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Ultimate Texas Hold 'Em -- Auckland Variant

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.

ULTIMATE TEXAS HOLD ’EM® is a registered trademark of Bally Gaming, Inc. and is used with permission on this website.

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 three or four times the Ante.
  5. The dealer turns over three community cards.
  6. 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.
  7. Two final community cards are turned over.
  8. 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.
  9. 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.
  10. The dealer will need at least a pair to open.
  11. 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

     

  12. 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

     

  13. 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

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

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. rules, is the addition of J/9 off-suit and a pair of deuces.

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
 

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Written by: Michael Shackleford