Ultimate Texas Hold’em features an optional bet, the Trips Bonus. Players win the Trips Bonus if their final five-card hand is three of a kind or higher. Odds printed on layout. HOW TO PLAY: To begin the game, players must make equal bets on the Ante and Blind. They may also make a Trips bet. Jun 03, 2010 But I've been really studying this ultimate texas holdem game and i'm convinced that if you play an optimal strategy, it may be beat. I have worked out a lot of the odds for the river bet a long time ago, but lost the calculations, and now am not sure if they are 100% correct. There is a 3-flush AND you have none AND pair is 2 or 3.
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On This Page
Introduction
The page addresses the Auckland variant of Ultimate Texas Hold 'Em®. The only change in rules is that both player and dealer must use both hole cards and three community cards, as opposed to any two cards under the usual rules.
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 open. This game was invented by Roger Snow of Shuffle Master. The same base game is also distributed by Galaxy Gaming under the name Heads Up Hold 'Em.
How To Play Ultimate Texas Holdem
ULTIMATE TEXAS HOLD ’EM® is a registered trademark of Bally Gaming, Inc. and is used with permission on this website.
Rules
- The game is played with a single ordinary 52-card deck.
- The player must make an equal bet on both the Ante and Blind, and can also make an optional Trips bet.
- Two cards are dealt face down to the player and dealer. The player may look at his own cards.
- The player can check or make a Play bet equal to three or four times the Ante.
- The dealer turns over three community cards.
- If the player previously checked, then he may make a Play bet equal to two times his Ante. If the player already made a Play bet, then he may not bet further.
- Two final community cards are turned over.
- If the player previously checked twice, then 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.
- The player and dealer will both make the best possible hand using both hole cards and any combination of three out of the five community cards.
- The dealer will need at least a pair to open.
- The following table shows how the Blind, Ante, and Play bets are scored, according to who wins, and whether the dealer opens.
Scoring Rules
Winner Dealer Opens Blind Ante Play Player Yes Win Win Win Player No Win Push Win Dealer Yes Lose Lose Lose Dealer No Lose Push Lose Tie Yes or No Push Push Push - Winning Ante and Play bets pay 1 to 1. Winning Blind bets pay according to the following pay table.
Blind Bet Pay Table
Player Hand Pays Royal flush 500 to 1 Straight flush 50 to 1 Four of a kind 10 to 1 Full house 3 to 1 Flush 3 to 2 Straight 1 to 1 All other Push - 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.
The following table shows the four known pay tables for the Trips bet. Wins are on a 'to one' basis.
Trip Bet Pay Tables
| Event | Pay Table 1 | Pay Table 2 | Pay Table 3 | Pay Table 4 |
|---|---|---|---|---|
| Royal flush | 50 | 50 | 50 | 50 |
| Straight flush | 40 | 40 | 40 | 40 |
| Four of a kind | 30 | 30 | 30 | 20 |
| Full house | 9 | 8 | 8 | 7 |
| Flush | 7 | 6 | 7 | 6 |
| Straight | 4 | 5 | 4 | 5 |
| Three of a kind | 3 | 3 | 3 | 3 |
Analysis
/royal-flush-172214648-bafb6213188744e981412665b63b6be2.jpg "Ultimate Texas Holdem Royal Flush Odds")
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.'
Return Table — Auckland Variant
Texas Holdem Royal Flush Odds
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Large raise, player wins with three of a kind or less, dealer qualifies | 5 | 4,154,655,748,320 | 0.149374 | 0.746869 |
| Large raise, player wins with straight, dealer qualifies | 6 | 178,818,546,360 | 0.006429 | 0.038575 |
| Large raise, player wins with flush, dealer qualifies | 6.5 | 136,699,574,080 | 0.004915 | 0.031946 |
| Large raise, player wins with full house, dealer qualifies | 8 | 212,372,345,280 | 0.007635 | 0.061084 |
| Large raise, player wins with four of a kind, dealer qualifies | 15 | 22,854,801,600 | 0.000822 | 0.012326 |
| Large raise, player wins with straight flush, dealer qualifies | 55 | 881,828,960 | 0.000032 | 0.001744 |
| Large raise, player wins with royal flush, dealer qualifies | 505 | 333,380,880 | 0.000012 | 0.006053 |
| Large raise, player wins with three of a kind or less, dealer doesn't qualify | 4 | 1,825,630,952,040 | 0.065638 | 0.262550 |
| Large raise, player wins with straight, dealer doesn't qualify | 5 | 70,504,500,240 | 0.002535 | 0.012674 |
| Large raise, player wins with flush, dealer doesn't qualify | 5.5 | 35,766,099,240 | 0.001286 | 0.007073 |
| Large raise, player wins with full house, dealer doesn't qualify | 7 | 0 | 0.000000 | 0.000000 |
| Large raise, player wins with four of a kind, dealer doesn't qualify | 14 | 0 | 0.000000 | 0.000000 |
| Large raise, player wins with straight flush, dealer doesn't qualify | 54 | 242,960,160 | 0.000009 | 0.000472 |
| Large raise, player wins with royal flush, dealer doesn't qualify | 504 | 94,695,120 | 0.000003 | 0.001716 |
| Large raise, push | 0 | 69,066,172,800 | 0.002483 | 0.000000 |
| Large raise, player loses, dealer qualifies | -6 | 4,106,483,964,120 | 0.147642 | -0.885851 |
| Large raise, player loses, dealer doesn't qualify | -5 | 134,922,358,800 | 0.004851 | -0.024255 |
| Medium raise, player wins with three of a kind or less, dealer qualifies | 3 | 2,328,748,656,060 | 0.083726 | 0.251179 |
| Medium raise, player wins with straight, dealer qualifies | 4 | 121,147,927,116 | 0.004356 | 0.017423 |
| Medium raise, player wins with flush, dealer qualifies | 4.5 | 91,859,867,620 | 0.003303 | 0.014862 |
| Medium raise, player wins with full house, dealer qualifies | 6 | 137,247,421,464 | 0.004935 | 0.029607 |
| Medium raise, player wins with four of a kind, dealer qualifies | 13 | 17,201,079,108 | 0.000618 | 0.008040 |
| Medium raise, player wins with straight flush, dealer qualifies | 53 | 1,320,287,588 | 0.000047 | 0.002516 |
| Medium raise, player wins with royal flush, dealer qualifies | 503 | 0 | 0.000000 | 0.000000 |
| Medium raise, player wins with three of a kind or less, dealer doesn't qualify | 2 | 1,185,280,897,212 | 0.042615 | 0.085230 |
| Medium raise, player wins with straight, dealer doesn't qualify | 3 | 50,692,947,828 | 0.001823 | 0.005468 |
| Medium raise, player wins with flush, dealer doesn't qualify | 3.5 | 27,454,846,560 | 0.000987 | 0.003455 |
| Medium raise, player wins with full house, dealer doesn't qualify | 5 | 0 | 0.000000 | 0.000000 |
| Medium raise, player wins with four of a kind, dealer doesn't qualify | 12 | 0 | 0.000000 | 0.000000 |
| Medium raise, player wins with straight flush, dealer doesn't qualify | 52 | 382,314,648 | 0.000014 | 0.000715 |
| Medium raise, player wins with royal flush, dealer doesn't qualify | 502 | 0 | 0.000000 | 0.000000 |
| Medium raise, push | 0 | 33,793,487,856 | 0.001215 | 0.000000 |
| Medium raise, player loses, dealer qualifies | -4 | 1,808,533,963,644 | 0.065023 | -0.260092 |
| Medium raise, player loses, dealer doesn't qualify | -3 | 6,402,094,056 | 0.000230 | -0.000691 |
| Small raise, player wins with three of a kind or less, dealer qualifies | 2 | 1,490,557,629,144 | 0.053591 | 0.107181 |
| Small raise, player wins with straight, dealer qualifies | 3 | 236,132,887,884 | 0.008490 | 0.025469 |
| Small raise, player wins with flush, dealer qualifies | 3.5 | 90,389,718,780 | 0.003250 | 0.011374 |
| Small raise, player wins with full house, dealer qualifies | 5 | 51,851,976 | 0.000002 | 0.000009 |
| Small raise, player wins with four of a kind, dealer qualifies | 12 | 5,815,932 | 0.000000 | 0.000003 |
| Small raise, player wins with straight flush, dealer qualifies | 52 | 742,442,652 | 0.000027 | 0.001388 |
| Small raise, player wins with royal flush, dealer qualifies | 502 | 0 | 0.000000 | 0.000000 |
| Small raise, player wins with three of a kind or less, dealer doesn't qualify | 1 | 771,646,676,244 | 0.027743 | 0.027743 |
| Small raise, player wins with straight, dealer doesn't qualify | 2 | 89,783,345,532 | 0.003228 | 0.006456 |
| Small raise, player wins with flush, dealer doesn't qualify | 2.5 | 21,453,564,600 | 0.000771 | 0.001928 |
| Small raise, player wins with full house, dealer doesn't qualify | 4 | 0 | 0.000000 | 0.000000 |
| Small raise, player wins with four of a kind, dealer doesn't qualify | 11 | 0 | 0.000000 | 0.000000 |
| Small raise, player wins with straight flush, dealer doesn't qualify | 51 | 184,074,552 | 0.000007 | 0.000338 |
| Small raise, player wins with royal flush, dealer doesn't qualify | 501 | 0 | 0.000000 | 0.000000 |
| Small raise, push | 0 | 40,181,819,100 | 0.001445 | 0.000000 |
| Small raise, player loses, dealer qualifies | -3 | 2,627,450,579,820 | 0.094466 | -0.283397 |
| Small raise, player loses, dealer doesn't qualify | -2 | 62,015,192,784 | 0.002230 | -0.004459 |
| Player folds | -2 | 5,623,820,706,240 | 0.202195 | -0.404391 |
| Total | 27,813,810,024,000 | 1.000000 | -0.079670 |
The lower right cell shows a house edge of 7.97% per ante bet. What this means, for example, is if you bet $1 and both the Ante and Blind initially, then you can expect to lose 7.97 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 4.187692 times the Ante bet. So the element of risk would be 7.97%/4.187692 = 1.90%.
Large bettors should be wary of maximum payouts. If your ante bet is more than 1/500 of the maximum payout, then you will get shortchanged on a royal flush. For every 100 the effective payout on a royal goes down, the house edge will go up by 0.308%. In other words, the increase in the house edge will be [500-(MP/500)]*0.0000308, where MP is the maximum payout.
The next table shows the average wager and return from each bet.
Ultimate Texas Hold 'Em® Return Table — Auckland Variant
| Bet Type | Average Wager | Average Pays | Average Win |
|---|---|---|---|
| Ante | 1 | -0.177763 | -0.177763 |
| Blind | 1 | -0.401446 | -0.401446 |
| Play | 2.187691612 | 0.228341 | 0.499539 |
| Total | 4.187691612 | -0.079670 |
Strategy
For the Auckland variant, I have only quantified the strategy for the large raise. The player should make the large raise with any of the following initial hands:
- Any ace
- Unsuited K/5 or higher
- Unsuited Q/8 or higher
- Unsuited J/9 or higher
- Suited king with anything
- Suited Q/6 or higher
- Suited J/8 or higher
- Any pair
The only changes compared to the usual U.S. 26 casino street welshpool wa 6106. rules, is the addition of J/9 off-suit and a pair of deuces.
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Trips Bet
Shufflemaster literature mentions the following four possible pay tables on the Trips bet. I do not know which one is being used in Auckland. I assume the same rule that the player's hole cards must be used also applies to the Trips bet.
Trips Bet — Pay Table 1
| Player Hand | Combinations | Pays | Probability | Return |
|---|---|---|---|---|
| Royal flush | 50 | 43,240 | 0.000015 | 0.000770 |
| Straight flush | 40 | 379,224 | 0.000135 | 0.005399 |
| Four of a kind | 30 | 4,047,264 | 0.001441 | 0.043217 |
| Full house | 9 | 35,914,320 | 0.012783 | 0.115050 |
| Flush | 7 | 41,883,800 | 0.014908 | 0.104356 |
| Straight | 4 | 79,953,072 | 0.028458 | 0.113833 |
| Three of a kind | 3 | 174,387,528 | 0.062071 | 0.186214 |
| All other | -1 | 2,472,867,312 | 0.880188 | -0.880188 |
| Total | 2,809,475,760 | 1.000000 | -0.311349 |
Trips Bet — Pay Table 2
| Player Hand | Combinations | Pays | Probability | Return |
|---|---|---|---|---|
| Royal flush | 50 | 43,240 | 0.000015 | 0.000770 |
| Straight flush | 40 | 379,224 | 0.000135 | 0.005399 |
| Four of a kind | 30 | 4,047,264 | 0.001441 | 0.043217 |
| Full house | 8 | 35,914,320 | 0.012783 | 0.102266 |
| Flush | 6 | 41,883,800 | 0.014908 | 0.089448 |
| Straight | 5 | 79,953,072 | 0.028458 | 0.142292 |
| Three of a kind | 3 | 174,387,528 | 0.062071 | 0.186214 |
| All other | -1 | 2,472,867,312 | 0.880188 | -0.880188 |
| Total | 2,809,475,760 | 1.000000 | -0.310582 |
Trips Bet — Pay Table 3
| Player Hand | Combinations | Pays | Probability | Return |
|---|---|---|---|---|
| Royal flush | 50 | 43,240 | 0.000015 | 0.000770 |
| Straight flush | 40 | 379,224 | 0.000135 | 0.005399 |
| Four of a kind | 30 | 4,047,264 | 0.001441 | 0.043217 |
| Full house | 8 | 35,914,320 | 0.012783 | 0.102266 |
| Flush | 7 | 41,883,800 | 0.014908 | 0.104356 |
| Straight | 4 | 79,953,072 | 0.028458 | 0.113833 |
| Three of a kind | 3 | 174,387,528 | 0.062071 | 0.186214 |
| All other | -1 | 2,472,867,312 | 0.880188 | -0.880188 |
| Total | 2,809,475,760 | 1.000000 | -0.324132 |
Trips Bet — Pay Table 4
| Player Hand | Combinations | Pays | Probability | Return |
|---|---|---|---|---|
| Royal flush | 50 | 43,240 | 0.000015 | 0.000770 |
| Straight flush | 40 | 379,224 | 0.000135 | 0.005399 |
| Four of a kind | 20 | 4,047,264 | 0.001441 | 0.028812 |
| Full house | 7 | 35,914,320 | 0.012783 | 0.089483 |
| Flush | 6 | 41,883,800 | 0.014908 | 0.089448 |
| Straight | 5 | 79,953,072 | 0.028458 | 0.142292 |
| Three of a kind | 3 | 174,387,528 | 0.062071 | 0.186214 |
| All other | -1 | 2,472,867,312 | 0.880188 | -0.880188 |
| Total | 2,809,475,760 | 1.000000 | -0.337771 |
Internal Links
- Ultimate Texas Hold — Analysis of the standard rules.
External Links
Ultimate Texas Holdem Strategy Guide
- How to play Ultimate Texas Hold 'Em — Entry SkyCity casino in Auckland.
- Discussion about the Auckland variant in my forum at Wizard of Vegas.