Royal 9 Baccarat Side Bet

Introduction

Royal 9 is a progressive baccarat side bet. The bet amount is $5. Wins are based on the Player and/or Banker hand having a "Royal 9," which is defined as a nine and any face card. Some wins depend on the Player and/or Banker hand matching a printed Royal 9 hand on each betting position. The side bet is marketed by AGS.

Rules

As usual, for baccarat I capitalize the Player and Banker when referring to the those bets and use low case for the word player to refer to the one playing the game. All wins are on a "for one" basis.

The bet amount is a flat $5.
Each betting position has a pre-printed two-card combination on it. At a six-seat table the pre-printed hands are K 9, K 9, K 9, K 9, K 9, K 9.
A "Royal 9" is defined as a nine combined with any face card in the original two cards in the Player and/or Banker hand.
The top award pays the "Star Jackpot." It is won if both the Player and Banker hands match the pre-printed cards at the player's position.
The "Spade Jackpot" pays if the Banker hand only matches the pre-printed cards at the player's position exactly.
The "Heart Jackpot" pays if the Player hand only matches the pre-printed cards at the player's position exactly.
A flat win of $5,000 is won if both the Player and Banker hands match any other pre-printed cards, besides those at player's position exactly.
A flat win of $1,500 is won if both the Player and Banker hands have a suited Royal 9. They do not have to be the same Royal 9.
A flat win of $250 is won if both the Player and Banker hands have a Royal 9. They do not have to be suited nor the same Royal 9.
A flat win of $50 is won if either the Player and Banker hands have a suited Royal 9.
A flat win of $25 is won if either the Player and Banker hands have a non-suited Royal 9.

Eight-Deck Analysis

Following is my analysis for an eight-deck game with six player positions. The return column shows the product of the win, probability, and 1/5. The reason for dividing by five is to show the relative return based on a $5 bet.

Eight Decks — Six Player Spots

Event	Pays	Combinations	Probability	Return
Player and Banker hand match layout hand exactly	Star	12,544	0.00000042	?
Banker hand matches layout hand exactly	Spade	21,873,152	0.00074100	?
Player hand matches layout hand exactly	Heart	21,873,152	0.00074100	?
Player and Banker hands match other layout hand exactly	$5,000	62,720	0.00000212	0.002125
Player and Banker have a Suited royal 9	$1,500	2,264,064	0.00007670	0.023010
Player and Banker have a Royal 9	$250	32,366,080	0.00109647	0.054824
Player or Banker have a suited Royal 9	$50	507,162,624	0.01718128	0.171813
Player or Banker have a Royal 9	$25	1,479,224,320	0.05011206	0.250560
Loser	$0	27,453,493,824	0.93004894	0.000000
Total		29,518,332,480	1.00000000	0.502332*

Notes:
* The return from all fixed wins is 50.23%. The value of each $100,000 in the Star Jackpot is 0.85%. The value of each $100 in the Spade and Heart Jackpots is 1.48%. The value of a seventh player spot is 0.04%.

Six-Deck Analysis

Following is my analysis for a six-deck game with six player positions. The return column shows the product of the win, probability, and 1/5. The reason for dividing by five is to show the relative return based on a $5 bet.

Six Decks — Six Player Spots

Event	Pays	Combinations	Probability	Return
Player and Banker hand match layout hand exactly	Star	3,600	0.00000039	?
Banker hand matches layout hand exactly	Spade	6,893,280	0.00074164	?
Player hand matches layout hand exactly	Heart	6,893,280	0.00074164	?
Player and Banker hands match other layout hand exactly	$5,000.00	21,600	0.00000232	0.002324
Player and Banker have a Suited royal 9	$1,500	706,752	0.00007604	0.022811
Player and Banker have a Royal 9	$250	10,092,240	0.00108581	0.054290
Player or Banker have a suited Royal 9	$50	159,881,472	0.01720137	0.172014
Player or Banker have a Royal 9	$25	466,320,960	0.05017066	0.250853
Loser	$0	8,643,882,096	0.92998015	0.000000
Total		9,294,695,280	1.00000000	0.501925*

Notes:
* The return from all fixed wins is 50.19%. The value of each $100,000 in the Star Jackpot is 0.77%. The value of each $100 in the Spade and Heart Jackpots is 1.48%. The value of a seventh player spot is 0.04%.