Ultimate Texas Hold 'Em

Last update: July 12, 2008

Introduction

Ultimate Texas Hold'em is a poker-based casino game in which the player may make one raise at any time during the course of the hand. The earlier the raise is made the higher it may be. Unlike other poker-based games, raises made after the ante still have action even if the dealer doesn't qualify. This game was invented by Roger Snow of Shuffle Master.

Rules

1. The game is played with a single ordinary 52-card deck.
2. The player must make an equal bet on both the Ante and Blind, and can also make an optional Trips bet.
3. Two cards are dealt face down to the player and dealer. The player may look at his own cards.
4. The player can check or make a Play bet equal to four times the Ante.
5. The dealer turns over three community cards.
6. If the player previously checked he may make a Play bet equal to two times his Ante. If the player already made a Play bet he may not bet further.
7. Two final community cards are turned over.
8. If the player previously checked twice he must either make a Play bet equal to exactly his Ante, or fold, losing both his Ante and Blind bets. If the player already raised he may not bet further.
9. The player and dealer will both make the best possible hand using any combination of their own two cards and the five community cards.
10. The dealer will need at least a pair to qualify.
11. If the player and dealer tie then the Ante, Blind, and Play bets will all push.
12. If the dealer qualifies and the player has the higher hand then the Ante will pay even money. If the dealer qualifies and the dealer has the higher hand then the Ante will lose. If the dealer does not qualify then the ante will push. (Note: The qualifying point only matters for purposes of the Ante bet.)
13. If the player has the higher hand the Play bet will pay even money. If the dealer has the higher hand the Play bet will lose.
14. If the player has the higher hand the Blind bet will pay according to the Blind Bet pay table below. If the dealer has the higher hand the Blind bet will lose.
15. The Trips bet will pay according to the poker value of the player's hand regardless of the value of the dealer's hand, according to one of the Trip bet pay tables below.

Analysis

There are 52 possible outcomes of each hand. The table below shows the probability of each and the contribution to the total return, assuming optimal strategy. A 4X raise is referred to as a "large raise," a 2X raise as "medium," and 1x as "small."

The lower right cell shows a house edge of 2.185% per ante bet. What this means, for example, is if you bet $1 and both the Ante and Blind initially you can expect to lose 2.185 cents on average. However for comparison to other games I believe the Element of Risk is more appropriate to look at. The average total amount bet by the end of the hand is 4.152252 times the ante bet. So the element of risk would be 2.185%/4.152252 = -0.526%.

The next table shows the average wager and return from each bet.

The next table shows the probability of a large, medium, or small raise, or fold for each initial 2-card hand, as well as the expected value.

Strategy

I never quantified a strategy to this game, because my computer figured out the optimal strategy on a hand by hand basis. However, the table above shows that that a large raise should be made on the following hands.

• Any hand with an ace
• Unsuited king and 5 or higher
• Unsuited queen and 8 or higher
• Unsuited jack and ten
• Suited king with any other card
• Suited queen with 6 or higher
• Suited jack with 8 or higher
• Any pair, 3's or higher

Trips Bet

Shufflemaster literature mentions the following four possible pay tables on the Trips bet.

I'm told that the most common pay table for the Trips bet is Pay Table 2, at a 1.9% house edge.

Links

Here's a link to Shufflemaster's Ultimate Texas Hold'em page.

Methodology

This was a difficult game to analyze and required 40 days of computer time to cycle through all the combinations. As with most other poker based games my analysis was combinatorial in C++, looping through all possible combinations of cards by brute force.

Shufflemaster literature states the element of risk to 0.8%. This figure is based on the analysis of Elliot Frome. As shown above my element of risk is slightly lower at 0.526%. So I respectfully disagree with Mr. Frome.