Ultimate Texas Holdem House Edge

Posted on3/31/2022by admin

efdisrafucilso.netlify.com › █ █ Ultimate Texas Holdem House Edge █ █

House Advantage Ultimate Texas Holdem
Unlimited Practice Holdem Poker Wizard
Ultimate Texas Holdem House Advantage
Ultimate Texas Holdem Strategy Chart

Introduction

Download this game from Microsoft Store for Windows 10, Windows 8.1. See screenshots, read the latest customer reviews, and compare ratings for Texas hold'em Poker Plus. Casino Hold’em house edge goes up to 2.5%, which are not be best odds ever, but not bad either. Follow optimal guidelines and you ought to be fine. Casino Holdem odds are generous to players who raise often and fold rarely, which is sort of an optimal strategic theory. Which Live Casino Software Providers Offer Casino Holdem. YOU ARE PLAYING AGAINST THE DEALER, NOT AGAINST OTHER PLAYERS. You do not have to try.

The house edge is defined as the ratio of the average loss to the initial bet. In some games the beginning wager is not necessarily the ending wager. For example in blackjack, let it ride, and Caribbean stud poker, the player may increase their bet when the odds favor doing so. In these cases the additional money wagered is not figured into the denominator for the purpose of determining the house edge, thus increasing the measure of risk. For games like Ultimate Texas Hold 'Em and Crazy 4 Poker, where there are two required initial wagers, the house edge is based on one of them only. House edge figures are based on optimal or near-optimal player strategy.

The table below shows the house edge of most popular casino games and bets.

Casino Game House Edge

Game	Bet/Rules	House Edge	Standard Deviation
Baccarat	Banker	1.06%	0.93
	Player	1.24%	0.95
	Tie	14.36%	2.64
Big Six	$1	11.11%	0.99
	$2	16.67%	1.34
	$5	22.22%	2.02
	$10	18.52%	2.88
	$20	22.22%	3.97
	Joker/Logo	24.07%	5.35
Bonus Six	No insurance	10.42%	5.79
Bonus Six	With insurance	23.83%	6.51
Blackjack^a	Liberal Vegas rules	0.28%	1.15
Caribbean Stud Poker	5.22%	2.24
Casino War	Go to war on ties	2.88%	1.05
	Surrender on ties	3.70%	0.94
	Bet on tie	18.65%	8.32
Catch a Wave	0.50%	d
Craps	Pass/Come	1.41%	1.00
	Don't pass/don't come	1.36%	0.99
	Odds — 4 or 10	0.00%	1.41
	Odds — 5 or 9	0.00%	1.22
	Odds — 6 or 8	0.00%	1.10
	Field (2:1 on 12)	5.56%	1.08
	Field (3:1 on 12)	2.78%	1.14
	Any craps	11.11%	2.51
	Big 6,8	9.09%	1.00
	Hard 4,10	11.11%	2.51
	Hard 6,8	9.09%	2.87
	Place 6,8	1.52%	1.08
	Place 5,9	4.00%	1.18
	Place 4,10	6.67%	1.32
	Place (to lose) 4,10	3.03%	0.69
	2, 12, & all hard hops	13.89%	5.09
	3, 11, & all easy hops	11.11%	3.66
	Any seven	16.67%	1.86
Crazy 4 Poker	Ante	3.42%*	3.13*
Double Down Stud	2.67%	2.97
Heads Up Hold 'Em	Blind pay table #1 (500-50-10-8-5)	2.36%	4.56
Keno	25%-29%	1.30-46.04
Let it Ride	3.51%	5.17
Pai Gow^c	1.50%	0.75
Pai Gow Poker^c	1.46%	0.75
Pick ’em Poker	0% - 10%	3.87
Red Dog	Six decks	2.80%	1.60
Roulette	Single Zero	2.70%	e
Roulette	Double Zero	5.26%	e
Sic-Bo	2.78%-33.33%	e
Slot Machines	2%-15%^f	8.74^g
Spanish 21	Dealer hits soft 17	0.76%	d
Spanish 21	Dealer stands on soft 17	0.40%	d
Super Fun 21	0.94%	d
Three Card Poker	Pairplus	7.28%	2.85
Three Card Poker	Ante & play	3.37%	1.64
Ultimate Texas Hold 'Em	Ante	2.19%	4.94
Video Poker	Jacks or Better (Full Pay)	0.46%	4.42
Wild Hold ’em Fold ’em	6.86%	d

Notes

a	Liberal Vegas Strip rules: Dealer stands on soft 17, player may double on any two cards, player may double after splitting, resplit aces, late surrender.
b	Las Vegas single deck rules are dealer hits on soft 17, player may double on any two cards, player may not double after splitting, one card to split aces, no surrender.
c	Assuming player plays the house way, playing one on one against dealer, and half of bets made are as banker.
d	Yet to be determined.
e	Standard deviation depends on bet made.
f	Slot machine range is based on available returns from a major manufacturer
g	Slot machine standard deviation based on just one machine. While this can vary, the standard deviation on slot machines are very high.

Guide to House Edge

The reason that the house edge is relative to the original wager, not the average wager, is that it makes it easier for the player to estimate how much they will lose. For example if a player knows the house edge in blackjack is 0.6% he can assume that for every $10 wager original wager he makes he will lose 6 cents on the average. Most players are not going to know how much their average wager will be in games like blackjack relative to the original wager, thus any statistic based on the average wager would be difficult to apply to real life questions.

The conventional definition can be helpful for players determine how much it will cost them to play, given the information they already know. However the statistic is very biased as a measure of risk. In Caribbean stud poker, for example, the house edge is 5.22%, which is close to that of double zero roulette at 5.26%. However the ratio of average money lost to average money wagered in Caribbean stud is only 2.56%. The player only looking at the house edge may be indifferent between roulette and Caribbean stud poker, based only the house edge. If one wants to compare one game against another I believe it is better to look at the ratio of money lost to money wagered, which would show Caribbean stud poker to be a much better gamble than roulette.

Many other sources do not count ties in the house edge calculation, especially for the Don’t Pass bet in craps and the banker and player bets in baccarat. The rationale is that if a bet isn’t resolved then it should be ignored. I personally opt to include ties although I respect the other definition.

Element of Risk

For purposes of comparing one game to another I would like to propose a different measurement of risk, which I call the 'element of risk.' This measurement is defined as the average loss divided by total money bet. For bets in which the initial bet is always the final bet there would be no difference between this statistic and the house edge. Bets in which there is a difference are listed below.

House Advantage Ultimate Texas Holdem

Element of Risk

Game	Bet	House Edge	Element of Risk
Blackjack	Atlantic City rules	0.43%	0.38%
Bonus 6	No insurance	10.42%	5.41%
Bonus 6	With insurance	23.83%	6.42%
Caribbean Stud Poker	5.22%	2.56%
Casino War	Go to war on ties	2.88%	2.68%
Crazy 4 Poker	Standard rules	3.42%*	1.09%
Heads Up Hold 'Em	Pay Table #1 (500-50-10-8-5)	2.36%	0.64%
Double Down Stud	2.67%	2.13%
Let it Ride	3.51%	2.85%
Spanish 21	Dealer hits soft 17	0.76%	0.65%
Spanish 21	Dealer stands on soft 17	0.40%	0.30%
Three Card Poker	Ante & play	3.37%	2.01%
Ultimate Texas Hold 'Em	2.19%*	0.53%
Wild Hold ’em Fold ’em	6.86%	3.23%

Standard Deviation

The standard deviation is a measure of how volatile your bankroll will be playing a given game. This statistic is commonly used to calculate the probability that the end result of a session of a defined number of bets will be within certain bounds.

The standard deviation of the final result over n bets is the product of the standard deviation for one bet (see table) and the square root of the number of initial bets made in the session. This assumes that all bets made are of equal size. The probability that the session outcome will be within one standard deviation is 68.26%. The probability that the session outcome will be within two standard deviations is 95.46%. The probability that the session outcome will be within three standard deviations is 99.74%. The following table shows the probability that a session outcome will come within various numbers of standard deviations.

I realize that this explanation may not make much sense to someone who is not well versed in the basics of statistics. If this is the case I would recommend enriching yourself with a good introductory statistics book.

Standard Deviation

Number	Probability
0.25	0.1974
0.50	0.3830
0.75	0.5468
1.00	0.6826
1.25	0.7888
1.50	0.8664
1.75	0.9198
2.00	0.9546
2.25	0.9756
2.50	0.9876
2.75	0.9940
3.00	0.9974
3.25	0.9988
3.50	0.9996
3.75	0.9998

Hold

Although I do not mention hold percentages on my site the term is worth defining because it comes up a lot. The hold percentage is the ratio of chips the casino keeps to the total chips sold. This is generally measured over an entire shift. For example if blackjack table x takes in $1000 in the drop box and of the $1000 in chips sold the table keeps $300 of them (players walked away with the other $700) then the game's hold is 30%. If every player loses their entire purchase of chips then the hold will be 100%. It is possible for the hold to exceed 100% if players carry to the table chips purchased at another table. A mathematician alone can not determine the hold because it depends on how long the player will sit at the table and the same money circulates back and forth. There is a lot of confusion between the house edge and hold, especially among casino personnel.

Hands per Hour, House Edge for Comp Purposes

The following table shows the average hands per hour and the house edge for comp purposes various games. The house edge figures are higher than those above, because the above figures assume optimal strategy, and those below reflect player errors and average type of bet made. This table was given to me anonymously by an executive with a major Strip casino and is used for rating players.

Hands per Hour and Average House Edge

Games	Hands/Hour	House Edge
Baccarat	72	1.2%
Blackjack	70	0.75%
Big Six	10	15.53%
Craps	48	1.58%
Car. Stud	50	1.46%
Let It Ride	52	2.4%
Mini-Baccarat	72	1.2%
Midi-Baccarat	72	1.2%
Pai Gow	30	1.65%
Pai Pow Poker	34	1.96%
Roulette	38	5.26%
Single 0 Roulette	35	2.59%
Casino War	65	2.87%
Spanish 21	75	2.2%
Sic Bo	45	8%
3 Way Action	70	2.2%

Footnotes

* — House edge based on Ante bet only as opposed to all mandatory wagers (for example the Blind in Ultimate Texas Hold 'Em and the Super Bonus in Crazy 4 Poker.

Translation

A Spanish translation of this page is available at www.eldropbox.com.

Written by: Michael Shackleford

By Anonymous

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.

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:
1. Check (do nothing); or
2. 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:
1. Check: or
2. 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:
1. Fold and forfeit their Ante and Blind bets; or
2. 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,

Unlimited Practice Holdem Poker Wizard

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:

Ultimate Texas Holdem House Advantage

(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:

Ultimate Texas Holdem Strategy Chart

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%.