Ultimate Texas Holdem Basic Strategy
- Basic Strategy For Ultimate Texas Holdem introduce you to the most popular table game in the casinos: Blackjack! Beat the dealers hand and grab winnings that can change your life instantly!
- Usually, ultimate Texas Hold’em is played with up to 6 players and the dealer in a casino, the dealer is also known as the house. This Texas Hold’em utilises a standard 52 card deck. However, when you play ultimate Texas Hold’em online, you will find many heads up games where you compete one-on-one against the house.
Ultimate Texas Hold'em (UTH) is one of the most popular novelty games in the market. For that reason, it is important to understand the multitude of ways that UTH may be vulnerable to advantage play. Many of my recent posts have concerned some of these possibilities. But the computations are tedious. It took my computer 5 days to run the cycle where the AP sees one dealer hole-card (see this post). Then my computer spent 8 days analyzing the situation where the AP sees one dealer hole-card and one Flop card (see this post). After that, my computer crunched hands for just over 2 days considering computer-perfect collusion with six players at the table (see this post). After all of this time spent on more advanced plays, I decided to take a step back to compute the house edge off the top, using perfect basic strategy and no advantage play. It took my computer three days to run the pre-Flop cycle and another two days to run the Flop cycle. Finally, I have some basic strategy data to present.
Jan 21, 2021 Ultimate Texas Hold'em - Basic Strategy While players who have a lot of experience playing Texas Holdem will immediately feel comfortable playing Ultimate Texas Hold'em as a casino game, the optimal strategy is slightly different given a few obvious factors: You are only playing against the dealer, not any other players. May 16, 2015 Ultimate Texas Hold'em (UTH) is one of the most popular novelty games in the U.S. For example, only Three Card Poker and Let it Ride have more placements in Nevada. What makes UTH so successful is its similarity to Hold'em poker together with the chance for a huge payday if the player makes a top hand.
This analysis has been done before and has been done better by both Michael Shackleford and James Grosjean. In particular, Michael Shackleford's extraordinary page on UTH includes a practical strategy for the Flop (check / raise 2x) and Turn/River (raise 1x / fold) bets, which I will borrow here in my presentation. In light of what has been done before, if I had nothing new to offer here, I would forgo this post. However, as the reader will soon see, this work includes megabytes of new fun.
As a reminder, here are the rules for UTH (taken from this document):
The player makes equal bets on the Ante and Blind.
Five community cards are dealt face down in the middle of the table.
The dealer gives each player and herself a set of two starting cards, face down.
Players now have a choice:
Check (do nothing); or
Make a Play bet of 3x or 4x their Ante.
The dealer then reveals the first three community cards (the 'Flop' cards).
Players who have not yet made a Play bet have a choice:
Check: or
Make a Play bet of 2x their Ante.
The dealer then reveals the final two community cards (the 'Turn/River' cards).
Player who have not yet made a Play bet have a choice:
Fold and forfeit their Ante and Blind bets; or
Make a Play bet of 1x their Ante.
The dealer the reveals her two starting cards and announces her best five-card hand. The dealer needs a pair or better to 'qualify.'
Now what? Well, either the dealer qualifies or she doesn't. The player beats, ties or loses to the dealer. Either the player's hand is good enough to qualify for a 'Blind' bonus payout, it doesn't. The following table hopefully clarifies all of these possibilities and gives the payouts in every case:
The final piece of the puzzle is the Blind bet. As the payout schedule above shows, if the player wins the hand, regardless if the dealer qualifies, then the player's Blind bet is paid according to the following pay table:
Royal Flush pays 500-to-1.
Straight Flush pays 50-to-1.
Four of a Kind pays 10-to-1.
Full House pays 3-to-1.
Flush pays 3-to-2.
Straight pays 1-to-1.
All others push.
Combinatorial Analysis
The following spreadsheet contains my full combinatorial analysis. It presents the 169 unique starting hands, together with the edge for checking and raising 4x. The sheet also gives the number of hands equivalent to the listed hand (the suit-permutations). For example, because the starting hand (2c,7d) is equivalent to (2h, 7s), only the hand (2c,7d) was analyzed.
In particular:
The house edge for UTH is 2.18497%.
The player checks pre-Flop on 62.29261% of the hands.
The player raises 4x pre-Flop on 37.70739% of the hands.
The player has a pre-Flop edge over the house on 35.29412% of the hands.
The player should never raise 3x pre-Flop.
Pre-Flop Strategy
Here is a summary of pre-Flop basic strategy taken from the spreadsheet above:
Raise 4x on the following hands, whether suited or not:
A/2 to A/K
K/5 to K/Q
Q/8 to Q/J
J/T
Raise 4x on the following suited hands:
K/2, K/3, K/4
Q/6, Q/7
J/8, J/9
Raise on any pair of 3's or higher.
Check all other hands.
Flop Strategy
A Flop decision to check or raise 2x is only possible if the player checked pre-Flop. By reference to the pre-Flop strategy above, it turns out there are exactly 100 equivalence classes of starting hands where the player checked pre-Flop. I re-ran my UTH basic strategy program to consider each of these 100 hands and each possible Flop that can appear with that starting hand. For each starting hand where the player checked pre-Flop, there are combin(50,3) = 19,600 Flops to consider. Thus, altogether, I had to evaluate the Flop decision to check or raise 2x for 100 x 19,600 = 1,960,000 situations.
The following four spreadsheets contain the analysis for each of these 1,960,000 possibilities. Each spreadsheet contains the full data for 25 starting hands for the player. Note, these spreadsheets are each approximately 20M in size:
To understand the data in these spreadsheets, the following image gives the first few Flop decisions for the player starting hand (8c, Jd) (see spreadsheet #3):
For example, consider the hand player = (8c, Jd), Flop = (2c, 3c, Jc). Then the EV for checking is 1.267304 and the EV for raising 2x is 1.848414. As is intuitively obvious (because the player paired his Jack), raising 2x is correct here.
Now look at the hand right below that, player = (8c, Jd) and Flop = (2c, 3c, Qc). This is also a hand where the player should raise 2x (the decision is very close), but I have very little intuition for why this might be the case. Perhaps because there is a runner-runner straight draw and a flush draw.
Now look at the very next row. When the player holds (8c, Jd) and the Flop is (2c, 3c, Kc), then it is correct to check. The runner-runner straight no longer exists.
Any attempt to quantify such subtleties into a full strategy must surely be a painstaking task. The reader is invited to cull these four spreadsheets (approx. 80M) and create such a complete strategy for himself: I am going to forgo this exercise.
Michael Shackleford's approximation to Flop strategy is simple and smart. The player should raise 2x with two pair or better, a hidden pair (except pocket 2's) or four to a flush with a kicker of T or higher. We see that the hand given above, where player = (8c, Jd), Flop = (2c, 3c, Qc), violates Shackleford's strategy. It is four to a flush with kicker 8c. Shackleford's incorrect strategy for this hand corresponds to a very small loss of EV (0.377%). This small loss of EV is well worth the investment, given the strategic simplicity it yields.
Turn/River Strategy
One can certainly use Shackleford's very easy Turn/River strategy for the final Turn/River decision: The player should raise 1x when he has a hidden pair, or there are fewer than 21 dealer outs that can beat the player, otherwise he should fold.(see the thread on WizardofVegas.com for a discussion about the meaning of '21 outs.') One can also use Grosjean's more complex strategy from Exhibit CAA, that I won't repeat here. Good luck getting a copy of CAA. (James, make your book available! Please!).
My complete method here, were I to do it, would be to post spreadsheets containing computer-perfect play so that the reader could devise his own Turn/River strategy. By reference to the Flop strategy spreadsheets given above, of the 1,960,000 Flop possibilities, exactly 1,273,842 of them correspond to the player checking on the Flop. Each of these checking possibilities yields an additional combin(47,2) = 1,081 Turn/River hands to complete the board, where the player then has to then choose to either fold or raise 1x on each. That is, the complete spreadsheet analysis of the Turn/River decision would mean posting a total of 1,960,000 x 1,081 = 1,377,023,202 hands for the reader to consider.
Yeah, well ... at any rate, for the curious, here is my derivation of Shackleford's result concerning playing hands with 20 or fewer dealer outs:
Clearly if the player folds, then his EV is -2.
Let N be the number of outs under consideration for the dealer to beat the player. Then the probability that the dealer's first card is an out is p = N/45. For his second card, the dealer who whiffed on his first card most likely has 3 additional 'pair outs' to pair his first card and beat the player. He may also generate new straight or flush outs (call these 1 additional 'out,' so-called 'runner-runner'). So, the probability of the dealer beating the player by hitting an out on his second card is approximately (N + 4)/44.
Overall, the probability that the dealer beats the player is then,
p = N/45 + [(45 - N)/45]*[(N + 4)/44].
Simplifying, we get:
p = (-N^2 + 85 N + 180)/(45*44)
Note that if the dealer doesn't hit an out, then he won't qualify. It follows that the EV for the player who raises 1x on the Turn/River bet is:
EV = p*(-3) + (1-p)*(1) = 1 - 4p.
We make the raise whenever EV > -2. That is, 1 - 4p > -2. Solving for p gives
p < 3/4.
That is, the player raises 1x when his chance of beating the dealer is 25% or higher.
Combining the two expressions for p, we see that EV > -2 whenever
(-N^2 + 85 N + 180)/(45*44) < 3/4.
Simplifying gives the quadratic equation,
N^2 - 85N + 1305 > 0
Solving this quadratic equation gives roots:
(1/2)*(85 + sqrt(2005)) = 64.9
(1/2)*(85 - sqrt(2005)) = 20.1
For the quadratic equation to be positive, N must be either larger than both roots or smaller than both roots. That is, either N ≥ 65 or N ≤ 20. The first case is the 'impossible solution,' leading to the conclusion that there can be at most 20 dealer outs that can beat the player.
Conclusion
Here is a summary of the edges for the strategies referenced above:
Computer-perfect strategy for UTH yields a house edge of 2.18497%.
Shackleford's practical strategy for UTH yields a house edge of about 2.43%.
Grosjean's strategy for UTH in Exhibit CAA yields a house edge of 2.35%.
Just a few months ago, I wrote about how I thought Ultimate Texas Hold’em has the perfect betting structure. This past Saturday night, I had an opportunity to see this in action.
My wife and I attended the new variety show at Wynn called Showstoppers. I definitely recommend it, but would suggest looking for discount tickets!
After the show, we stopped to watch an Ultimate Texas Hold’em table game in action. It was a $15 table, which is not for the faint of heart. You have to be ready to wager $75-$100 per hand, including the Ante, Blind, Trips and Play wagers.
In one hand, I saw everything that makes this game the blockbuster it is. First there was a player who had a marginal 4x hand. He had a King-8 offsuit. The player will win this hand about 54% of the time and lose about 42.5%.
The player clearly did not have a strong grasp of the game or the rules. After seeing his first two cards, he attempted to make a play wager that was only 1x his Ante. I don’t know how you sit down with hundreds of dollars at risk and have little idea of the strategy and knowledge of the basics of the game!
The dealer told the player he could not bet 1x at this point. He asked the player to show him the cards. Upon seeing the K-8, the dealer said this hand was worth the wager, but only 3x and not 4x!
At this point, I was ready to smack my head against the table (or maybe the dealer’s). There is no hand in UTH that would make you want to bet 3x instead of 4x. Being able to bet 4x is an advantage to the player. By betting only 3x, you’re giving some of this back to the house.
While there are some hands betting 3x is better than waiting for the flop, there are none you are better off betting 3x over 4x. The right play was to bet 4x and this player cost himself some potential payback.
Lesson No. 1:Don’t listen to the Dealers.
I’m sure many are knowledgeable at some basic games like Blackjack or games that have simple strategy like Three Card Poker. But why would you think the dealer knows the strategy for UTH?
I developed the only known strategy for the game. I haven’t had a chance to yet complete my booklet, so the likelihood the dealer really knows the right strategy is very slim.
Lesson No. 2:Know the rules of the game you are playing.
I didn’t notice if the table had instruction cards for the game, but here in Las Vegas, the tables frequently do. Read them before you play.
The story doesn’t end there. From what I’ve told you so far, it would explain why the game holds so much for the casino, but it doesn’t necessarily explain why the game is so popular despite holding so well for the casino. We have to move to our second player for that. He had an even stronger hand. A-10 offsuit.
Again, not a massive hand, but this one will win 59% of the time vs. losing 38%. I watched as he chose not to make a 4x wager at all. I guess only a pair of bullets will do. The flop came – J-5-3. No real help.
He decided to make a 2x wager shaking his head, as if he wasn’t too happy about doing it. He had the top card. There was little chance of a Straight or Flush on the board. The hand still wasn’t great, but not bad.
Along comes the turn and the river. The 5 paired up and an 8. He shook his head further. I didn’t understand why. Sure, he didn’t pull an Ace or a 10, but still had the top kicker. The dealer had now automatically qualified because the board had a pair. Realistically, there were 11 outs for the dealer, who would need a J, 8, 5 or 3 to beat the player.
On a very rough calculation we can go with 11 outs times 2 Dealer Cards, which gives us 22 out of 45 remaining. The player was in a 50/50 position at this point, if we allow for pocket pairs. Again, not exactly where you want to be, but you could be doing a lot worse.
I don’t remember the exact cards the dealer had, but I do know he didn’t have a J, 8, 5 or 3 or a pocket pair. The player won $15 for the Ante and $30 on the Play. The Blind pushed. He won $45. He was as happy as can be!
At that very moment, my thoughts on UTH’s betting structure were completely confirmed. The player made a wrong decision and cost himself money. He should have had $75, but won only $45. He was happy as a clam.
A few months ago, I likened this to a player playing blackjack who doesn’t double down when he should and is still happy he wins the hand for $10 instead of $20. The only difference is in blackjack an opportunity to double down occurs about 5-10% of the time.
In UTH, the opportunity to bet 4x occurs around 50% of the time.
This means if you chicken out of all but the top hands, you’ll be doing the wrong thing 25-40% of the time. This is going to cost you big bucks over time.
The ultimate irony is that you’ll probably be as happy as can be while doing it!
Buy his book now!
Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected].
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