Last Updated: November 25, 2017

# 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.

### Royal Match — Version 1 — Six Decks

Event Pays Combinations Probability Return
Royal match 25 144 0.002968 0.074202
Easy match 2.5 11,868 0.244620 0.611551
No match -1 36,504 0.752412 -0.752412
Total   48,516 1.000000 -0.066658

### Royal Match — Version 2 — One Deck

Event Pays Combinations Probability Return
Royal match 10 4 0.003017 0.030166
Easy match 3 308 0.232278 0.696833
No match -1 1,014 0.764706 -0.764706
Total   1,326 1.000000 -0.037707

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

### Royal Match House Edge

Number of Decks Version 1 Version 2
1 0.108597 0.037707
2 0.083271 0.008215
4 0.070792 -0.006317
6 0.066658 -0.011130
8 0.064597 -0.013531

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%.

### Royal Match Version 3- Six Decks

Hand Combinations Probability Pays Return
Royal match 144 0.002968 25 0.074202
Suited blackjack 576 0.011872 5 0.059362
All other matches 11292 0.232748 2.5 0.58187
Loss 36504 0.752412 -1 -0.752412
Total 48516 1   -0.036977

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

Decks House Edge
1 7.84%
2 5.34%
3 4.52%
4 4.11%
5 3.86%
6 3.70%
7 3.58%
8 3.49%

## 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.

### Royal Match — Version 4 — Six Decks

Event Pays Combinations Probability Return
Player and Dealer Royal Match 1000 19152 0.000008 0.008242
Player royal match 25 6877728 0.00296 0.073996
Suited 2.5 568417860 0.24462 0.611551
Loser -1 1748359080 0.752412 -0.752412
Total   2323673820 1 -0.058622

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

Number
of Decks
House
Edge
1 10.14%
2 7.59%
3 6.73%
4 6.3%
5 6.04%
6 5.86%
7 5.74%
8 5.64%

## 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.

### Six-Deck Progressive Royal Match — \$10,000 Jackpot and No Other Players

Event Pays Combinations Probability Return
Crown Treasure \$10,000 19,152.00 0.000008 0.082421
Royal Match \$60 6,877,728.00 0.002960 0.177591
Straight Flush \$10 82,762,560.00 0.035617 0.356171
Loser \$0 2,234,014,380.00 0.961415 0.000000
Total   2,323,673,820.00 1.000000 0.616183

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.

### Progressive Royal Match Breakeven Points

Other Players Breakeven Point
6 \$53,567.70
5 \$54,067.70
4 \$54,567.70
3 \$55,067.70
2 \$55,567.70
1 \$56,067.70
0 \$56,567.70

## 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.

### Royal Match — Version 6 — Six Decks

Event Pays Combinations Probability Return
Royal match 50 144 0.002968 0.148405
Two suited cards 2 11,868 0.244620 0.489241
All other -1 36,504 0.752412 -0.752412
Total   48,516 1.000000 -0.114766

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.

### Return with Crown Treasure

Bet Return
\$25 -0.114437
\$10 -0.113942
\$5 -0.113118
\$1 -0.106524

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

### Version 6 Summary

Decks Return Value CT
1 -0.149321 0.007388
2 -0.128454 0.007539
6 -0.114766 0.008242
8 -0.113068 0.008360

Written by: