Mulligan Poker

Introduction

Three Card Mulligan is an alternative version of Three Card Poker where players can swap their initial hand for a second one if they wish. This game was developed and patented by me and is distributed by Shuffle Entertainment. It first launched in January 2013 at the Cowboys Casino in Calgary, Alberta.

Rules

1. A single 52-card deck is used.
2. The ranking order for poker hands is outlined as follows:

• Straight flush
• Three of a kind
• Straight
• Flush
• Pair
• Ace high and less

Gameplay commences with the player placing an Ante bet, and they also have the option to make an additional bet known as a Pair Plus.

The dealer will deal three cards each to both the player and themselves, with the dealer's cards being face down.

Players can decide whether to stick with their hand or opt for a Mulligan.

If a player selects the Mulligan option, they must then place a Mulligan bet that matches their initial Ante and will receive three new cards in exchange for their original hand.

In the event of taking a Mulligan, the player has the opportunity to place a new Pair Plus bet based on their updated hand.

The dealer will turn over his cards.

Should the dealer's hand reveal a king high or better, they will stand. Conversely, if the dealer's hand is a queen high or lower, they will take a Mulligan, discarding their hand in exchange for three new cards.

The dealer will evaluate their hand in comparison to the player's hand, with the higher hand declared the winner. If the dealer has the upper hand, the player will lose both the Ante and any Mulligan bet placed. If the player’s hand is superior, both the Ante and the Mulligan bets will pay out based on the payout table. A tie will simply result in no winner.

Payout for the Pair Plus wager(s) will be determined according to the payout table provided below.

Ante Analysis

The following table outlines the probabilities and expected returns for every possible outcome of the Ante bet in Three Card Mulligan, with the bottom right cell indicating a house edge of 3.57%.

Players will typically place the Mulligan bet about 50.0% of the time, resulting in an average wager of 1.5 units and an Element of Risk of 2.38%.

Pair Plus Analysis

The next table depicts the probabilities and potential returns for all outcomes related to the initial Pair Plus wager in Three Card Mulligan, showing a house edge of 7.28% in the bottom right cell.

The subsequent table illustrates the probabilities and expected returns for later Pair Plus bets in Three Card Mulligan under the assumption that players employ an optimal strategy, with the bottom right cell revealing a house edge of 7.66%. This variation in house edge occurs due to the impact of the discarded cards.

Strategy

Players should refrain from playing with hands lower than K-10; otherwise, they should consider taking a Mulligan.

Written by: Michael Shackleford