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Last Updated: October 31, 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.

Royal Match Version 3- 1 to 8 Decks

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.

Royal Match — Version 4 — 1-8 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


Written by: Michael Shackleford

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