Three Card Mulligan Poker

Introduction

Introduction

Three Card 2nd Chance is an innovative poker variant that I developed and patented, and it is being promoted by Shuffle Entertainment. The main idea is that if a player is unsatisfied with their initial hand, they can simply increase their bet to exchange it for a new one. The dealer can also change their hand under specific conditions. Ultimately, the hand with the higher value wins, guaranteeing at least even money payouts.

Rules

1. The game utilizes a standard 52-card deck. All hands are evaluated based on traditional poker rules, although the ranking order differs for 3-card hands.
2. Gameplay commences when the player places an Ante bet. There is also an option for the player to add a Pair Plus bet at this stage.
3. The dealer will deal three cards to the player and three to themselves, with the player’s cards revealed and the dealer’s cards concealed.
4. Players can decide either to keep their current hand or exchange it for a new set of three cards, a choice referred to as taking a 'Mulligan.'
5. If the player opts for a Mulligan, they must discard their existing cards and place a Raise bet equivalent to their initial Ante. Additionally, they have the option to make a new Pair Plus bet for their Mulligan hand.
6. After the player makes their move, the dealer will reveal their cards.
7. Should the dealer's hand be a king high or better, they will stick with their current hand.
8. Conversely, if the dealer possesses a queen high or lower, they will discard their hand in exchange for a new set of three cards.
9. Once the dealer's hand is revealed, it will be compared to the player's hand, with the higher hand declared the winner. If the dealer wins, the player forfeits both their Ante and Raise bets. On the other hand, if the player secures the higher hand, they will be rewarded based on the respective Ante and Raise payout tables. In the case of a tie, no bets are lost or gained.

Strategy

Players should retain hands that are king-ten or better; anything lower should prompt a Mulligan. This means the minimum hand worth keeping is king-ten-2, while a hand as high as king-9-8 would necessitate opting for a Mulligan.

Ante Only Analysis

The upcoming table outlines potential results if a player bets the Ante alone and chooses to fold on K87 or less.

The bottom right cell indicates a house edge of 3.57%. Players will raise their bet approximately 49.95% of the time, resulting in an average final wager of about 1.4995 units.Element of Risk 0.035744/1.4995 = 2.38%.

Pair Plus

The Pair Plus wager on the original hand shares the same payout structure and probabilities as in Three Card Poker. The subsequent table details the exact odds, revealing a house edge of 7.28% in the lower right cell.

If the player decides to place a Pair Plus bet again on the Mulligan hand, the odds will be adjusted, particularly if they adhere to the optimal strategy of opting for a Mulligan when holding king-ten or lower. In this case, the lower right cell of the next table shows that the house edge for the Pair Plus on the Mulligan is 7.65%, which is an increase of 0.38% compared to the original situation.

Methodology

This analysis was performed through random simulation, excluding the initial Pair Plus wager. It is based on the assumption that the dealer reshuffles the deck after each round.

Given that both the player and dealer are capable of exchanging cards, the total number of possible combinations for the game is astonishing, calculated as (52,3) × combin(49,3) × combin(46,3) × combin(43,3) = 76,277,828,779,152,000, a computation that would take an extraordinary amount of time to complete. combin Strategies and insights rooted in mathematical principles are available for a wide array of casino games, including blackjack, craps, roulette, and many others.

Written by: Michael Shackleford