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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
Royal Match — Version 2 — One Deck
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|
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
|All other matches||11292||0.232748||2.5||0.58187|
The next table shows the house edge for various number of decks for version 3.
Royal Match Version 3- 1 to 8 Decks
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
|Player and Dealer Royal Match||1000||19152||0.000008||0.008242|
|Player royal match||25||6877728||0.00296||0.073996|
The next table shows the house edge by number of decks.
Royal Match — Version 4 — 1-8 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.
Six-Deck Progressive Royal Match — $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.
Progressive Royal Match Breakeven Points
|Other Players||Breakeven Point|
Written by: Michael Shackleford