Ultimate Texas Hold 'Em - Rules and Strategy Chart - Wizard

graceacupuncture - 26/04/2022 - STRATEGY - 237 Views

Ultimate Texas Hold 'Em - Rules and Strategy ChartUltimate Texas Hold 'Em - Rules and Strategy Chart - Wizard

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, with some minor rule changes, is also distributed by Galaxy Gaming under the name Heads Up Hold 'Em. Evolution Gaming, a supplier of live dealer games to Internet casinos, refers to the game as "Extreme Texas Hold 'Em" in some jurisdictions, for legal reasons.

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

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Rules

Following 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.

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 any combination of their own two cards and 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.WinnerDealer OpensBlindAntePlayPlayerYesWinWinWinPlayerNoWinPushWinDealerYesLoseLoseLoseDealerNoLosePushLoseTieYes or NoPushPushPushWinning Ante and Play bets pay 1 to 1. Winning Blind bets pay according to the following pay table.Player HandPaysRoyal flush500 to 1Straight flush50 to 1Four of a kind10 to 1Full house3 to 1Flush3 to 2Straight1 to 1All otherPushThe 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."

RaiseDealerQualifiesPlayer HandWinnerPaysCombinationsProbabilityReturnLargeYesLess than straightPlayer53,671,050,165,8800.1319870.659933LargeYesStraightPlayer6246,174,692,1600.0088510.053105LargeYesFlushPlayer6.5241,047,929,0800.0086660.056332LargeYesFull housePlayer8295,405,180,9200.0106210.084966LargeYesFour of a kindPlayer1523,008,208,7600.0008270.012408LargeYesStraight flushPlayer551,818,135,7600.0000650.003595LargeYesRoyal flushPlayer505596,356,9200.0000210.010828LargeNoLess than straightPlayer41,556,797,035,8400.0559720.223888LargeNoStraightPlayer581,416,649,9600.0029270.014636LargeNoFlushPlayer5.550,874,988,6800.0018290.010060LargeNoFull housePlayer700.0000000.000000LargeNoFour of a kindPlayer1400.0000000.000000LargeNoStraight flushPlayer54229,686,8400.0000080.000446LargeNoRoyal flushPlayer50490,386,2800.0000030.001638Large0 Push0285,142,270,6000.0102520.000000LargeYes Dealer-63,931,554,359,9200.141353-0.848116LargeNo Dealer-5102,655,952,4000.003691-0.018454MediumYesLess than straightPlayer32,114,839,654,7640.0760360.228107MediumYesStraightPlayer4133,100,158,9920.0047850.019142MediumYesFlushPlayer4.5152,618,008,7840.0054870.024692MediumYesFull housePlayer6289,401,836,8800.0104050.062430MediumYesFour of a kindPlayer1318,537,793,6200.0006660.008664MediumYesStraight flushPlayer532,704,129,5040.0000970.005153MediumYesRoyal flushPlayer503112,333,5000.0000040.002031MediumNoLess than straightPlayer21,083,763,469,5920.0389650.077930MediumNoStraightPlayer345,053,788,3560.0016200.004860MediumNoFlushPlayer3.538,820,798,3960.0013960.004885MediumNoFull housePlayer500.0000000.000000MediumNoFour of a kindPlayer1200.0000000.000000MediumNoStraight flushPlayer52358,131,4560.0000130.000670MediumNoRoyal flushPlayer5028,830,6200.0000000.000159MediumPush0191,611,691,0600.0068890.000000MediumYes Dealer-41,841,155,221,0880.066196-0.264783MediumNo Dealer-37,978,353,1080.000287-0.000861SmallYesLess than straightPlayer21,375,033,295,0720.0494370.098874SmallYesStraightPlayer3395,087,247,7680.0142050.042614SmallYesFlushPlayer3.5190,959,227,1360.0068660.024030SmallYesFull housePlayer543,297,986,8400.0015570.007784SmallYesFour of a kindPlayer12859,737,9840.0000310.000371SmallYesStraight flushPlayer521,962,591,5760.0000710.003669SmallYesRoyal flushPlayer50242,135,6600.0000020.000760SmallNoLess than straightPlayer1720,579,458,7480.0259070.025907SmallNoStraightPlayer2136,018,223,4840.0048900.009781SmallNoFlushPlayer2.540,911,000,8040.0014710.003677SmallNoFull housePlayer400.0000000.000000SmallNoFour of a kindPlayer1100.0000000.000000SmallNoStraight flushPlayer51269,696,3040.0000100.000495SmallNoRoyal flushPlayer5016,109,0200.0000000.000110SmallPush0418,339,128,0880.0150410.000000SmallYes Dealer-32,700,150,685,6920.097079-0.291238SmallNo Dealer-247,223,220,3440.001698-0.003396Fold-25,335,144,079,7600.191816-0.383633Total 27,813,810,024,0001.000000-0.021850

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.Ultimate Texas Hold 'Em - Rules and Strategy Chart - Wizard

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.

Bet TypeAverageWagerAveragePaysAverageWinAnte1-0.165757-0.165757Blind1-0.314685-0.314685Play2.1522520.2130760.458593Total4.152252 -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.

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%.Ultimate Texas Hold 'Em - Rules and Strategy Chart - Wizard

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.

Playing Blind

I've been asked about "playing blind," meaning making the same raise bet every hand. The following table shows the win, combinations, probability, and contribution to the return for all possible event playing blindly with a 1x Play bet every hand. The lower right cell shows an expected loss of 40.7%, relative to the Ante bet. Compared to the total three units bet per hand (Ante, Blind, and Play), the element of risk, defined as the ratio of expected loss to total amount bet, is 13.57%.

EventPaysCombinationsProbabilityReturnPlayer loses, dealer doesn't qualify-276,626,795,6000.027550-0.055100Player loses, dealer qualifies-31,257,498,573,6920.452113-1.356339Push0113,130,263,8160.0406740.000000Player wins with royal flush, dealer doesn't qualify50110,532,5920.0000040.001897Player wins with straight flush, dealer doesn't qualify5185,751,4600.0000310.001572Player wins with four of a kind, dealer doesn't qualify11-0.0000000.000000Player wins with full house, dealer doesn't qualify4-0.0000000.000000Player wins with flush, dealer doesn't qualify2.513,060,678,7880.0046960.011739Player wins with straight, dealer doesn't qualify226,248,866,1800.0094370.018875Player wins with three of a kind or less, dealer doesn't qualify1356,577,881,2200.1282020.128202Player wins with royal flush, dealer qualifies50275,082,6080.0000270.013551Player wins with straight flush, dealer qualifies52648,485,6840.0002330.012124Player wins with four of a kind, dealer qualifies124,240,864,8000.0015250.018297Player wins with full house, dealer qualifies562,810,500,4640.0225820.112912Player wins with flush, dealer qualifies3.558,462,516,5000.0210190.073567Player wins with straight, dealer qualifies377,436,209,8920.0278410.083523Player wins with three of a kind or less, dealer qualifies2734,467,999,1040.2640660.528132Total 2,781,381,002,4001.000000-0.407047

The next table shows the same information but with a 4x raise. Note that the bottom line shows an expected loss of the same 40.7% of the Ante bet. This is because the Play bet is perfectly balanced, if always made, so it contains no house edge. However, the total amount bet would be six units, making the element of risk 40.7%/6 = 6.78%.

EventPaysCombinationsProbabilityReturnPlayer loses, dealer doesn't qualify-576,626,795,6000.027550-0.137750Player loses, dealer qualifies-61,257,498,573,6920.452113-2.712678Push0113,130,263,8160.0406740.000000Player wins with royal flush, dealer doesn't qualify50410,532,5920.0000040.001909Player wins with straight flush, dealer doesn't qualify5485,751,4600.0000310.001665Player wins with four of a kind, dealer doesn't qualify14-0.0000000.000000Player wins with full house, dealer doesn't qualify7-0.0000000.000000Player wins with flush, dealer doesn't qualify5.513,060,678,7880.0046960.025827Player wins with straight, dealer doesn't qualify526,248,866,1800.0094370.047187Player wins with three of a kind or less, dealer doesn't qualify4356,577,881,2200.1282020.512807Player wins with royal flush, dealer qualifies50575,082,6080.0000270.013632Player wins with straight flush, dealer qualifies55648,485,6840.0002330.012823Player wins with four of a kind, dealer qualifies154,240,864,8000.0015250.022871Player wins with full house, dealer qualifies862,810,500,4640.0225820.180660Player wins with flush, dealer qualifies6.558,462,516,5000.0210190.136625Player wins with straight, dealer qualifies677,436,209,8920.0278410.167046Player wins with three of a kind or less, dealer qualifies5734,467,999,1040.2640661.320330Total 2,781,381,002,4001.000000-0.407047

In conclusion about playing blind, it is a terrible idea. However, if you must do so, make the maximum 4x raise.

Trips Bet

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

Player HandCombinationsPaysProbabilityReturnRoyal flush4324500.0000320.001616Straight flush37260400.0002790.01114Four of a kind224848300.0016810.05042Full house347318490.0259610.233649Flush404764470.0302550.211785Straight618002040.0461940.184775Three of a kind646162030.0482990.144896All other113355660-10.8473-0.8473Total133784560 1-0.009018Player HandCombinationsPaysProbabilityReturnRoyal flush4324500.0000320.001616Straight flush37260400.0002790.01114Four of a kind224848300.0016810.05042Full house347318480.0259610.207688Flush404764460.0302550.18153Straight618002050.0461940.230969Three of a kind646162030.0482990.144896All other113355660-10.8473-0.8473Total133784560 1-0.01904Player HandCombinationsPaysProbabilityReturnRoyal flush4324500.0000320.001616Straight flush37260400.0002790.01114Four of a kind224848300.0016810.05042Full house347318480.0259610.207688Flush404764470.0302550.211785Straight618002040.0461940.184775Three of a kind646162030.0482990.144896All other113355660-10.8473-0.8473Total133784560 1-0.034979

Pay table #3 seen at the Mirage.

Player HandCombinationsPaysProbabilityReturnRoyal flush4324500.0000320.001616Straight flush37260400.0002790.01114Four of a kind224848200.0016810.033613Full house347318470.0259610.181727Flush404764460.0302550.18153Straight618002050.0461940.230969Three of a kind646162030.0482990.144896All other113355660-10.8473-0.8473Total133784560 1-0.061808

Pay table #4 seen at Shufflemaster TableMax units.

In Florida, the player must also beat the dealer to win the Trips bet. There is also an increase in the pay table to adjust for this. For the full rules, please see my page on the Florida Variant of Trips Bet.

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.

EventPaysEnvyBonusCombinationsProbabilityReturnEnvyReturnRoyal flush100% of jackpot100040.0000020.0000000.001539Straight flush10% of jackpot300360.0000140.0000000.004156Four of a kind300 6240.0002400.0720290.000000Full house50 3,7440.0014410.0720290.000000Flush40 5,1080.0019650.0786160.000000Straight30 10,2000.0039250.1177390.000000Three of a kind9 54,9120.0211280.1901560.000000Total74,6280.0287150.5305690.005695

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).

OtherPlayers$1 Bet$5 Bet0$160,530.53$802,652.631$158,583.16$792,915.792$156,635.79$783,178.953$154,688.42$773,442.114$152,741.05$763,705.265$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.

EventPaysEnvyCombinationsProbabilityReturnHidden royal flushJackpot$10086,4800.000031?Community royal flush$1000$04,3240.0000020.001539Straight flush$250$0782,4600.0002790.069627Four of a kind$75$04,721,8080.0016810.126050Full house$10$072,936,8640.0259610.259610All other$0$02,730,943,8240.9720470.000000Total2,809,475,7601.0000000.456827 + ?

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.

OtherPlayersJackpot5$17,146.074$17,246.073$17,346.072$17,446.071$17,546.070$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.

EventPaysPermutationsProbabilityReturnPlayer flops royal100% of jackpot10377600.000002?Royal partially on board5% of jackpot197174400.000029?Royal entirely on board300010377600.0000020.004617Straight flush2501877904000.0002790.069627Four of a kind10011332339200.0016810.168067Full house10175048473600.0259610.25961All other06554265177600.9720470Total 67427418240010.502077 + ?

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.

Losing HandPaysCombinationsProbabilityReturnStraight flush7,50010,300,5920.0000040.027776Four of a kind500471,040,5120.0001690.084677Full house508,435,225,3760.0030330.151637Flush3019,434,208,5920.0069870.209618Straight2018,271,076,9760.0065690.131381Three of a kind964,049,759,4480.0230280.207252Low hand win*-12,557,579,127,0880.919536-0.919536Tie-1113,130,263,8160.040674-0.040674Total 2,781,381,002,4001.000000-0.147868Losing HandPaysCombinationsProbabilityReturnStraight flush10,00010,300,5920.0000040.037034Four of a kind500471,040,5120.0001690.084677Full house408,435,225,3760.0030330.121310Flush2519,434,208,5920.0069870.174681Straight2018,271,076,9760.0065690.131381Three of a kind964,049,759,4480.0230280.207252Low hand win*-12,557,579,127,0880.919536-0.919536Tie-1113,130,263,8160.040674-0.040674Total 2,781,381,002,4001.000000-0.203873

*: 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%.

BetPaysCombinationsProbabilityReturnPlayer and dealer have aces100060.0000040.003694Pair of aces307,3440.0045210.135636A/K suited254,9000.0030170.075415A/Q or A/J suited209,8000.0060330.120664AK off-suit1514,7000.0090500.135747Pair J's - K's1022,0500.0135750.135747A/Q or A/J off-suit529,4000.0181000.090498Pair 2's - 10's366,1500.0407240.122172All other-11,470,0000.904977-0.904977Total 1,624,3501.000000-0.085406

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.

Play for Free

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Calculator

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Written by:

Michael Shackleford