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Heads Up Hold 'Em is an Ultimate Texas Hold 'Em variant by Galaxy Gaming, based on Texas Hold 'Em. The player may raise his bet one time, and has three opportunities to do so. The earlier he raises, the more he can bet. The main differences between Heads Up Hold 'Em and Ultimate Texas Hold 'Em are in the former the player may raise only 3x his Ante bet before the flop, but the game includes bad beat bonuses for losing with a straight or higher.
Following are the rules for Heads Up Hold 'Em. For those used to the terminology in Ultimate Texas Hold 'Em, what is called the Blind there called the Odds bet here.
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 |
Hand | Pays |
---|---|
Royal Flush | 500 |
Straight Flush | 50 |
Quads | 10 |
Full House | 3 |
Flush | 1.5 |
Straight | 1 |
All Other | Push |
Galaxy Gaming, the game owner, has four different pay tables for losing blind bets, as follows.
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 |
The player should make the 3X raise with any pair except deuces. Otherwise, use the following table shows when to make the large 3X raise.
The strategy for the medium and small raise are the same as in Ultimate Texas Hold 'Em, as follows:
Medium Raise: Make the 2X raise with any of the following:
* 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:
For a more powerful small and medium raise strategy, I recommend the James Grossjean strategy card for Ultimate Texas Hold 'Em.
The following table shows all possible outcomes of each hand, what it pays, the probability, and contribution to the return under the losing Odds bet pay table number 1 (the one that goes 500-50-10-8-5). The lower right cell shows a house edge of 2.36%.
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 shown in the lower right cell, the house edge is 2.36%. This is the expected loss to the Ante wager only. For example, if the player bets $5 on both the Ante and Odds, then his expected loss would be $5 × 0.023584 = 11.79¢.
The average final wager per hand is 3.67 units. That makes the element of risk 2.36%/3.67 = 0.64%. This means for every dollar you wager in the game, on anything, other than the side bets, you can expect to lose 0.64¢.
By comparison, the element of risk in Ultimate Texas Hold 'Em is 0.53%.
The standard deviation, relative to to the Ante bet, is 4.56.
The next table shows the house edge and element of risk under all four losing Odds bet pay tables according to the pay table for a losing Odds bet.
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.
The Trips Plus bet will pay according to the poker value of the player's hand regardless of the value of the dealer's hand. Following is an analysis of the most common pay 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 next table shows four known pay tables for the Trips Plus.
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% |
The Pocket Bonus bet will pay according to the value of the player's two hole cards. The follow tables show what each two cards pays, the probability, and contribution to the total return for each known pay table for the Pocket Bonus.
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 |
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 |
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 |
I would like to thank Charles Mousseau and Stephen How for their assistance, which confirmed my analysis. Thanks to Charles also for his advice on the medium and small raise strategy.
Detailed calculations on some starting hands.
Play Heads Up Hold 'Em at the Galaxy Gaming web site. One click and you're playing.