Royal Match

Introduction

The royal match is a simple bet that pays a bonus if the first two cards are suited (an easy match) and a top bonus for a suited king and queen (a royal match). Below are probability tables for various versions I have seen through the years.

 

 

 

 

The following table displays the house edge for each version given the number of decks used.

The probabilities for the royal match are easy to derive.Lets use n for the number of decks of cards. The number of two card combinations is combin(52×n,2). The number of ways to make a royal match is 4*n². This is because there are 4 suits and n ways to choose the queen and n ways to choose the king. The number of ways to make an easy match is 4×(combin(13×n,2)-n²). The 4 is the number of suits and combin(13×n,2) is the number of ways to arrange 2cards from a given suit. You must also subtract the number of ways to make a royal match.

The probability of an easy match is 4×(combin(13×n,2)-n²)/combin(52×n,2).

The probability of a royal match is 4×n²/combin(52×n,2).

Royal Match - Version 3

In a third version there is a separate pay for a suited blackjack as follows.

 

• Royal Match pays 25 to 1
• Suited Blackjack pays 5 to 1
• Easy Match pays 5 to 2

 

The following table shows the expected value for a 6-deck game is -3.70%.

The next table shows the house edge for various number of decks for version 3.

Royal Match - Version 4

 

The Shufflemaster TMS 300 is an electronic blackjack game, played facing a giant video screen of a dealer. It features a Royal Match side bet, adding a pay for the player and dealer both having a royal match. Following is the return table for six decks.

 

 

The next table shows the house edge by number of decks.

 

 

Royal Match — Version 5

 

Version 5 of the Royal Match is a progressive jackpot on ShuffleMaster TableMax units. These are the electronic blackjack games with a big screen, usually showing a pretty and very buxom dealer.

In this version, the side bet is always $1. It pays a progressive jackpot for a "Crown Treasure," which is both the dealer and player having a Royal Match. Smaller pays are $60 for a player only royal match, and $10 for a player straight flush, which I assume means the player's first two cards are suited and consecutive, including A-2.

There is also a $500 envy bonus, which pays if you make the side bet, and another player gets a Crown Treasure. The other player does not have to make the side bet for other players to qualify for the Envy Bonus.

The following table shows a hypothetical return table, for six decks, a $10,000 jackpot, and no other players.

 

 

The general formula for the return in a six-deck game is 0.533762 + 0.082421×j + 0.004121× p, where j is the jackpot divided by $10,000, and p is the number of other players (not counting yourself).

The next table shows the breakeven points, in which the expected return is exactly 100%, given the number of other players, in a six-deck game.

 

Version 6

On January 29, 2021, at the Rampart casino in Las Vegas I noticed yet another version of Royal Match. This one had a simple 2-50 pay table, but threw in a $1,000 bonus if both the player and dealer have a Royal Match. Before considering that bonus, here is the return table, based on the player's hand only and six decks.

The table above shows a house edge of 11.48%.

There is a $1,000 bonus if both the player and dealer have a Royal Match. In a six-deck game, the probability of that is 1 in 121,328. This makes the value of bonus $0.008242121, or about 82% of a penny.

The next table shows the expected return with the Crown Treasure for various bet amounts. Remember, the Crown Treasure bonus is a fixed $1,000, so the value of the bet decreases as the bet size goes up.

The final version 6 table shows the expected return by number of decks and the fixed value of the Crown Treasure (CT) bonus.

Written by: Michael Shackleford