EZ-9

Introduction

EZ-9 is a pan/baccarat variant invented and owned by Johnny Ma. As of this writing, January 2013, it can be found at the Hollywood Park casino in California.

Rules

Following are the rules of EZ-9.

The game is played with 12 modified 36-card decks, consisting of aces to sixes and all face cards only. In other words, the sevens, eights, nines and tens are removed.
Cards are scored as in baccarat, with aces one point, two to six according to pip value, and face cards zero.
The point value of two or more cards is the same as baccarat, equaling the terminal digit of the sum of the cards.
After making a wager, the player and dealer shall each receive three cards.
The player may use any combination of two or three of his cards to form his best hand.
If the player has a 9-point hand consisting of 2-3-4 or 3-3-3, then it shall immediately win and pay 3 to 2.
The dealer shall then turn over his cards and make the best hand using any two or three of his cards.
If the dealer has a 0-point hand, consisting of three face cards, then all remaining wagers shall push.
Otherwise, if the player has more points, the player shall win and be paid even money. An equal number of points results in a push. If the dealer has more points, the player's wager will lose.

In addition, there is also an optional Triple Match side bet, which pays if the player gets a three of a kind. More information about that is in the analysis section.

Analysis

The following table shows the probability and return of all possible outcomes in EZ-9. The lower right cell reflects a house edge of 2.85%.

EZ-9 Return
Event	Pays	Probability	Return
Player 2/3/4 or 3/3/3	1.5	0.009584	0.014376
Player wins	1	0.393818	0.393818
Dealer three face cards	0	0.036165	0.000000
Push	0	0.123725	0.000000
Dealer wins	-1	0.436708	-0.436708
Total		1.000000	-0.028514

The following table shows my analysis of the $1 Triple Match side bet. The win for a 3-3-3 in diamonds is a progressive jackpot. This jackpot starts at $2,000 and grows by 5% of money bet. The win shown in the table below is based on the average win.

Wins on the Triple Match are paid on a "for one" basis. In other words, the original wager is never returned. The return of 88.768% reflects a house edge of 11.232%.

Triple Match Return
Event	Pays	Combinations	Probability	Return
3-3-3 in Diamonds	5032.67	220	0.000016	0.082974
Suited three of a kind	250	7,700	0.000577	0.144262
Colored three of a kind	100	28,512	0.002137	0.213673
Three of a kind	50	119,232	0.008935	0.446771
Total		155,664	0.011666	0.887680

The break-even meter (with no house edge) is at $11,845.27.

The formula for the return at any given time is 80.47% + 1.65% × jackpot.

Acknowledgment

I would like to thank game owner Johnny Ma for providing me the math report by Eliot Jacobson, which saved me the trouble of analyzing it myself.

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