# Pan N9ne

## Introduction

Pan N9ne could be loosely described as a simplified version of baccarat. The game is simple, fast, and easy to learn. I first heard of the game when it appeared at the Palace Station in Las Vegas in June, 2022.

## Rules

1. The game can be played with any number of 52-card decks of cards, but I will presume six or eight for this analysis.
2. The point value of each card is the same as baccarat, as follows:
• Ace = 1 point.
• 2-9 = Pip value.
• 10s and faces = 0 points.
3. The score of mutliple cards is calculated as the sum of the points of all cards in that hand. Then, if that total is 10 or more, drop the tens digit. For example, a 5-6-7 hand would be worth 8 points, because the total points are 18, but the tens digit is dropped.
4. Play begins with the player making an Ante wager. The player may also make the optional Tie and Dragon side bets at this time.
5. The dealer shall give the player and himself two cards. Player cards are dealt face up and dealer cards face down.
6. The player may draw a third card or stand.
7. The dealer shall expose his cards.
8. If the dealer has a score of 5 or less with two cards, he shall draw a third card.
9. The winner is the side with more points.
10. The Ante bet wins, and pays even money, if the player has more points. Except, if the player wins with a three-card total of 6, then the Ante bet shall push.
11. If the dealer has more points, then the Ante bet shall lose.
12. If the player and dealer tie, then the Ante bet shall push.
13. The Tie bet wins if the player and banker tie. Otherwise, it loses.
14. The Dragon bonus wins if the player wins by a margin of victory of at least 5 points. The win depends on that margin of victory and the pay table below.

### Dragon Pay Table

Margin of
Player Victory
Pays
9 15
8 8
7 6
7 4
5 2
All other -1

Baccarat players should take note that there is no "natural" rule with 8 or 9 points. Both sides always have the opportunity to draw a third card.

## Strategy

To minimize the house edge on the Ante bet, the player should follow the same strategy as the dealer, hit with five or less points and stand with six or more.

A total of five is a borderline play, but the odds marginally favor hitting. If the player always stands on five, the house edge increases by 0.02%.

## Ante Analysis

The following table shows the probability and contribution to the return for the Ante bet with six decks of cards. The lower right cells shows a house edge of 2.05%.

### Ante Return Table — Six Decks

Event Pays Combinations Probability Return
Player (except with three-card 6) 1 372,282,196,157,568 0.423592 0.423592
Player with three-card 6 0 18,039,211,873,920 0.020525 0.000000
Tie 0 98,226,390,832,704 0.111765 0.000000
Dealer -1 390,321,408,031,488 0.444118 -0.444118
Total   878,869,206,895,680 1.000000 -0.020525

The following table shows the probability and contribution to the return for the Ante bet with eight decks of cards. The lower right cells shows a house edge of 2.05%. If the player were to always stand in five, the house edge would be 2.07%.

### Ante Return Table — Eight Decks

Event Pays Combinations Probability Return
Player (except with three-card 6) 1 2,117,008,374,859,770 0.423537 0.423537
Player with three-card 6 0 102,634,053,576,704 0.020533 0.000000
Tie 0 559,113,418,630,400 0.111859 0.000000
Dealer -1 2,219,642,428,436,480 0.444071 -0.444071
Total   4,998,398,275,503,350 1.000000 -0.020533

## Tie Analysis

The following table shows the probability and contribution to the return for the Tie bet with six decks of cards. The lower right cells shows a house edge of 10.59%.

### Tie Return Table — Six Decks

Event Pays Combinations Probability Return
Win 7 98,226,390,832,704 0.111765 0.782352
Loss -1 780,642,816,062,976 0.888235 -0.888235
Total   878,869,206,895,680 1.000000 -0.105884

The following table shows the probability and contribution to the return for the Tie bet with eight decks of cards. The lower right cells shows a house edge of 10.51%.

### Tie Return Table — Eight Decks

Event Pays Combinations Probability Return
Win 7 559,113,418,630,400 0.111859 0.783010
Loss -1 4,439,284,856,872,950 0.888141 -0.888141
Total   4,998,398,275,503,350 1.000000 -0.105132

## Dragon Analysis

The following table shows the probability and contribution to the return for the Dragon bet with six decks of cards. The lower right cells shows a house edge of 5.59%.

### Dragon Return Table — Six Decks

Margin of Victory Pays Combinations Probability Return
9 15 10,221,186,746,880 0.011630 0.174449
8 8 18,944,921,011,968 0.021556 0.172448
7 6 27,691,235,467,776 0.031508 0.189047
7 4 36,420,252,322,176 0.041440 0.165760
5 2 39,909,690,291,456 0.045410 0.090821
All other -1 745,681,921,055,424 0.848456 -0.848456
Total   878,869,206,895,680 1.000000 -0.055932

The following table shows the probability and contribution to the return for the Dragon bet with eight decks of cards. The lower right cells shows a house edge of 5.57%.

### Dragon Return Table — Eight Decks

Margin of Victory Pays Combinations Probability Return
9 15 58,184,781,799,424 0.011641 0.174610
8 8 107,793,005,719,552 0.021566 0.172524
7 6 157,499,290,492,928 0.031510 0.189060
7 4 207,129,583,343,616 0.041439 0.165757
5 2 226,956,638,048,256 0.045406 0.090812
All other -1 4,240,834,976,099,580 0.848439 -0.848439
Total   4,998,398,275,503,350 1.000000 -0.055676