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Heads Up Hold 'Em

Introduction

2013 Global Gaming Expo.

Heads Up Hold 'Em is an Ultimate Texas Hold 'Em This variant from Galaxy Gaming is inspired by Texas Hold 'Em. Players are allowed to raise their bets only once and have three chances to do this. The sooner a player makes a raise, the larger the amount he can wager. Key distinctions between Heads Up Hold 'Em and Ultimate Texas Hold 'Em include that in the former, the player is restricted to a maximum raise of 3 times the Ante bet before the flop, although there are bad beat bonuses for players who lose with a straight or stronger hand.

In November 2022, I came across another game named Big Blind UTH. I'll provide more insights about it once I acquire the Blind pay table.

Rules

Here are the rules for playing Heads Up Hold 'Em. For those familiar with Ultimate Texas Hold 'Em, the term 'Blind' is known as the 'Odds' bet in this variant.

  1. This game is played using a standard 52-card deck.
  2. Players are required to place equal bets for both the Ante and Odds.
  3. Each player and the dealer are dealt two face-down cards. Players are allowed to view their own cards.
  4. Players can either check or place a Play bet that is triple the Ante.
  5. The dealer reveals three community cards.
  6. If the player chose to check earlier, they can either make a Play bet that is double their Ante or check again. If a Play bet has already been placed, no further bets can be made.
  7. Finally, two additional community cards are revealed.
  8. If the player has checked twice already, they must either place a Play bet equal to their Ante or fold, which results in losing both the Ante and Odds bets. Players who have already raised cannot make further bets.
  9. Both the player and dealer will form the best possible hand by combining their two personal cards with the five community cards.
  10. The dealer needs to have at least a pair to qualify.
  11. The table below outlines how Ante, Odds, and Play bets are evaluated depending on the winner and whether the dealer qualifies.

    Scoring Rules

    Winner Dealer Opens Ante Play Odds
    Player Yes Win Win See rule 12
    Player No Push Win See rule 12
    Dealer Yes Lose Lose See rule 12
    Dealer No Push Lose Lose
    Tie Yes or No Push Push Push

    This is each player's betting area.

  12. Winning Ante and Play bets receive even money. Meanwhile, winning Odds bets are paid out based on the strength of the hand and the outcome. The subsequent pay table details the payouts for successful Odds bets.

    Winning Odds Bet Pay Table

    Hand Pays
    Royal Flush 500
    Straight Flush 50
    Quads 10
    Full House 3
    Flush 1.5
    Straight 1
    All Other Push

    Galaxy Gaming, the creator of the game, has established four different pay tables for losing blind bets.

    Losing Odds Bet Pay Table

    Hand Pay Table
    1 2 3 4
    Straight Flush 500 500 500 500
    Quads 50 50 50 25
    Full House 10 10 10 6
    Flush 8 6 5 5
    Straight 5 5 4 4
    All Other Loss Loss Loss Loss
  13. Additionally, there are two side bets, the Trips Plus and Pocket Bonus, which pay out based solely on the player's cards. Details on these side bets can be found after the base game analysis.

Strategy

Players should opt for a 3X raise with any pair other than deuces. For other situations, the table below indicates when to execute a substantial 3X raise.

The strategies for medium and small raises parallel those used in Ultimate Texas Hold 'Em, as detailed below:

Medium Raise : Place a 2X raise with any of the following scenarios:

  • Two pair or better.
  • Hidden pair*, except pocket deuces.
  • A four-card flush can be made, provided there is a hidden 10 or better included.

* A hidden pair indicates any pair in your hole cards, making the pair unknown to the dealer.

Small Raise : Make a 1X raise in any of the following cases, or otherwise fold:

  • Hidden pair or better.
  • Less than 21 dealer outs beat you.

For a more robust strategy regarding small and medium raises, I suggest utilizing the James Grossjean strategy card specifically for Ultimate Texas Hold 'Em. .

Analysis

The table below illustrates each hand's potential outcomes, detailing the payouts, probabilities, and their contributions to overall returns based on the losing Odds bet pay table number 1 (that pays 500-50-10-8-5). The bottom-right corner indicates a house edge of 2.36%.

Return TableExpand

Player Raise Dealer
Qualifies
Winner Pays Combinations Probability Return
Fold -2 5,498,078,560,920 0.197674 -0.395349
Less than pair 1 No Dealer -2 60,518,663,424 0.002176 -0.004352
Straight flush 1 Yes Dealer 498 20,279,100 0.000001 0.000363
Four of a kind 1 Yes Dealer 48 1,726,735,980 0.000062 0.002980
Full house 1 Yes Dealer 8 10,082,720,220 0.000363 0.002900
Flush 1 Yes Dealer 6 49,072,032,216 0.001764 0.010586
Straight 1 Yes Dealer 3 47,952,010,720 0.001724 0.005172
Less than straight 1 Yes Dealer -3 3,006,630,550,164 0.108098 -0.324295
Anything 1 Y/N Push 0 455,081,939,824 0.016362 0.000000
Royal flush 1 No Player 501 6,914,880 0.000000 0.000125
Straight flush 1 No Player 51 279,004,320 0.000010 0.000512
Four of a kind 1 No Player 11 - 0.000000 0.000000
Full house 1 No Player 4 - 0.000000 0.000000
Flush 1 No Player 2.5 43,096,215,600 0.001549 0.003874
Straight 1 No Player 2 145,034,240,580 0.005214 0.010429
Less than straight 1 No Player 1 816,981,676,824 0.029373 0.029373
Royal flush 1 Yes Player 502 46,580,760 0.000002 0.000841
Straight flush 1 Yes Player 52 2,023,968,588 0.000073 0.003784
Four of a kind 1 Yes Player 12 964,337,328 0.000035 0.000416
Full house 1 Yes Player 5 46,108,374,192 0.001658 0.008289
Flush 1 Yes Player 3.5 202,016,746,236 0.007263 0.025421
Straight 1 Yes Player 3 421,268,280,080 0.015146 0.045438
Less than straight 1 Yes Player 2 1,600,861,520,204 0.057556 0.115113
Less than pair 2 No Dealer -3 11,023,268,784 0.000396 -0.001189
Straight flush 2 Yes Dealer 497 16,724,460 0.000001 0.000299
Four of a kind 2 Yes Dealer 47 311,575,460 0.000011 0.000527
Full house 2 Yes Dealer 7 18,705,932,580 0.000673 0.004708
Flush 2 Yes Dealer 5 27,615,003,664 0.000993 0.004964
Straight 2 Yes Dealer 2 21,031,977,440 0.000756 0.001512
Less than straight 2 Yes Dealer -4 1,979,644,169,384 0.071175 -0.284699
Anything 2 Y/N Push 0 214,144,135,720 0.007699 0.000000
Royal flush 2 No Player 502 11,938,680 0.000000 0.000215
Straight flush 2 No Player 52 397,598,400 0.000014 0.000743
Four of a kind 2 No Player 12 - 0.000000 0.000000
Full house 2 No Player 5 - 0.000000 0.000000
Flush 2 No Player 3.5 45,718,738,920 0.001644 0.005753
Straight 2 No Player 3 53,068,201,380 0.001908 0.005724
Less than straight 2 No Player 2 1,207,385,216,712 0.043410 0.086819
Royal flush 2 Yes Player 503 147,692,880 0.000005 0.002671
Straight flush 2 Yes Player 53 3,016,851,612 0.000108 0.005749
Four of a kind 2 Yes Player 13 20,440,911,312 0.000735 0.009554
Full house 2 Yes Player 6 320,575,227,408 0.011526 0.069155
Flush 2 Yes Player 4.5 183,447,763,404 0.006596 0.029680
Straight 2 Yes Player 4 158,035,798,360 0.005682 0.022728
Less than straight 2 Yes Dealer 3 2,415,318,761,280 0.086839 0.260516
Less than pair 3 No Dealer -4 66,873,993,600 0.002404 -0.009617
Straight flush 3 Yes Dealer 496 14,499,400 0.000001 0.000259
Four of a kind 3 Yes Dealer 46 316,891,120 0.000011 0.000524
Full house 3 Yes Dealer 6 13,387,474,080 0.000481 0.002888
Flush 3 Yes Dealer 4 20,484,007,080 0.000736 0.002946
Straight 3 Yes Dealer 1 22,371,396,720 0.000804 0.000804
Less than straight 3 Yes Dealer -5 3,136,124,565,400 0.112754 -0.563771
Anything 3 Y/N Push 0 223,641,379,520 0.008041 0.000000
Royal flush 3 No Player 503 86,472,360 0.000003 0.001564
Straight flush 3 No Player 53 180,911,880 0.000007 0.000345
Four of a kind 3 No Player 13 - 0.000000 0.000000
Full house 3 No Player 6 - 0.000000 0.000000
Flush 3 No Player 4.5 41,791,833,360 0.001503 0.006762
Straight 3 No Player 4 64,386,219,840 0.002315 0.009260
Less than straight 3 No Player 3 1,317,173,128,560 0.047357 0.142070
Royal flush 3 Yes Player 504 556,552,440 0.000020 0.010085
Straight flush 3 Yes Player 54 1,444,036,640 0.000052 0.002804
Four of a kind 3 Yes Player 14 21,003,399,360 0.000755 0.010572
Full house 3 Yes Player 7 261,421,403,040 0.009399 0.065793
Flush 3 Yes Player 5.5 199,160,655,360 0.007160 0.039383
Straight 3 Yes Player 5 195,058,020,480 0.007013 0.035065
Less than straight 3 Yes Player 4 3,140,424,343,760 0.112909 0.451635
Total 27,813,810,024,000 1.000000 -0.023584

As presented in the bottom-right corner, the house edge stands at 2.36%. This statistic reflects the expected loss tied solely to the Ante bet. For example, with a $5 wager on both Ante and Odds, the anticipated loss would amount to $5 × 0.023584 = 11.79¢.

Typically, the average final bet per hand is about 3.67 units, leading to a calculation of 2.36% divided by 3.67 = 0.64%. In essence, for each dollar wagered in this game, except for side bets, you can expect an average loss of 0.64¢. element of risk In comparison, the risk factor associated with Ultimate Texas Hold 'Em shows a figure of 0.53%.

The standard deviation linked to the Ante bet is 4.56.

The upcoming table illustrates the house edge and risk level across all four losing Odds bet pay tables based on the specific pay structure for losing Odds bets.

The Trips Plus bet payout depends on the poker ranking of the player's hand, independent of the dealer's hand value. Below is an analysis of the most frequently encountered pay table.

House Edge Summary

Hand Losing Odds Bet Pay Table
1 2 3 4
Straight Flush 500 500 500 500
Quads 50 50 50 25
Full House 10 10 10 6
Flush 8 6 5 5
Straight 5 5 4 4
All Other Loss Loss Loss Loss
House edge 2.36% 3.06% 3.73% 4.55%
Element of Risk 0.64% 0.83% 1.02% 1.24%

This is full table cloth.

Trips Plus

The next table provides four recognized pay tables for the Trips Plus.

Trips Plus Return Table

Hand Pays Combinations Probability Return
Royal flush 100 4,324 0.000032 0.003232
Straight flush 40 37,260 0.000279 0.011140
Four of a kind 30 224,848 0.001681 0.050420
Full house 8 3,473,184 0.025961 0.207688
Flush 7 4,047,644 0.030255 0.211785
Straight 4 6,180,020 0.046194 0.184775
Three of a kind 3 6,461,620 0.048299 0.144896
All other -1 113,355,660 0.847300 -0.847300
Total   133,784,560 1.000000 -0.033363

The Pocket Bonus bet payouts are determined by the value of the player's two hole cards. The tables that follow present the payouts for each combination of two cards, along with probabilities and their contributions to the total return for each known Pocket Bonus pay table.

Trips Plus Pay Tables

Hand Pay Table
1 2 3 4
Royal flush 100 100 100 100
Straight flush 40 40 40 40
Four of a kind 30 30 30 30
Full house 9 8 8 7
Flush 7 6 7 6
Straight 4 5 4 5
Three of a kind 3 3 3 3
All other -1 -1 -1 -1
Total -0.74% -1.74% -3.34% -4.34%

Pocket Bonus

I want to express my gratitude to Charles Mousseau and Stephen How for their invaluable help, which validated my analysis. I also appreciate Charles's guidance on the strategies for medium and small raises.

Pocket Bonus — Pay Table 1

Hand Pays Combinations Probability Return
Pair of aces 30 6 0.004525 0.135747
Ace & face suited 20 12 0.009050 0.180995
Ace & face unsuited 10 36 0.027149 0.271493
Pair 2s - Ks 5 72 0.054299 0.271493
Loser -1 1,200 0.904977 -0.904977
Total   1,326 1.000000 -0.045249

Pocket Bonus — Pay Table 2

Hand Pays Combinations Probability Return
Pair of aces 25 6 0.004525 0.113122
Ace & face suited 20 12 0.009050 0.180995
Ace & face unsuited 10 36 0.027149 0.271493
Pair 2s - Ks 5 72 0.054299 0.271493
Loser -1 1,200 0.904977 -0.904977
Total   1,326 1.000000 -0.067873

Pocket Bonus — Pay Table 3

Hand Pays Combinations Probability Return
Pair of aces 30 6 0.004525 0.135747
Ace & face suited 20 12 0.009050 0.180995
Ace & face unsuited 10 36 0.027149 0.271493
Pair 2s - Ks 4 72 0.054299 0.217195
Loser -1 1,200 0.904977 -0.904977
Total   1,326 1.000000 -0.099548

Acknowledgments

Visit the Galaxy Gaming website. Just one click, and you are ready to play.

Internal Links

Detailed calculations on some starting hands.

External Links

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