Heads Up Poker
Jan 13, 2021 Aggression is Critical in Heads-Up Poker! Aggression is an important part of any form of poker but with heads-up it's critical. You're in the blinds every hand. If you buy-in for $200 for a $1/$2 heads-up match and fold every hand, you will lose half your stack in just 66 hands. Description Improve your poker game! Play no-limit Texas Hold ’em poker in a 3D first-person perspective against one of three sophisticated AI opponents.
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In this lesson we’re going to run through a number of heads-up match-ups that will help give you an idea of where you stand in a variety of pre-flop situations when playing hold’em. Be aware that we’re only going to focus on individual hand match-ups. When playing hold’em it’s essential that you put your opponent on a range of hands, rather than specific holdings. However, knowing the odds of common pre-flop match-ups is a good starting point. Pick out and study what will help you. While it’s not essential that these statistics be committed to memory, it won’t hurt you if you do.
Let’s start by looking at hand match-ups when holding a pair:
Pair vs. Pair
The higher pair is an 80 percent favourite. We can get very technical and highlight the fact that if the underpair didn’t have any clean suits and/or the maximum number of straight outs then the high pair’s equity would increases by one or two percent.
Pair vs. Overcards
This is the classic coin flip hand that you’ll see many times late in tournaments with one player being all-in. The term coin flip indicates an even money situation which is really a 55 to 45 percent situation, as the pair is a slight favourite.
Pair vs. Undercards
In this situation the pair is normally about a 5-to-1 favourite and can vary depending on whether the two undercards are suited and/or connectors.
Pair vs. Overcard and an undercard
The pair is about a 70 percent favourite. Another example of this holding would be J-J against A-9. The underdog non-paired hand has three outs while the favourite has redraws.
Pair vs. Overcard and one of that pair
The classic example of this situation is the confrontation between a pair of cowboys and big slick. The A-K has three outs and it becomes a 70-30 percent situation or a 2.3-to-1 dog for the cowboys. This is a far cry from the next situation where even though one of the pair is matched the other card is lower.
Pair vs. Undercard and one of that pair
The non pair has to hit its undercard twice or make a straight or flush to prevail. The pair is better than a 90 percent favourite or slightly better than 10-to-1 odds. I’ll take those odds anytime.
Pair vs. Lower suited connectors
You see this match-up late in tournaments when a player is getting desperate and pushes all-in with middle suited connectors. A hand such as Q-Q against 7-6 suited would be a prime example. The pair is a strong favourite to win.
Pair vs. Higher suited connectors
Here is the real coin flip situation. A pair of eights heads-up against a suited Q-J is a fifty-fifty proposition. The higher suited cards would have an edge against a lower pair, such as 2’s or 3’s, since the board itself can sometimes destroy little pairs.
Common Pre-Flop Match-Ups (Non Pairs)
The following heads-up confrontations contain no pairs.
Two high cards vs. Two undercards
The two higher cards are usually a 65% favourite to win, but it can vary depending on whether any of the cards are suited and/or connectors.
High card, low card vs. Two middle cards
In this match-up the high card gives it the edge. But it’s only a marginal winner, approximately 57% to the hand containing the high card.
High card, middle card vs. Second highest, low card
The edge is increased by around 5% when the low card becomes the third highest card, as shown in this example, which gives approx 62% to 38% for high card/middle card combination.
High card, same card vs. Same card, low card
In this example the A-J is in a very strong position. If we discount any flush or straight possibilities, it only leaves the player holding J-8 with three outs (the three remaining 8’s).
Same high card, high kicker vs. Same card, low kicker
The high kicker gives this hand a fairly big edge. It’s very common for A-K run into A-Q, A-J, and lower, and it’s why Ace-King is such a powerful hand, particularly at the business end of no-limit hold’em tournaments when people move all-in with any sort of Ace.
Statistical Variations
For any math maniacs reading this who do not find these odds precise enough, I acknowledge that the math is rounded and for the most part does not take into account the possibilities of ties and back door straights and flushes. What players need to be equipped with is the general statistical match-up – not the fact that in the example of a pair of eights against a suited Q-J the percents are exactly 50.61 for the eights to 48.99 for the suited connectors with the balance going to potential ties. I call that a fifty-fifty proposition.
Of greater importance than quibbling over tenths of a percent is the fact that in most heads-up confrontations you can never be a prohibitive underdog. That is one reason why poker is so challenging and fun. Of course, while true, I’m not attempting to embolden the reader to ignore the odds and become a maniac. Math is the underpinning of poker and if you regularly get your money into the middle with the worst of it you will go broke.
One statistic that hasn’t been mentioned, and it’s one that I particularly like is this – the odds of both players being dealt Aces when playing heads up (one on one) is 270,724-to-1. It’s my favourite statistic because it provides me with almost total confidence when I’m playing heads up and receive pocket Aces that I’m the boss! That confident feeling lasts right up to the river when my Aces get cracked by some rotten piece of cheese which my opponent elected to play. As mentioned already, rarely are you a prohibitive underdog – so remember that to keep those losing hands in perspective.
Related Lessons
By Tom 'TIME' Leonard
Tom has been writing about poker since 1994 and has played across the USA for over 40 years, playing every game in almost every card room in Atlantic City, California and Las Vegas.
On This Page
Introduction
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.
Rules
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.
- The game is played with a single ordinary 52-card deck.
- The player must make an equal bet on both the Ante and Odds.
- 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 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 or check again. 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 Odds bets. If the player already raised he may not bet further.
- The player and dealer will both make the best possible hand using any combination of their own two cards and the five community cards.
- The dealer will need at least a pair to open.
- The following table shows how the Ante, Odds, and Play bets are scored, according to who wins, and whether the dealer opens.
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 - Winning Ante and Play bets pay 1 to 1. Winning Odds bets pay according to value of the hand and whether it wins or loses. The following pay table shows what winning Odds bets pay.
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 game owner, has four different pay tables for losing blind bets, as follows.
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 - In addition, there are two side bets, that pay based on the player's cards only, the Trips Plus and Pocket Bonus. These side bets are explained after the analysis of the base game.
Strategy
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:
- Two pair or better.
- Hidden pair*, except pocket deuces.
- Four to a flush including a hidden 10 or better to that flush
* 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:
- Hidden pair or better.
- Less than 21 dealer outs beat you.
For a more powerful small and medium raise strategy, I recommend the James Grossjean strategy card for Ultimate Texas Hold 'Em.
Analysis
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%.
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 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.
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 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.
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 next table shows four known pay tables for the Trips Plus.
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
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.
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
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.
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