# Show Pai

Show Pai is a fairly simple table game that combines the scoring of baccarat with the format of pai gow. The game made its debut at the Las Vegas Palace Station in early 2016. The game is easy to learn and play and offers a comparatively low house edge.

## Rules

Rack card

1. The game is played with ordinary 52-card decks. At the Palace Station, six decks were used.
2. All cards are scored as in baccarat (aces = 1 point, 2-9 = pip value, 10's & faces = 0). The suit does not matter.
3. The point value of combined cards is taken by adding the point value of each card and looking only at the terminal digit of the total. For example, a 3, 5, and 9 would have a total of 17, and thus be worth seven points.
4. The player must make a Play bet. He may also make an optional Bonus side bet.
5. The player and dealer shall each receive four cards.
6. The player must divide his cards between a one-card low hand and a three-card high hand.
7. The point value of the low hand must be equal or less than the high hand.
8. If it is impossible for the player to set his hand per rules 6 and 7, for example with four fours, then it is said the player has a "No Pai," which is an automatic loser for the player.
9. The dealer shall also set his cards in the same manner.
10. The dealer shall follow a simple house way of maximizing the low hand.
11. As in pai gow or pai gow poker, the player's high hand shall be compared with the dealer's high hand. Likewise, the player's low hand shall be compared with the dealer's low hand. The Play bet shall be adjudicated as follows:
• If the player wins both ways, then the Play wager shall pay 1 to 1.
• If the dealer wins both ways, then the Play wager shall lose.
• If the player wins one way and loses one way, then Play bet shall push.
• If the player wins one way and ties the other, then the Play bet shall pay 1 to 1.
• If the dealer wins one way and ties the other, then the Play bet shall lose.
• If there is a double tie, then the Play bet shall lose.
12. The Bonus bet shall pay according to the pay table below.

### Table Title

Event Pays
Double No Pai 80 to 1
Player all tens 25 to 1
One No Pai 10 to 1
Player 9-9 5 to 1
Player 8-8 4 to 1
Double copy 2 to 1

## Strategy

Following is my Wizard strategy for Show Pai. For purposes of this strategy, the "total points" is the sum of the points of the low hand and points of the high hand.

• With six or less total points, balance the low hand.
• With seven total points, play 3-4 if you can, otherwise maximize the high hand.
• With eight total points, if you can make at least 7 in the high hand, then maximize the high, otherwise balance the hands.
• With nine or more total points, maximize the high hand.

For example, if the player's cards were 2-3-5-6, there are two viable ways to play the hand 2-4 or 3-3. The total points are six either way, so follow the first rule that says to balance the hand, and play 3-3.

## Analysis

The following table shows the possible outcomes of the Play bet. This table was done by a random simulation of 21 billion hands.

### Full Play Analysis

Event Pays Probability Return
Win/win 1 0.251290 0.251290
win/tie 1 0.107878 0.107878
Win/loss 0 0.250568 0.000000
Dealer no pai 0 0.016868 0.000000
loss/loss -1 0.227452 -0.227452
loss/tie -1 0.111565 -0.111565
Player no pai -1 0.017148 -0.017148
Tie/tie -1 0.017232 -0.017232
Total   1.000000 -0.014230

Next is a summary of the table above.

### Play Analysis Summary

Event Pays Probability Return
Win 1 0.359167 0.359167
Push 0 0.267436 0.000000
Loss -1 0.373397 -0.373397
Total   1.000000 -0.014230

The standard deviation per hand played is 0.855781

## Bonus Bet

The following table shows an analysis of the Bonus bet. This is based on the Palace Station pay table and six decks. The strategy employed is the same as the Wizard strategy above, except the player will play 8-8 over 7-9. The lower right cell shows a house edge of 7.77%.

### Bonus Analysis

Event Pays Probability Return
Double no pai 80 0.000278 0.022231
Player all 10's 25 0.008577 0.214429
One no pai 10 0.033585 0.335854
Player 9-9 5 0.024959 0.124793
Player 8-8 4 0.021921 0.087685
Double copy 2 0.015984 0.031969
Loser -1 0.894695 -0.894695
Total   1.000000 -0.077735

Playing 8-8 over 7-9 lowers the house edge on the Bonus bet by 1.44% but increases it on the Play bet by 0.03%.

## Methodology

This analysis is entirely based on random simulations.