Last Updated: July 2, 2006

# Tequila Poker

## Introduction

I noticed Tequila Poker on field trial the Hard Rock Casino in Las Vegas on August 8, 2005. The game lets the player either bet on a poker hand or the total number of points. I find it easy to learn and an interesting twist on poker. It is also refreshing to see a new game without a side bet.

## Rules

Following are the rules according to the game owner. Some rule cards were printed and distributed to players incorrectly stating a 52-point hand pays 5 to 1. Unless otherwise noted this analysis is based on a 52 paying 7 to 1.

1. A single 52-card deck is used.
2. The player makes an ante wager.
3. The player is dealt four cards face down. The player may look at his cards but sharing of information between players is frowned upon.
4. The player has three options: (1) make a "High Tequila" bet, (2) make a "Tequila Poker" bet, or (3) fold. There are designated circles on the table for the ante and both "Tequila" bets.
5. If the player makes either it bet it must be exactly equal to the ante.
6. If the player folds he forfeits his cards and his ante.
7. If the player made either bet he shall get two more cards.
8. If the player made the "High Tequila" bet cards will be scored according to their blackjack value, with aces always as 11 points. The sum of the point value of the highest five cards will be taken. If the player has 46 points or more then his ante bet shall pay even money and his "High Tequila" bet according to the pay table below.
9. If the player made the "Tequila Poker" bet cards will be scored according to their poker value. The best five of the six cards will be used to form the highest possible poker hand. If the player has a pair of aces or more then his ante bet shall pay even money and his "Tequila Poker" bet according to the pay table below.

Hand Pays
54 200 to 1
53 15 to 1
52 7to 1
51 4 to 1
50 3 to 1
49 2 to 1
46 to 48 1 to 1
45 or less Loss

### Tequila Poker Pay Table

Hand Pays
Royal flush 200 to 1
Straight flush 50 to 1
Four of a kind 15 to 1
Full house 8 to 1
Flush 7 to 1
Straight 5 to 1
Three of a kind 3 to 1
Two pair 2 to 1
Pair of aces 1 to 1
Other Loss

## Analysis

The following table shows the possible outcomes when the player makes the High Tequila bet. The probability and return columns are relative to all hands, including when the player plays the Tequila Poker bet or folds. The bottom row shows the player will make the High Tequila bet 30.09% of the time when playing the proper strategy, for an average win of 0.2036 units per hand.

### High Tequila Return Table

Hand Pays Combinations Probability Return
54 201 7896 0.000026 0.005197
53 16 216858 0.00071 0.011362
52 8 1662006 0.005442 0.04354
51 5 4709738 0.015423 0.077113
50 4 6835090 0.022382 0.08953
49 3 8185326 0.026804 0.080412
46 to 48 2 26528458 0.086871 0.173742
45 or less -2 42122828 0.137937 -0.275874
Total 90268200 0.295595 0.205022

The next table shows the possible outcomes when the player makes the Tequila Poker bet. The probability and return columns are relative to all hands, including when the player plays the High Tequila bet or folds. The bottom row shows the player will make the Tequila Poker bet 31.805% of the time when playing the proper strategy, for an average win of 0.1442 units per hand.

### Tequila Poker Return Table

Hand Pays Combinations Probability Return
Royal flush 201 1216 0.000004 0.0008
Straight flush 51 19968 0.000065 0.003335
Four of a kind 16 190116 0.000623 0.009961
Full house 9 2075976 0.006798 0.061183
Flush 8 1832708 0.006001 0.048012
Straight 6 2097204 0.006868 0.041205
Three of a kind 4 7276704 0.023829 0.095314
Two pair 3 22930308 0.075088 0.225265
Pair of aces 2 3806232 0.012464 0.024928
Other -2 56344416 0.184507 -0.369014
Total 96574848 0.316247 0.140988

Finally, the player should fold 38.798% of the time, for a net loss of one unit.

The final table summarizes the three possible actions and the contribution to the total return of each.

### Tequila Poker Return Table

Action Combinations Probability Expected Value Return
High Tequila 90268200 0.295595 0.69359 0.205022
Tequila Poker 96574848 0.316247 0.445817 0.140988
Fold 118534752 0.388158 -1 -0.388158
Total 305377800 1 0 -0.042147

The table above shows the house edge is 4.21%. With an average wager of 1.612 units the element of risk is 2.61%.

## Rule Variations

If a total of 52 were to pay 5 to 1, as opposed to 7 to 1, then the house edge would be 5.27% and the element of risk 3.27%.

## Strategy

To prepare my analysis above I wrote a computer program to determine the proper strategy for each possible hand. As with video poker games the optimal strategy is quite complicated, so here is a greatly abbreviated version which will help in most situations.

1. Between folding and playing the Tequila Poker bet, the player should make the bet with any pair, or four to any flush or straight (including an inside straight).
2. Between folding and playing the High Tequila bet, the player should play the High Tequila bet if his highest three cards total 28 points or more.
3. When both the above conditions are satisfied you're on your own.

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