Heads Up Holdem Online
2021年9月5日Register here: http://gg.gg/vwqsv
*Play Texas Hold’em Online
*Heads Up Holdem Poker
*Heads Up Holdem Strategy
*Texas Holdem Heads Up Rules
*Heads Up Poker Online What Is This?
This is your opportunity to play heads up holdem against Cleverpiggy and Hibiscus Biscuit, two super duper awesome heads up poker playing agents.
I created them using state of the art artificial intelligence techniques as well as my own secret sauce. They recently competed in the annual computer poker competition and did well, only finishing behind entries from top research universities. Cleverpiggy, the limit holdem player, only lost a single match.
Heads-Up Hold’em is a fun variant of Texas Hold’em Poker that gives you the chance to win big thanks to two side bets, and also gives you the chance to win even when you lose thanks to a. Fans of Texas Hold’em Poker will love playing online poker games without the stress of the casino! Don’t settle for the all-in poker fests in OTHER social poker games! Play the best online poker games and aim for the royal flush with PlayWPT Poker, the best Vegas-style poker app that brings authentic Texas Hold’em poker to your hands. Playing online table games has never been more realistic, thanks to the invention of the free Poker 3 Heads Up Hold’em game. Sit at the virtual poker table and experience 3D graphics like no other. Do They Cheat?
No. They only know the cards in their hand and on the board. You’ll just have to take my word for it. Are They Good?
Cleverpiggy will probably beat your pants off. Vegas casinos are confident enough to use a limit holdem computer poker player as a slot machine and this one has proven to hold its own with the best.
You should have a better chance against Hibiscus Biscuit. No limit holdem is a much tougher game for a computer. The best human players often raise an eyebrow at some of the plays made by the best bots. Also, my main design for HB is not yet working so you and the computer competition opponents are just playing the weaker backup implemetation. Can I Watch some Bot vs Bot?
I uploaded some hand histories to a site that does that sort of thing. These might take a few seconds to get started.
*Cleverpiggy vs Escabeche(the winner)
*Cleverpiggy vs SmooCT(the runner up)
*Cleverpiggy vs 652(the guy we lost to)Hisbiscus Misclicks:
*Hibiscus Biscuit vs Tartanian7(who won both NLH events)
*Hibiscus Biscuit vs Prelude(who placed in both NLH events)
*Hibiscus Biscuit vs Lucifer(this should be funny)Please enable JavaScript to view the comments powered by Disqus.comments powered by DisqusOn This PageIntroduction
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 RulesWinnerDealer OpensAntePlayOddsPlayerYesWinWinSee rule 12PlayerNoPushWinSee rule 12DealerYesLoseLoseSee rule 12DealerNoPushLoseLoseTieYes or NoPushPushPush
*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 TableHandPaysRoyal Flush500Straight Flush50Quads10Full House3Flush1.5Straight1All OtherPush
Galaxy Gaming, the game owner, has four different pay tables for losing blind bets, as follows.Losing Odds Bet Pay TableHandPay Table1234Straight Flush500500500500Quads50505025Full House1010106Flush8655Straight5544All OtherLossLossLossLoss
*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.Play Texas Hold’em OnlineStrategy
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 PlayerRaiseDealer
QualifiesWinnerPaysCombinationsProbabilityReturnFold-25,498,078,560,9200.197674-0.395349Less than pair1NoDealer-260,518,663,4240.002176-0.004352Straight flush1YesDealer49820,279,1000.0000010.000363Four of a kind1YesDealer481,726,735,9800.0000620.002980Full house1YesDealer810,082,720,2200.0003630.002900Flush1YesDealer649,072,032,2160.0017640.010586Straight1YesDealer347,952,010,7200.0017240.005172Less than straight1YesDealer-33,006,630,550,1640.108098-0.324295Anything1Y/NPush0455,081,939,8240.0163620.000000Royal flush1NoPlayer5016,914,8800.0000000.000125Straight flush1NoPlayer51279,004,3200.0000100.000512Four of a kind1NoPlayer11-0.0000000.000000Full house1NoPlayer4-0.0000000.000000Flush1NoPlayer2.543,096,215,6000.0015490.003874Straight1NoPlayer2145,034,240,5800.0052140.010429Less than straight1NoPlayer1816,981,676,8240.0293730.029373Royal flush1YesPlayer50246,580,7600.0000020.000841Straight flush1YesPlayer522,023,968,5880.0000730.003784Four of a kind1YesPlayer12964,337,3280.0000350.000416Full house1YesPlayer546,108,374,1920.0016580.008289Flush1YesPlayer3.5202,016,746,2360.0072630.025421Straight1YesPlayer3421,268,280,0800.0151460.045438Less than straight1YesPlayer21,600,861,520,2040.0575560.115113Less than pair2NoDealer-311,023,268,7840.000396-0.001189Straight flush2YesDealer49716,724,4600.0000010.000299Four of a kind2YesDealer47311,575,4600.0000110.000527Full house2YesDealer718,705,932,5800.0006730.004708Flush2YesDealer527,615,003,6640.0009930.004964Straight2YesDealer221,031,977,4400.0007560.001512Less than straight2YesDealer-41,979,644,169,3840.071175-0.284699Anything2Y/NPush0214,144,135,7200.0076990.000000Royal flush2NoPlayer50211,938,6800.0000000.000215Straight flush2NoPlayer52397,598,4000.0000140.000743Four of a kind2NoPlayer12-0.0000000.000000Full house2NoPlayer5-0.0000000.000000Flush2NoPlayer3.545,718,738,9200.0016440.005753Straight2NoPlayer353,068,201,3800.0019080.005724Less than straight2NoPlayer21,207,385,216,7120.0434100.086819Royal flush2YesPlayer503147,692,8800.0000050.002671Straight flush2YesPlayer533,016,851,6120.0001080.005749Four of a kind2YesPlayer1320,440,911,3120.0007350.009554Full house2YesPlayer6320,575,227,4080.0115260.069155Flush2YesPlayer4.5183,447,763,4040.0065960.029680Straight2YesPlayer4158,035,798,3600.0056820.022728Less than straight2YesDealer32,415,318,761,2800.0868390.260516Less than pair3NoDealer-466,873,993,6000.002404-0.009617Straight flush3YesDealer49614,499,4000.0000010.000259Four of a kind3YesDealer46316,891,1200.0000110.000524Full house3YesDealer613,387,474,0800.0004810.002888Flush3YesDealer420,484,007,0800.0007360.002946Straight3YesDealer122,371,396,7200.0008040.000804Less than straight3YesDealer-53,136,124,565,4000.112754-0.563771Anything3Y/NPush0223,641,379,5200.0080410.000000Royal flush3NoPlayer50386,472,3600.0000030.001564Straight flush3NoPlayer53180,911,8800.0000070.000345Four of a kind3NoPlayer13-0.0000000.000000Full house3NoPlayer6-0.0000000.000000Flush3NoPlayer4.541,791,833,3600.0015030.006762Straight3NoPlayer464,386,219,8400.0023150.009260Less than straight3NoPlayer31,317,173,128,5600.0473570.142070Royal flush3YesPlayer504556,552,4400.0000200.010085Straight flush3YesPlayer541,444,036,6400.0000520.002804Four of a kind3YesPlayer1421,003,399,3600.0007550.010572Full house3YesPlayer7261,421,403,0400.0093990.065793Flush3YesPlayer5.5199,160,655,3600.0071600.039383Straight3YesPlayer5195,058,020,4800.0070130.035065Less than straight3YesPlayer43,140,424,343,7600.1129090.451635Total27,813,810,024,0001.000000-0.023584
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 SummaryHandLosing Odds Bet Pay Table1234Straight Flush500500500500Quads50505025Full House1010106Flush8655Straight5544All OtherLossLossLossLossHouse edge2.36%3.06%3.73%4.55%Element of Risk0.64%0.83%1.02%1.24%
This is full table cloth. Fair go no deposit bonus for new players.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 TableHandPaysCombinationsProbabilityReturnRoyal flush1004,3240.0000320.003232Straight flush4037,2600.0002790.011140Four of a kind30224,8480.0016810.050420Full house83,473,1840.0259610.207688Flush74,047,6440.0302550.211785Straight46,180,0200.0461940.184775Three of a kind36,461,6200.0482990.144896All other-1113,355,6600.847300-0.847300Total133,784,5601.000000-0.033363
The next table shows four known pay tables for the Trips Plus.Trips Plus Pay TablesHandPay Table1234Royal flush100100100100Straight flush40404040Four of a kind30303030Full house9887Flush7676Straight4545Three of a kind3333All other-1-1-1-1Total-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 1HandPaysCombinationsProbabilityReturnPair of aces3060.0045250.135747Ace & face suited20120.0090500.180995Ace & face unsuited10360.0271490.271493Pair 2s - Ks5720.0542990.271493Loser-11,2000.904977-0.904977Total1,3261.000000-0.045249Pocket Bonus — Pay Table 2HandPaysCombinationsProbabilityReturnPair of aces2560.0045250.113122Ace & face suited20120.0090500.180995Ace & face unsuited10360.0271490.271493Pair 2s - Ks5720.0542990.271493Loser-11,2000.904977-0.904977Total1,3261.000000-0.067873Pocket Bonus — Pay Table 3HandPaysCombinationsProbabilityReturnPair of aces3060.0045250.135747Ace & face suited20120.0090500.180995Ace & face unsuited10360.0271490.271493Pair 2s - Ks4720.0542990.217195Loser-11,2000.904977-0.904977Total1,3261.000000-0.099548AcknowledgmentsHeads Up Holdem Poker
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.Internal Links
Detailed calculations on some starting hands.Extneral LinksHeads Up Holdem Strategy
Play Heads Up Hold ’Em at the Galaxy Gaming web site. One click and you’re playing.Texas Holdem Heads Up Rules
Heads Up Poker OnlineWritten by:Michael Shackleford
Register here: http://gg.gg/vwqsv
https://diarynote-jp.indered.space
*Play Texas Hold’em Online
*Heads Up Holdem Poker
*Heads Up Holdem Strategy
*Texas Holdem Heads Up Rules
*Heads Up Poker Online What Is This?
This is your opportunity to play heads up holdem against Cleverpiggy and Hibiscus Biscuit, two super duper awesome heads up poker playing agents.
I created them using state of the art artificial intelligence techniques as well as my own secret sauce. They recently competed in the annual computer poker competition and did well, only finishing behind entries from top research universities. Cleverpiggy, the limit holdem player, only lost a single match.
Heads-Up Hold’em is a fun variant of Texas Hold’em Poker that gives you the chance to win big thanks to two side bets, and also gives you the chance to win even when you lose thanks to a. Fans of Texas Hold’em Poker will love playing online poker games without the stress of the casino! Don’t settle for the all-in poker fests in OTHER social poker games! Play the best online poker games and aim for the royal flush with PlayWPT Poker, the best Vegas-style poker app that brings authentic Texas Hold’em poker to your hands. Playing online table games has never been more realistic, thanks to the invention of the free Poker 3 Heads Up Hold’em game. Sit at the virtual poker table and experience 3D graphics like no other. Do They Cheat?
No. They only know the cards in their hand and on the board. You’ll just have to take my word for it. Are They Good?
Cleverpiggy will probably beat your pants off. Vegas casinos are confident enough to use a limit holdem computer poker player as a slot machine and this one has proven to hold its own with the best.
You should have a better chance against Hibiscus Biscuit. No limit holdem is a much tougher game for a computer. The best human players often raise an eyebrow at some of the plays made by the best bots. Also, my main design for HB is not yet working so you and the computer competition opponents are just playing the weaker backup implemetation. Can I Watch some Bot vs Bot?
I uploaded some hand histories to a site that does that sort of thing. These might take a few seconds to get started.
*Cleverpiggy vs Escabeche(the winner)
*Cleverpiggy vs SmooCT(the runner up)
*Cleverpiggy vs 652(the guy we lost to)Hisbiscus Misclicks:
*Hibiscus Biscuit vs Tartanian7(who won both NLH events)
*Hibiscus Biscuit vs Prelude(who placed in both NLH events)
*Hibiscus Biscuit vs Lucifer(this should be funny)Please enable JavaScript to view the comments powered by Disqus.comments powered by DisqusOn This PageIntroduction
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 RulesWinnerDealer OpensAntePlayOddsPlayerYesWinWinSee rule 12PlayerNoPushWinSee rule 12DealerYesLoseLoseSee rule 12DealerNoPushLoseLoseTieYes or NoPushPushPush
*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 TableHandPaysRoyal Flush500Straight Flush50Quads10Full House3Flush1.5Straight1All OtherPush
Galaxy Gaming, the game owner, has four different pay tables for losing blind bets, as follows.Losing Odds Bet Pay TableHandPay Table1234Straight Flush500500500500Quads50505025Full House1010106Flush8655Straight5544All OtherLossLossLossLoss
*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.Play Texas Hold’em OnlineStrategy
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 PlayerRaiseDealer
QualifiesWinnerPaysCombinationsProbabilityReturnFold-25,498,078,560,9200.197674-0.395349Less than pair1NoDealer-260,518,663,4240.002176-0.004352Straight flush1YesDealer49820,279,1000.0000010.000363Four of a kind1YesDealer481,726,735,9800.0000620.002980Full house1YesDealer810,082,720,2200.0003630.002900Flush1YesDealer649,072,032,2160.0017640.010586Straight1YesDealer347,952,010,7200.0017240.005172Less than straight1YesDealer-33,006,630,550,1640.108098-0.324295Anything1Y/NPush0455,081,939,8240.0163620.000000Royal flush1NoPlayer5016,914,8800.0000000.000125Straight flush1NoPlayer51279,004,3200.0000100.000512Four of a kind1NoPlayer11-0.0000000.000000Full house1NoPlayer4-0.0000000.000000Flush1NoPlayer2.543,096,215,6000.0015490.003874Straight1NoPlayer2145,034,240,5800.0052140.010429Less than straight1NoPlayer1816,981,676,8240.0293730.029373Royal flush1YesPlayer50246,580,7600.0000020.000841Straight flush1YesPlayer522,023,968,5880.0000730.003784Four of a kind1YesPlayer12964,337,3280.0000350.000416Full house1YesPlayer546,108,374,1920.0016580.008289Flush1YesPlayer3.5202,016,746,2360.0072630.025421Straight1YesPlayer3421,268,280,0800.0151460.045438Less than straight1YesPlayer21,600,861,520,2040.0575560.115113Less than pair2NoDealer-311,023,268,7840.000396-0.001189Straight flush2YesDealer49716,724,4600.0000010.000299Four of a kind2YesDealer47311,575,4600.0000110.000527Full house2YesDealer718,705,932,5800.0006730.004708Flush2YesDealer527,615,003,6640.0009930.004964Straight2YesDealer221,031,977,4400.0007560.001512Less than straight2YesDealer-41,979,644,169,3840.071175-0.284699Anything2Y/NPush0214,144,135,7200.0076990.000000Royal flush2NoPlayer50211,938,6800.0000000.000215Straight flush2NoPlayer52397,598,4000.0000140.000743Four of a kind2NoPlayer12-0.0000000.000000Full house2NoPlayer5-0.0000000.000000Flush2NoPlayer3.545,718,738,9200.0016440.005753Straight2NoPlayer353,068,201,3800.0019080.005724Less than straight2NoPlayer21,207,385,216,7120.0434100.086819Royal flush2YesPlayer503147,692,8800.0000050.002671Straight flush2YesPlayer533,016,851,6120.0001080.005749Four of a kind2YesPlayer1320,440,911,3120.0007350.009554Full house2YesPlayer6320,575,227,4080.0115260.069155Flush2YesPlayer4.5183,447,763,4040.0065960.029680Straight2YesPlayer4158,035,798,3600.0056820.022728Less than straight2YesDealer32,415,318,761,2800.0868390.260516Less than pair3NoDealer-466,873,993,6000.002404-0.009617Straight flush3YesDealer49614,499,4000.0000010.000259Four of a kind3YesDealer46316,891,1200.0000110.000524Full house3YesDealer613,387,474,0800.0004810.002888Flush3YesDealer420,484,007,0800.0007360.002946Straight3YesDealer122,371,396,7200.0008040.000804Less than straight3YesDealer-53,136,124,565,4000.112754-0.563771Anything3Y/NPush0223,641,379,5200.0080410.000000Royal flush3NoPlayer50386,472,3600.0000030.001564Straight flush3NoPlayer53180,911,8800.0000070.000345Four of a kind3NoPlayer13-0.0000000.000000Full house3NoPlayer6-0.0000000.000000Flush3NoPlayer4.541,791,833,3600.0015030.006762Straight3NoPlayer464,386,219,8400.0023150.009260Less than straight3NoPlayer31,317,173,128,5600.0473570.142070Royal flush3YesPlayer504556,552,4400.0000200.010085Straight flush3YesPlayer541,444,036,6400.0000520.002804Four of a kind3YesPlayer1421,003,399,3600.0007550.010572Full house3YesPlayer7261,421,403,0400.0093990.065793Flush3YesPlayer5.5199,160,655,3600.0071600.039383Straight3YesPlayer5195,058,020,4800.0070130.035065Less than straight3YesPlayer43,140,424,343,7600.1129090.451635Total27,813,810,024,0001.000000-0.023584
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 SummaryHandLosing Odds Bet Pay Table1234Straight Flush500500500500Quads50505025Full House1010106Flush8655Straight5544All OtherLossLossLossLossHouse edge2.36%3.06%3.73%4.55%Element of Risk0.64%0.83%1.02%1.24%
This is full table cloth. Fair go no deposit bonus for new players.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 TableHandPaysCombinationsProbabilityReturnRoyal flush1004,3240.0000320.003232Straight flush4037,2600.0002790.011140Four of a kind30224,8480.0016810.050420Full house83,473,1840.0259610.207688Flush74,047,6440.0302550.211785Straight46,180,0200.0461940.184775Three of a kind36,461,6200.0482990.144896All other-1113,355,6600.847300-0.847300Total133,784,5601.000000-0.033363
The next table shows four known pay tables for the Trips Plus.Trips Plus Pay TablesHandPay Table1234Royal flush100100100100Straight flush40404040Four of a kind30303030Full house9887Flush7676Straight4545Three of a kind3333All other-1-1-1-1Total-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 1HandPaysCombinationsProbabilityReturnPair of aces3060.0045250.135747Ace & face suited20120.0090500.180995Ace & face unsuited10360.0271490.271493Pair 2s - Ks5720.0542990.271493Loser-11,2000.904977-0.904977Total1,3261.000000-0.045249Pocket Bonus — Pay Table 2HandPaysCombinationsProbabilityReturnPair of aces2560.0045250.113122Ace & face suited20120.0090500.180995Ace & face unsuited10360.0271490.271493Pair 2s - Ks5720.0542990.271493Loser-11,2000.904977-0.904977Total1,3261.000000-0.067873Pocket Bonus — Pay Table 3HandPaysCombinationsProbabilityReturnPair of aces3060.0045250.135747Ace & face suited20120.0090500.180995Ace & face unsuited10360.0271490.271493Pair 2s - Ks4720.0542990.217195Loser-11,2000.904977-0.904977Total1,3261.000000-0.099548AcknowledgmentsHeads Up Holdem Poker
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.Internal Links
Detailed calculations on some starting hands.Extneral LinksHeads Up Holdem Strategy
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Heads Up Poker OnlineWritten by:Michael Shackleford
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