysis

Outcome Dealer Qualified Net Combinations Probability Frequency Return
Fold - -1 93,119,328,972 0.301316 1 in 3.3 -0.301316
Player Wins no 1 755,514,209,224,548 0.198095 1 in 5.0 0.198095
Ties no 0 50,992,983,876 0.000013 1 in 74,792 0.000000
Dealer Wins no -1 2,937,744,249,924 0.000770 1 in 1,298 -0.000770
Player Wins yes 2 1,040,023,036,938,352 0.272693 1 in 3.7 0.545387
Ties yes 0 210,847,746,240 0.000055 1 in 18,088 0.000000
Dealer Wins yes -2 865,968,968,971,212 0.227057 1 in 4.4 -0.454113
Total       1   -0.012717
Strategy

Two basic playing strategies are presented below.

Intermediate basic strategy:
1. Fold if dealer has a higher ranked hand using his three up cards alone. This rule supersedes all other rules.
2. Fold with ace-10 or lower.
3. Raise with ace-king or higher.
4. With ace-queen, fold if the dealer is showing an ace or king.
5. With ace-jack, fold if the dealer is showing an ace, king, or queen.

Simple basic strategy:
1. Fold if dealer has a higher ranked hand using his three up cards alone. This rule supersedes all other rules.
2. Raise with ace-king. Fold otherwise.

• With optimal play, the house edge is 1.27%.
• Using the intermediate basic strategy, the house edge is 1.48 %.
• Using the simple basic strategy, the house edge is 1.63%.