Last Updated: Nov. 6, 2014

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.

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
    Delaer 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.




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%.

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.

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.


For each rank on the board there are three more that can beat you. For example, if the dealer has the jack of hearts, diamonds, or spades he will pair up and beat you. So, 5×3=15 cards will give the dealer a hidden pair. Also, all four queens and aces will beat you. So, 15+8=23 cards will beat you. You need to have less than 21 outs to stay in, so fold.

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.

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

Big 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 also no Envy Bonus with the Big Progressive.

Buffalo Thunder Progressive — $100,000 Jackpot

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%.

Michigan Progressive

I have a report that the Firekeeper's casino in Michigan has a $1 progressive jackpot based on the flop and the player's two hole cards. I hear the jackpot seed is $10,000. I don't know the contribution rate. The win for a royal flush is 100% of the jackpot, and 10% for a straight flush. The following return table shows the probability and return for each hand. All pays are on a "for one" basis, meaning the player never gets his original bet back, even if he wins.

Michigan Progressive — $100,000 Jackpot

Event Pays Combinations Probability Return
Royal flush 100% of jackpot 4 0.000002 ?
Straight flush 10% of jackpot 36 0.000014 ?
Four of a kind 300 624 0.00024 0.072029
Full house 50 3744 0.001441 0.072029
Flush 40 5108 0.001965 0.078616
Straight 30 10200 0.003925 0.117739
Three of a kind 9 54912 0.021128 0.190156
All other 0 2524332 0.971285 0
Total 2598960 1 0.530569

For any given jackpot amount, the return is 53.057% + 2.924% for every $10,000 in the jackpot meter. The breakeven point, where there would be zero house edge is at a mater of $160,530.53.

I have an unconfirmed report that the "Michigan Progressive" offers envy bonuses of $300 if another player has a straight flush, and $1,000 for a royal flush. If true, this would add 0.57% to the return for each additional player.

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  • 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.
  • James Grosjean strategy. For $5.95 you get a laminated strategy card and one the size of a business card. It is short, intuitive, and powerful. The house edge is 2.3%, also 0.1% higher than optimal. In my opinion, this one is easily the best, and well worth the six bucks.

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