Wizard Recommends
On this page
Six Card Poker
Rules
- In Six Card Poker, players compete directly against the dealer in a one-on-one format. The goal is to form a winning five-card hand using a total of six cards, outshining the dealer's hand.
- The game is conducted with a standard deck of 52 playing cards, following traditional poker guidelines for evaluating hands and scoring.
- To begin, the player makes an Ante Bet.
- The dealer distributes six cards facedown to the player while giving three cards faced up and three faced down to himself.
- The player reviews their cards and faces a decision: they can either fold, forfeiting their Ante bet, or they can raise their bet by matching the Ante amount. It's important to note that players are prohibited from disclosing their card information to others.
- Once the player has made their decision, the dealer uncovers his hidden cards and evaluates his top five-card combination against the player's top five-card combination. To qualify, the dealer needs at least an ace and a king.
- If the dealer fails to qualify, the player’s Ante bet results in a push. The resolution of the raise bet occurs in the following manner:
- Should the dealer's hand surpass the player's hand, the player loses their raise bet.
- Conversely, if the player’s hand is stronger than the dealer's, they receive a 1:1 payout on their raise bet.
- In cases where the hands tie, the player’s raise bet will also be a push.
- If the dealer does qualify:
- If the dealer's hand is superior, the player forfeits both their Ante and raise bets.
- On the other hand, if the player's hand defeats the dealer's, they will be rewarded with a 1:1 return on both their Ante and raise bets.
- Ties in hands will result in both the Ante and raise bets being pushed.
- Additionally, there are two optional side bets called Aces Up and Two-Way Bad Beat, which will be detailed later.
Analysis
A thorough analysis of the game was conducted using brute force and combinatorial methods, leading to the conclusion summarized in the following table. The house edge is calculated at 1.2717%. With an average wager size of 1.6987, the element of risk is 0.7486%.Ante Bet Analysis
| Outcome | Dealer Qualifies | Net Win | Combinations | Probability | Return |
|---|---|---|---|---|---|
| Player Wins | yes | 2 | 1,040,023,036,938,350 | 0.272693 | 0.545387 |
| Player Wins | no | 1 | 755,514,209,224,548 | 0.198095 | 0.198095 |
| Ties | yes | 0 | 210,847,746,240 | 0.000055 | 0.000000 |
| Ties | no | 0 | 50,992,983,876 | 0.000013 | 0.000000 |
| Fold | - | -1 | 1,149,186,512,820,950 | 0.301316 | -0.301316 |
| Dealer Wins | no | -1 | 2,937,744,249,924 | 0.000770 | -0.000770 |
| Dealer Wins | yes | -2 | 865,968,968,971,212 | 0.227056 | -0.454113 |
| Total | 3,813,892,312,935,100 | 1.000000 | -0.012717 |
Strategy
The basic strategies for playing the game are outlined below.
Intermediate basic strategy:
- Players are advised to fold if the dealer presents a superior hand with just his three face-up cards. This rule takes precedence over all others.
- Fold with ace-10 or lower.
- Raise with ace-king or higher.
- With an ace-queen hand, players should fold if the dealer shows an ace or a king.
- If holding an ace-jack, folding is recommended if the dealer reveals an ace, king, or queen.
Simple basic strategy:
- Players are advised to fold if the dealer presents a superior hand with just his three face-up cards. This rule takes precedence over all others.
- Raise with ace-king. Fold otherwise.
- With optimal play, the house edge is 1.27%.
- By implementing the intermediate basic strategy, the house edge is recorded at 1.48%.
- Adopting the simpler basic strategy results in a house edge of 1.63%.
Aces Up
Aces Up is a side bet that relies solely on the poker strength of the player's hand. The following table delineates payouts for various hands, their probabilities, and their expected returns. The lower right cell indicates a house edge of 3.30%.
Aces Up Analysis
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | 500 | 188 | 0.000009 | 0.004617 |
| Straight flush | 100 | 1,656 | 0.000081 | 0.008134 |
| Four of a kind | 30 | 14,664 | 0.000720 | 0.021609 |
| Full house | 10 | 165,984 | 0.008153 | 0.081530 |
| Flush | 8 | 205,792 | 0.010108 | 0.080867 |
| Straight | 6 | 361,620 | 0.017763 | 0.106576 |
| Three of a kind | 4 | 732,160 | 0.035963 | 0.143853 |
| Two pair | 2 | 2,532,816 | 0.124411 | 0.248821 |
| Aces | 1 | 751,332 | 0.036905 | 0.036905 |
| Loser | -1 | 15,592,308 | 0.765886 | -0.765886 |
| Total | 20,358,520 | 1.000000 | -0.032973 |
Two-Way Bad Beat
The 'Two-Way Bad Beat' bet yields a payout if either the player or the dealer holds a pair of aces or better and loses. Payouts vary based on the severity of the losing hand; higher losing hands will receive better payouts, as long as there is no tie.
The table below provides detailed odds. The zeroes representing the probability and payout of a losing straight flush are not a typographical error; it happens approximately once in 25 trillion times. This occurrence inspired the plot of the film Honeymoon in Vegas, but I digress. The table's lower right cell shows a house edge of 10.84%.
| Two-Way Bad Beat Analysis | |||
|---|---|---|---|
| Event | Pays | Probability | Return |
| Straight Flush | 10000 | 0.000000 | 0.000000 |
| Four of a Kind | 5000 | 0.000001 | 0.006250 |
| Full House | 500 | 0.000099 | 0.049370 |
| Flush | 200 | 0.000307 | 0.061440 |
| Straight | 100 | 0.000972 | 0.097168 |
| Three of a Kind | 35 | 0.004056 | 0.141965 |
| Two Pair | 10 | 0.034513 | 0.345127 |
| Pair of Aces | 9 | 0.015036 | 0.135328 |
| Loser | -1 | 0.945016 | -0.945016 |
| Total | 1.000000 | -0.108367 | |
Acknowledgments
While I usually prefer to calculate metrics independently, in this instance, ShuffleMaster, the game's promoter, generously provided a mathematical report prepared by mathematician Cindy Liu, which informs the Ante bet analysis. The Two-Way Bad Beat is based on analytical work by Elliot Frome, while I carried out the analysis regarding Aces Up.