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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.
- A single 52-card deck is used.
- The player makes an ante wager.
- The player is dealt four cards face down. The player may look at his cards but sharing of information between players is frowned upon.
- 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.
- If the player makes either it bet it must be exactly equal to the ante.
- If the player folds he forfeits his cards and his ante.
- If the player made either bet he shall get two more cards.
- 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.
- 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.
High Tequila Pay Table
| 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.
- 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).
- 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.
- When both the above conditions are satisfied you're on your own.