This is a calculator designed to provide the user with a complete analysis of all the strategies and odds in a game of Ultimate Texas Hold ‘Em poker, so it Ultimate Texas Hold'Em - Wizard of Odds. Away from the poker rooms, players can enjoy the excitement and intrigue of Hold’Em in online casinos and in the table games pits of live casinos. Ultimate Texas Hold’Em translates that Hold’Em experience to table games play against the dealer. Here are 10 things every beginner should know before playing Ultimate Texas Hold’Em. Wizard Of Odds Free Ultimate Texas Holdem the best casinos that offer certain types of bonuses. Anything from no-deposit to reload bonuses and much more.
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.
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 |
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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 |
Internal Links
- Ultimate Texas Hold — Analysis of the standard rules.
External Links
- How to play Ultimate Texas Hold 'Em — Entry SkyCity casino in Auckland.
- Discussion about the Auckland variant in my forum at Wizard of Vegas.
Written by:Michael Shackleford
On This Page
Introduction
Rules
- A single 52-card deck is used. All cards count as its poker value. Aces may be high or low.
- One player is designated as the dealer, usually with a laminated marker. This person does not have to physically deal the game. However it is important that a symbolic dealer position rotate around the table.
- The player to the dealer's left must make a 'small blind' bet. The player to the left of the small blind must make a 'big blind' bet. The amounts of both blinds should be specified in advance. The purpose of the blinds is to get the ball rolling with some money in the pot.
- Two cards shall be dealt down to each player, starting with the person to the dealer's left.
- The player to the left of the big blind must either call or raise the big blind bet. The play in turn will go around the table according to normal poker rules, which I assume the reader already knows. Table rules will specify any limits on the size or number of allowed raises.
- The small blind may also raise the big blind. If nobody raises the big blind the player making the big blind has the option to raise his own bet. The term for this is the 'big blind option.'
- Three community cards will be dealt face up in the center of the table. This is called the 'flop.'
- Another round of betting will ensue, starting with the player to the dealer's left.
- A fourth community card will be dealt face up in the center of the table. This card is called the 'turn.'
- Another round of betting will ensue, starting with the player to the dealer's left. Generally the minimum bet is double the first two rounds of betting.
- A fifth and final community card will be dealt face up in the center of the table. This card is called the 'river.'
- Another round of betting will ensue, starting with the player to the dealer's left. The minimum bet is generally the same as the previous round.
- Each player still in the game at the end will determine the highest poker value among his own two cards and the five community cards. It is NOT a requirement that the player use both of his own cards. The player with the hand of highest poker value shall win. Following are the hand rankings.
- Straight flush: Five consecutive and suited cards. For example 5, 6, 7, 8, 9.
- Four of a kind: Four cards of the same rank, plus any fifth card. For example Q, Q, Q, Q ,4.
- Full house: Three of a kind and a pair. For example 6, 6, 6, J , J.
- Flush: Any five cards of the same suit, except for a higher ranking straight flush. For example A, Q, 8, 4 , 3.
- Straight: Five consecutive cards, except for a higher ranking straight flush. For example 8, 9, 10, J, Q.
- Three of a kind: Three cards of the same rank, plus any other two cards. For example 5, 5, 5, Q ,2 .
- Two pair: Two pairs, plus any fifth card. For example 8, 8, 2, 2 ,Q .
- Pair: A pair and any other three cards. For example 7, 7, 2, 5 ,A .
- ? High: Any five cards that do not form any higher poker hand. A king high hand for example might be K, Q, 7, 5 ,4 .
- If two or more players have poker values of the same rank then the individual cards will be used to break the tie. If necessary all five cards will be considered.
- I get asked a lot whether the two unused cards in a player's hand are used to break a tie. The answer is a firm NO. The two unused cards do not matter.
- If a new player arrives at the table he should either wait for the big blind position or put up an amount equal to the big blind, amounting to a call of the big blind.
- If a bet is made after another player runs out of money, then a separate pot is created. The player that ran out of money is not eligible to win the second pot. If more than one player runs out of money then multiple separate pots can be created.
- In formal games players may not bet with cash or buy chips with cash in the middle of a hand.
- There are numerous rules of etiquette, which I won't get into.
- There house may set the betting rules. There are three main types. A 'structured' game features raises of specified amounts. For example a '3/6 game' would mean that raises after the deal and flop are $3, and after the turn and river are $6. There is usually a limit to the number of raises a player may make, typically three. A 'pot limit' game has structured minimum raises but the maximum raise may be anything up to the amount in the pot at the time the raise is made. A 'no limit' game also has structured minimum raises but there is no maximum raise.
Examples
Example 1
Board: A, 2, 4, 5, 6
Player 1: J, 6
Player 2: 7, Q
Player 1: J, 6
Player 2: 7, Q
Player 1 wins. Both have an ace high flush, so the second highest card is considered. Player 1's jack beats player 2's 7. The only way to have a flush tie is if the flush is entirely on the board and no hole cards are higher than the lowest card on the board in the same suit.
Example 2
Board: J, A, 7, 5, 6
Player 1: 2, J
Player 2: 10, J
Player 1: 2, J
Player 2: 10, J
Player 2 wins. Both have a pair of jacks so the singletons are considered. High highet singleton in both hands is an ace so the second highest singleton is considered. Player 1's second highest singleton is a 7, compared to player 2's 10. A 10 beats a 7 so player 2 wins.
Example 3
Board: A, A, K, Q, J
Player 1: Q, J
Player 2: Q, 2
Player 1: Q, J
Player 2: Q, 2
Tie. Both have a two pair of aces and queens, with a king singleton. Some people incorrectly believe that in such cases the unused cards are considered, in this case player 1's pair of jacks beating player 2's jack/2. Only the top five cards matter. The jacks and deuce are irrelevant.
One of the most important aspects of Texas Hold'em is the value of each two-card hand before the flop. The decision of how to play your first two cards is something you face every hand, and the value of your first two cards is highly correlated to your probability of winning.
The following table shows my power rating for each initial 2-card hand in a 10-player game. The numbers are on a 0 to 40 scale. Basically, you should only play hands that are dark green, blue, or purple. Of course you should be more be more liberal in late position and picky in early position. If forced I would say you should need 10 points in late position and 19 points in early position to call the big blind. If your table is loose, as if often the case online, you can play a bit looser yourself.
Use the top table if you have a pair, the middle table if your cards are suited, and the bottom table if your cards are unsuited. Except for a pair,look up your high card along the left and your low card along the top.
Following are the links to my tables of the value of each intial hand according to the number of players. The 10-player section explains the methodology for creating the table table.
Pot Odds
The following table shows the probability of making various hands after the flop and the correct 'pot odds.' The pot odds are the breakeven ratio of money in the pot to the amount you have to bet for the player to be indifferent about calling, assuming the player would definitely win if he makes the hand (a big if) and there are no additional bets (another big if). This table is a good starting point the player should make mental adjustments for the probability of winning without making the hand, losing with making the hand, and expected future bets. The odds of a two pair improving to a full house are the same as those for four to an inside straight.
Pot Odds — After Flop
Hand | Probability of Making Hand | Pot Odds |
---|---|---|
Four to a flush | 34.97% | 1.86 |
Four to an outside straight | 31.45% | 2.18 |
Four to an inside straight | 16.47% | 5.07 |
The next table shows the pot odds after the turn. Free slots video poker games.
Pot Odds — After Turn
Hand | Probability of Making Hand | Pot Odds |
---|---|---|
4 to a flush | 19.57% | 4.11 |
4 to an outside straight | 17.39% | 4.75 |
4 to an inside straight | 8.70% | 10.50 |
Hand Strength Calculator
I'm proud to present my new and improved Poker Odds Calculator. Enter any situation in Texas Hold 'Em, and it will tell you the probability of each possible outcome.
Poker Tournament Calculator
My Poker Tournament Calculator will determine each player's probability, for up to nine players, of finishing in each place, and his expected share of any prize pool, assuming equal skill among all players. It produces the same results as what is known as the Independent Chip Model.
Internal Links
- Pinapple — Strategy and analysis of which card to discard before the flop.
- Bad Beat Jackpots: What is the Probability of Hitting one?
- Texas Hold 'Em Dominated Hand Probabilities: What is the probability one of your opponents has similar, and better, hole cards than yours?