Wizard Recommends
On this page
Five-Card Mulligan Poker
Introduction
Five-Card Mulligan Poker is a variation on traditional poker that is no longer in circulation, previously offered by online casinos that utilized specific software. The concept is protected by a patent (patent number Odds On Below are the guidelines for the five-card variant as documented by Odds On. It's worth noting that both three and seven card forms have been explored and are included in the patent application. 7,735,830 ) by yours truly.
All poker hands are evaluated using the standard poker scoring system.
Rules
- A single 52-card deck is used.
- The game begins with players placing an ante wager, and they also have the option to make an additional bonus wager if they so choose.
- The dealer will deal five cards to each player and five cards for themselves, with the dealer's cards placed face down.
- Players can either keep their current hand or opt for a Mulligan.
- If a player decides to take a Mulligan, they are required to place an additional bet equal to their original ante. This option allows them to discard their initial five cards in exchange for five new cards from the deck. However, opting for a Mulligan will also cause them to lose their bonus bet, if one was placed.
- Should the dealer have an ace or better, they will choose to stand.
- The dealer will turn over his cards.
- If the dealer's highest card is a king or less, they will opt for a Mulligan, discarding their current hand for a new one.
- After the dealer has received their new hand, they will compare it to the player's hand; the hand with the higher rank claims victory. If the dealer's hand is superior, the player loses both their ante and any additional wagers they made. Conversely, if the player's hand wins, they will receive payouts for both their ante and raise according to the pay structure provided. A tie leads to no winnings.
- The bonus bet payout is determined according to the designated payout table.
- For instance, a player who initially bet $25 could find themselves with a poor hand, choose to swap it for a new one, and place a raised bet of $25 in accordance with the rules. If the dealer reveals an ace or better, they will stand. In this scenario, the player would have won with the higher hand, resulting in both the ante and raise being paid back at a rate of 1 to 1, totaling a win of $50.
Ante and Raise Pay Table
| Player Hand | Pays |
|---|---|
| Royal flush | 100 to 1 |
| Straight flush | 50 to 1 |
| Four of a kind | 10 to 1 |
| Full house | 3 to 1 |
| All other | 1 to 1 |
Bonus Bet Pay Table
| Player Original Hand | Pays |
|---|---|
| Royal flush | 10,000 to 1 |
| Straight flush | 1,000 to 1 |
| Four of a kind | 200 to 1 |
| Full house | 100 to 1 |
| Flush | 50 to 1 |
| Straight | 30 to 1 |
| Three of a kind | 10 to 1 |
| Two pair | 5 to 1 |
| All other | Lose |
The chart below outlines all possible results for Five-Card Mulligan Poker. The house edge is calculated at 3.152%. Players will decide to raise their bets approximately 45.24% of the time, averaging about 1.4524 units in wagers. This translates to a risk factor of 3.152% divided by 1.4524, which equals approximately 2.170%. The standard deviation for the game is 1.610.
Analysis
A player achieves victory with three of a kind, and the minimum bet is 1.
Five-Card Mulligan Return Table
| Event | Pays | Probability | Return |
|---|---|---|---|
| Player wins with nothing, bet of 1 | 1 | 0.015127 | 0.015127 |
| Player wins with pair, bet of 1 | 1 | 0.263124 | 0.263124 |
| Player wins with a two pair, bet of 1 | 1 | 0.044279 | 0.044279 |
| A player claims a win with a straight flush, with a minimum bet of 1. | 1 | 0.020721 | 0.020721 |
| Player wins with straight, bet of 1 | 1 | 0.003902 | 0.003902 |
| Player wins with flush, bet of 1 | 1 | 0.001956 | 0.001956 |
| Player wins with full house, bet of 1 | 3 | 0.00145 | 0.004349 |
| Player wins with four of a kind, bet of 1 | 10 | 0.000243 | 0.002431 |
| When betting 2, a player wins with three of a kind. | 50 | 0.000014 | 0.000693 |
| Player wins with royal flush, bet of 1 | 100 | 0.000002 | 0.000153 |
| Player wins with nothing, bet of 2 | 2 | 0.0257 | 0.051401 |
| Player wins with pair, bet of 2 | 2 | 0.119065 | 0.238129 |
| Player wins with a two pair, bet of 2 | 2 | 0.01975 | 0.0395 |
| When betting 2, a player wins with a straight flush. | 2 | 0.009114 | 0.018228 |
| Player wins with straight, bet of 2 | 2 | 0.001762 | 0.003523 |
| Player wins with flush, bet of 2 | 2 | 0.000889 | 0.001779 |
| Player wins with full house, bet of 2 | 6 | 0.00063 | 0.003781 |
| Player wins with four of a kind, bet of 2 | 20 | 0.000103 | 0.002056 |
| It is advisable for players to change their hand if they hold cards AK953 or lower, while they should stick with cards AK954 or higher. | 100 | 0.000006 | 0.000623 |
| Player wins with royal flush, bet of 2 | 200 | 0.000001 | 0.000141 |
| Player loses with bet of 1 | -1 | 0.196808 | -0.196808 |
| Player loses with bet of 2 | -2 | 0.275306 | -0.550612 |
| Player ties with bet of 1 | 0 | 0.000021 | 0 |
| Player ties with bet of 2 | 0 | 0.000028 | 0 |
| Total | 1 | -0.031523 |
Strategy
This game was thoroughly examined through random simulations conducted in C++, and the return table is derived from analysis of over 22 billion hands played.
Methodology
Offering mathematically sound strategies and insights for casino games like blackjack, craps, roulette, and various others available for play.