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Ultimate Texas Hold 'Em

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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 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.

Collusion

Knowledge of other player cards can reduce the house edge, if the information is used properly. For an in-depth analysis of this topic, please see my page on Ultimate Texas Hold 'Em Collusion.

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Rules

Ultimate Texas Hold 'EmFollowing are the standard rules as played in the United States. There is a variant played in Auckland, New Zealand, I address following the standard 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 any combination of their own two cards and 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 Trips bet pay tables below.

Notes:

* While the standard rules let both player and dealer use any five cards to make their best poker hand, in Auckland, New Zeland, both sides must make use of both hole cards and three of the five community cards. An analysis of the game under this rule can be found in my page on Ultimate Texas Hold 'Em -- Auckland Variant.

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 TableExpand

Raise Dealer
Qualifies
Player Hand Winner Pays Combinations Probability Return
Large Yes Less than straight Player 5 3,671,050,165,880 0.131987 0.659933
Large Yes Straight Player 6 246,174,692,160 0.008851 0.053105
Large Yes Flush Player 6.5 241,047,929,080 0.008666 0.056332
Large Yes Full house Player 8 295,405,180,920 0.010621 0.084966
Large Yes Four of a kind Player 15 23,008,208,760 0.000827 0.012408
Large Yes Straight flush Player 55 1,818,135,760 0.000065 0.003595
Large Yes Royal flush Player 505 596,356,920 0.000021 0.010828
Large No Less than straight Player 4 1,556,797,035,840 0.055972 0.223888
Large No Straight Player 5 81,416,649,960 0.002927 0.014636
Large No Flush Player 5.5 50,874,988,680 0.001829 0.010060
Large No Full house Player 7 0 0.000000 0.000000
Large No Four of a kind Player 14 0 0.000000 0.000000
Large No Straight flush Player 54 229,686,840 0.000008 0.000446
Large No Royal flush Player 504 90,386,280 0.000003 0.001638
Large 0   Push 0 285,142,270,600 0.010252 0.000000
Large Yes   Dealer -6 3,931,554,359,920 0.141353 -0.848116
Large No   Dealer -5 102,655,952,400 0.003691 -0.018454
Medium Yes Less than straight Player 3 2,114,839,654,764 0.076036 0.228107
Medium Yes Straight Player 4 133,100,158,992 0.004785 0.019142
Medium Yes Flush Player 4.5 152,618,008,784 0.005487 0.024692
Medium Yes Full house Player 6 289,401,836,880 0.010405 0.062430
Medium Yes Four of a kind Player 13 18,537,793,620 0.000666 0.008664
Medium Yes Straight flush Player 53 2,704,129,504 0.000097 0.005153
Medium Yes Royal flush Player 503 112,333,500 0.000004 0.002031
Medium No Less than straight Player 2 1,083,763,469,592 0.038965 0.077930
Medium No Straight Player 3 45,053,788,356 0.001620 0.004860
Medium No Flush Player 3.5 38,820,798,396 0.001396 0.004885
Medium No Full house Player 5 0 0.000000 0.000000
Medium No Four of a kind Player 12 0 0.000000 0.000000
Medium No Straight flush Player 52 358,131,456 0.000013 0.000670
Medium No Royal flush Player 502 8,830,620 0.000000 0.000159
Medium     Push 0 191,611,691,060 0.006889 0.000000
Medium Yes   Dealer -4 1,841,155,221,088 0.066196 -0.264783
Medium No   Dealer -3 7,978,353,108 0.000287 -0.000861
Small Yes Less than straight Player 2 1,375,033,295,072 0.049437 0.098874
Small Yes Straight Player 3 395,087,247,768 0.014205 0.042614
Small Yes Flush Player 3.5 190,959,227,136 0.006866 0.024030
Small Yes Full house Player 5 43,297,986,840 0.001557 0.007784
Small Yes Four of a kind Player 12 859,737,984 0.000031 0.000371
Small Yes Straight flush Player 52 1,962,591,576 0.000071 0.003669
Small Yes Royal flush Player 502 42,135,660 0.000002 0.000760
Small No Less than straight Player 1 720,579,458,748 0.025907 0.025907
Small No Straight Player 2 136,018,223,484 0.004890 0.009781
Small No Flush Player 2.5 40,911,000,804 0.001471 0.003677
Small No Full house Player 4 0 0.000000 0.000000
Small No Four of a kind Player 11 0 0.000000 0.000000
Small No Straight flush Player 51 269,696,304 0.000010 0.000495
Small No Royal flush Player 501 6,109,020 0.000000 0.000110
Small     Push 0 418,339,128,088 0.015041 0.000000
Small Yes   Dealer -3 2,700,150,685,692 0.097079 -0.291238
Small No   Dealer -2 47,223,220,344 0.001698 -0.003396
Fold -2 5,335,144,079,760 0.191816 -0.383633
Total   27,813,810,024,000 1.000000 -0.021850
 

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, then 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 standard deviation, relative to the Ante bet, is 4.94.

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

Bet Type Average
Wager
Average
Pays
Average
Win
Ante 1 -0.165757 -0.165757
Blind 1 -0.314685 -0.314685
Play 2.152252 0.213076 0.458593
Total 4.152252   -0.02185

Wizard Strategy

The following is my "Wizard Strategy" for Ultimate Texas Hold 'Em®.

Large Raise: The following table shows when to make the 4X raise.

Medium Raise: Make the 2X raise with any of the following:

  • Two pair or better.
  • Hidden pair*, except pocket deuces.
  • Four to a flush including a hidden 10 or better to that flush

* Hidden pair = Any pair with at least one card in your hole cards (thus the pair is hidden to the dealer).

Small Raise: Make the 1X raise with any of the following, otherwise fold:

  • Hidden pair or better.
  • Less than 21 dealer outs beat you.

Example

What I mean by an "out" is a dealer hole card that will cause you to lose. Let's look at this situation as an example.

In the example above, there 15 cards that will pair the dealer and beat you (three suits each of K, 7, 2, A, and 10). Then there are the two ranks (jacks and queens) which will out-kick the player. All four jacks and queens remain in the decks, so that is 2×4=8 more cards that will beat you. So, we're up to 15+8=23. We don't count the other three nines because those will result in a push. So, because there are only 23 outs (21 or more), we fold.

BTW, using my Ultimate Texas Hold 'Em® calculator, we see that the expected value of raising this hand is -2.136364, which is less than the -2 of folding.

I get asked a lot about combinations of cards that will beat the player. For example, any two dealer spades that would give the dealer a flush in the example above. The answer is no. It would really make things complicated if the strategy accounted for double-card combinations that would beat the player.

Following my Wizard strategy will result in a house edge of 2.43% and an Element of Risk of 0.58%.

The second and third decision points are influenced by the James Grosjean strategy, for which I have great respect, as I do for all of Grosjean's work. I highly recommend his strategy if you want to something even more powerful than my simple strategy above.

Trips Bet

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

Trips Bet - Pay Table 1

Player Hand Combinations Pays Probability Return
Royal flush 4324 50 0.000032 0.001616
Straight flush 37260 40 0.000279 0.01114
Four of a kind 224848 30 0.001681 0.05042
Full house 3473184 9 0.025961 0.233649
Flush 4047644 7 0.030255 0.211785
Straight 6180020 4 0.046194 0.184775
Three of a kind 6461620 3 0.048299 0.144896
All other 113355660 -1 0.8473 -0.8473
Total 133784560   1 -0.009018

Trips Bet - Pay Table 2

Player Hand Combinations Pays Probability Return
Royal flush 4324 50 0.000032 0.001616
Straight flush 37260 40 0.000279 0.01114
Four of a kind 224848 30 0.001681 0.05042
Full house 3473184 8 0.025961 0.207688
Flush 4047644 6 0.030255 0.18153
Straight 6180020 5 0.046194 0.230969
Three of a kind 6461620 3 0.048299 0.144896
All other 113355660 -1 0.8473 -0.8473
Total 133784560   1 -0.01904

Trips Bet — Pay Table 3

Player Hand Combinations Pays Probability Return
Royal flush 4324 50 0.000032 0.001616
Straight flush 37260 40 0.000279 0.01114
Four of a kind 224848 30 0.001681 0.05042
Full house 3473184 8 0.025961 0.207688
Flush 4047644 7 0.030255 0.211785
Straight 6180020 4 0.046194 0.184775
Three of a kind 6461620 3 0.048299 0.144896
All other 113355660 -1 0.8473 -0.8473
Total 133784560   1 -0.034979

Pay table #3 seen at the Mirage.

Trips Bet - Pay Table 4

Player Hand Combinations Pays Probability Return
Royal flush 4324 50 0.000032 0.001616
Straight flush 37260 40 0.000279 0.01114
Four of a kind 224848 20 0.001681 0.033613
Full house 3473184 7 0.025961 0.181727
Flush 4047644 6 0.030255 0.18153
Straight 6180020 5 0.046194 0.230969
Three of a kind 6461620 3 0.048299 0.144896
All other 113355660 -1 0.8473 -0.8473
Total 133784560   1 -0.061808

Pay table #4 seen at Shufflemaster TableMax units.

Common Progressive

This is the most common progressive jackpot, in my experience, so I'll title it the "Common Progressive." I used to title it the "Michigan Progressive," when the only known placement was in Michigan, but now it is seen all over the place.

There is just a single bet amount, which can be $1 or $5, depending on the table. Wins are based on the player's two hole cards and the three flop cards. The following table shows the probability and contribution to the return for the various wins. Wins are relative to the amount bet and are on a "for one" basis.

Common Progressive

Event Pays Envy
Bonus
Combinations Probability Return Envy
Return
Royal flush 100% of jackpot 1000 4 0.000002 0.000000 0.001539
Straight flush 10% of jackpot 300 36 0.000014 0.000000 0.004156
Four of a kind 300   624 0.000240 0.072029 0.000000
Full house 50   3,744 0.001441 0.072029 0.000000
Flush 40   5,108 0.001965 0.078616 0.000000
Straight 30   10,200 0.003925 0.117739 0.000000
Three of a kind 9   54,912 0.021128 0.190156 0.000000
Total     74,628 0.028715 0.530569 0.005695

What the table above immediately shows us is fixed wins return 53.06% to the player. For each additional player at the table, besides yourself, your return goes up by 0.57% from the Envy Bonus.

For a $1 bet, every $10,000 in the meter adds 2.924% to the return. Likewise, for a $5 bet, every $50,000 in the meter adds 2.924% to the return.

The next table shows the break-even point, where the Progressive side bet has zero house edge, according to the bet amount and number of other players (not counting yourself).

Common Progressive

Other
Players
$1 Bet $5 Bet
0 $160,530.53 $802,652.63
1 $158,583.16 $792,915.79
2 $156,635.79 $783,178.95
3 $154,688.42 $773,442.11
4 $152,741.05 $763,705.26
5 $150,793.68 $753,968.42

Small Progressive

Many tables in Las Vegas offer a $1 progressive side bet. The top win is for a royal flush using at least one hole card, which I call a "hidden royal flush." There is also a $100 envy bonus if another player gets a hidden royal. The following table shows the return of the fixed wins only, not counting the envy bonus. It shows a return of 45.68%, before considering the jackpot and envy bonuses.

Small Progressive

Event Pays Envy Combinations Probability Return
Hidden royal flush Jackpot $100 86,480 0.000031 ?
Community royal flush $1000 $0 4,324 0.000002 0.001539
Straight flush $250 $0 782,460 0.000279 0.069627
Four of a kind $75 $0 4,721,808 0.001681 0.126050
Full house $10 $0 72,936,864 0.025961 0.259610
All other $0 $0 2,730,943,824 0.972047 0.000000
Total     2,809,475,760 1.000000 0.456827 + ?

The return per $1000 in jackpot is 3.08%. The return for the Envy Bonus is 0.308% for each additional player at the table. So each additional player at the table is worth $100 in the meter.

The next table shows how big the jackpot has to be for the Small Progressive to have exactly a 100% return, or zero house advantage.

Break Even Jackpots

Other
Players
Jackpot
5 $17,146.07
4 $17,246.07
3 $17,346.07
2 $17,446.07
1 $17,546.07
0 $17,646.07

Buffalo Thunder Progressive

The Big Progressive tends to be much larger, because the player must flop a royal flush to win it. In other words, the player cannot make use of the Turn and River cards to win the progressive, unlike in the Small Progressive. There is no Envy Bonus. It was seen at the Buffalo Thunder casino in New Mexico.

Buffalo Thunder Progressive

Event Pays Permutations Probability Return
Player flops royal 100% of jackpot 1037760 0.000002 ?
Royal partially on board 5% of jackpot 19717440 0.000029 ?
Royal entirely on board 3000 1037760 0.000002 0.004617
Straight flush 250 187790400 0.000279 0.069627
Four of a kind 100 1133233920 0.001681 0.168067
Full house 10 17504847360 0.025961 0.25961
All other 0 655426517760 0.972047 0
Total   674274182400 1 0.502077 + ?

The return for at any given time is 50.19% plus 3.00% for each $10,000 in the meter. For exactly zero house edge, the meter would need to be $165,959.74. I'm told the meter is seeded at $5,000, and 27% of money bet goes towards the meter. Fixed wins are not deducted from the meter. That would make the overall return 77.96%.

Bad Beat Bonus

At the Admiral casino in Liechtenstein there is a Bad Beat Bonus side bet. It pays if either the player or dealer lose with a three of a kind or better. Gaming literature mentions two different pay tables. My analysis of both is below. The bottom line is a house edge of 14.79% on pay table 1 and 20.39% on pay table 2.

Bad Beat Bonus — Pay Table 1

Losing Hand Pays Combinations Probability Return
Straight flush 7,500 10,300,592 0.000004 0.027776
Four of a kind 500 471,040,512 0.000169 0.084677
Full house 50 8,435,225,376 0.003033 0.151637
Flush 30 19,434,208,592 0.006987 0.209618
Straight 20 18,271,076,976 0.006569 0.131381
Three of a kind 9 64,049,759,448 0.023028 0.207252
Low hand win* -1 2,557,579,127,088 0.919536 -0.919536
Tie -1 113,130,263,816 0.040674 -0.040674
Total   2,781,381,002,400 1.000000 -0.147868

Bad Beat Bonus — Pay Table 2

Losing Hand Pays Combinations Probability Return
Straight flush 10,000 10,300,592 0.000004 0.037034
Four of a kind 500 471,040,512 0.000169 0.084677
Full house 40 8,435,225,376 0.003033 0.121310
Flush 25 19,434,208,592 0.006987 0.174681
Straight 20 18,271,076,976 0.006569 0.131381
Three of a kind 9 64,049,759,448 0.023028 0.207252
Low hand win* -1 2,557,579,127,088 0.919536 -0.919536
Tie -1 113,130,263,816 0.040674 -0.040674
Total   2,781,381,002,400 1.000000 -0.203873

*: A "low hand win" is a winning hand of two pair or less.

Hole Card Bonus

I'm told this side bet can be found in Washington state, the Flamingo in Las Vegas, and Norwegian cruise ship casinos. It pays based on the player's hole cards, except the top award also involves the dealer's hole cards. The lower right cell in the following table shows a house edge of 8.54%.

Hole Card Bonus

Bet Pays Combinations Probability Return
Player and dealer have aces 1000 6 0.000004 0.003694
Pair of aces 30 7,344 0.004521 0.135636
A/K suited 25 4,900 0.003017 0.075415
A/Q or A/J suited 20 9,800 0.006033 0.120664
AK off-suit 15 14,700 0.009050 0.135747
Pair J's - K's 10 22,050 0.013575 0.135747
A/Q or A/J off-suit 5 29,400 0.018100 0.090498
Pair 2's - 10's 3 66,150 0.040724 0.122172
All other -1 1,470,000 0.904977 -0.904977
Total   1,624,350 1.000000 -0.085406

Australian Rules

I have an unconfirmed report that at the Crown casino in Perth, Australia, the blind bet pushes if the dealer doesn't qualify and the dealer wins. Assuming no change in strategy, this happens 1 in every 176 hands. When it happens, the player will lose one less unit. The effect is a reduction in the house edge from 2.185% to 1.617%.

6-Card Bonus

Some casinos add on a side bet known as the 6-Card Bonus. This side bet is found on multiple poker-derivative games, so I created a special page for it. For more information, please see my page on the 6-Card Bonus.

Millionaire Progressive

This is a $5 "red light" progressive side bet that pays $1,000,000 for a royal flush in spades, I believe using the player's two hole cards and the flop. For all the rules and analysis, please see my page on the Millionaire Progressive.

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Calculator

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Ask Michael Anything - Ultimate Texas Hold'em Edition

 
See the transcript of the interview here.

Internal Links

External Links

  • Wikipedia — Entry on Ultimate Texas Hold 'Em.
  • Discountgambling.net has an outstanding analysis of this game, including what I call his "nut kicker" strategy for the second and third decision points.
  • Shufflemaster's Ultimate Texas Hold 'Em® page.
  • Demo game — Play this licensed demo game at our sister site Latest Casino Bonuses.