Poker Heads Up Odds
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Whilst this 88.67% probability of winning is not as high as 96.01% for the straight poker game, or the 100% for the flush scenario, it is still gives a reasonably high guaranteed edge. To take this further, in The Mathematics of Poker, by Bill Chen and Jerrod Ankenman, a near optimal strategy is given for heads-up play when both player’s stacks are less than 50 big blinds. You will improve it on the turn: 9.2=18% and real poker odds are around 19%; You have a straight draw on the flop with 8 outs. You will improve it on the turn: 8.2=16% and real poker odds are around 17%; You have two over cards on the turn with 6 outs. You will improve it on the turn: 6.2=12% and real poker odds. The numbers are exact to the rounding I used, which was to chop off the space and bandwidth consuming digits without rounding (i.e. 84.93 for AAo meanas somewhere between 84.93 and 84.94, the exact probability of winning with AAo is 890,754,209/1,048,786,200, about.4777).
Pre-Flop Odds for Heads Up Poker A-A (220/1 or 0.45%) A-K (81.9/1 or 1.1%) A-A, K-K, Q-Q or 10-10 (54.3/1 or 1.8%) Any Pocket Pair (16:1 or 6.25%) Any 2 Cards Jack or Higher (10.1/1 or 9.05%). A Heads-Up Display, or HUD for short, is an online poker tool that allows you to display information directly on a poker table. This information ranges from statistics out of a tracking and analysis software database such as PokerTracker 3 or Holdem Manager to probability information provided by a calculator tool such as Holdem Indicator.On 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.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 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. 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-11,2000.904977-0.904977Total1,3261.000000-0.099548AcknowledgmentsPoker Heads Up Odds Calculator
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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Detailed calculations on some starting hands.Extneral Links
Play Heads Up Hold ’Em at the Galaxy Gaming web site. One click and you’re playing.
Written by:Michael ShacklefordTable Of Contents
With Daniel Negreanu confirming that his heads-up match against Doug Polk will commence this week on November 4th, we take a look at the betting markets available on PokerShares to see if any would be worth wagering on.
The site currently has 14 separate markets relating to the match, and here PokerNews runs through some of the more interesting ones.About PokerShares
First set up in 2017, PokerShares has given players the opportunity to bet on all manner of markets, both inside the world of poker and out.
From the Aussie Millions and the Galfond Challenge to the US Election and how many cases of coronavirus there will be in the US (although the latter was ultimately pulled after ten hours due to ’negative feedback on social media and reconsideration’.)
PokerShares founder Mike ’Timex’ McDonald said that they wanted to make the challenge as engaging as possible for viewers, therefore offering more than just the normal bets on how the market plays out.
Therefore players are able to place bets on anything from ’Will Doug return to professional poker?’ to ’Will there be any slowrolling?’The Main Markets
McDonald says that PokerShares opened the markets ’very early’ within only a few minutes of the pair challenging each other to the match.
’The odds started out as even,’ said McDonald. ’I believe 1.93 on each player as we were only going by details on Twitter and didn’t even know the format of the match.’
However, at time of publication (November 2nd), Doug Polk has moved ahead as a strong favorite to win the match according to the odds:Poker Heads Up Odds AgainstDoug Polk vs Daniel NegreanuPlayerDecimalAmericanFractionalDaniel Negreanu5.40+44022/5Doug Polk1.17-5887/41Other Markets
There are several markets relating to the first session, scheduled to take place live on PokerGO on November 4th. These include whether a player will slowroll during Session 1 (No +105, Yes -128), the size of the biggest pot (Over $100k +105, Under $100k -128) and who will get stacked first (Polk +100, Negreanu -116).
Other markets relate to the potential fallout from the match including:Heads Up Poker Preflop Odds
*Will Doug Polk return to being a pro player after this challenge? (Yes +660, No -1000)
*Will Daniel Negreanu cease to be a poker player because of this challenge? (Yes +1400, No -5000)
*What date will the challenge conclude? (February 1st 2021 or later +105, January 31st 2021 or earlier -128)
Odds correct at time of publication - 2nd November 2020Timex Tells All
McDonald told PokerNews that he thinks the match has the potential to be ’the most exciting grudge match poker has ever seen.’Heads Up Poker Calculator
’What makes the challenge especially exciting, is that Daniel decided he wanted to beat Doug at his own game. Originally we expected them to each pick their best game and rotate what they play.
’..the most exciting grudge match poker has ever seen’
’On one hand, you’ve got Doug, once the clear number one Heads-Up No Limit (HUNL) player in the world, but he’s four years removed from competitive play.
’On the other hand, you’ve got Daniel. Not a heads-up specialist but the most famous and among the most successful all-around poker players of all time.’Poker Heads Up Odds Wild Card
McDonald says that there has been an interesting dynamic when it comes to those betting on either Negreanu or Polk.
’Generally the guys betting on Doug have never played live, and the guys betting on Daniel have never played online! It’s an interesting dynamic where I think online players tend to estimate Daniel, and live players tend to underestimate Doug.’Poker Heads Up Odds Nfl Week 11
However, he went on to say that PokerShares has seen ’shockingly little’ volume from any of the players who have substantial experience playing with both.
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Whilst this 88.67% probability of winning is not as high as 96.01% for the straight poker game, or the 100% for the flush scenario, it is still gives a reasonably high guaranteed edge. To take this further, in The Mathematics of Poker, by Bill Chen and Jerrod Ankenman, a near optimal strategy is given for heads-up play when both player’s stacks are less than 50 big blinds. You will improve it on the turn: 9.2=18% and real poker odds are around 19%; You have a straight draw on the flop with 8 outs. You will improve it on the turn: 8.2=16% and real poker odds are around 17%; You have two over cards on the turn with 6 outs. You will improve it on the turn: 6.2=12% and real poker odds. The numbers are exact to the rounding I used, which was to chop off the space and bandwidth consuming digits without rounding (i.e. 84.93 for AAo meanas somewhere between 84.93 and 84.94, the exact probability of winning with AAo is 890,754,209/1,048,786,200, about.4777).
Pre-Flop Odds for Heads Up Poker A-A (220/1 or 0.45%) A-K (81.9/1 or 1.1%) A-A, K-K, Q-Q or 10-10 (54.3/1 or 1.8%) Any Pocket Pair (16:1 or 6.25%) Any 2 Cards Jack or Higher (10.1/1 or 9.05%). A Heads-Up Display, or HUD for short, is an online poker tool that allows you to display information directly on a poker table. This information ranges from statistics out of a tracking and analysis software database such as PokerTracker 3 or Holdem Manager to probability information provided by a calculator tool such as Holdem Indicator.On 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.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 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. 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-11,2000.904977-0.904977Total1,3261.000000-0.099548AcknowledgmentsPoker Heads Up Odds Calculator
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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Detailed calculations on some starting hands.Extneral Links
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Written by:Michael ShacklefordTable Of Contents
With Daniel Negreanu confirming that his heads-up match against Doug Polk will commence this week on November 4th, we take a look at the betting markets available on PokerShares to see if any would be worth wagering on.
The site currently has 14 separate markets relating to the match, and here PokerNews runs through some of the more interesting ones.About PokerShares
First set up in 2017, PokerShares has given players the opportunity to bet on all manner of markets, both inside the world of poker and out.
From the Aussie Millions and the Galfond Challenge to the US Election and how many cases of coronavirus there will be in the US (although the latter was ultimately pulled after ten hours due to ’negative feedback on social media and reconsideration’.)
PokerShares founder Mike ’Timex’ McDonald said that they wanted to make the challenge as engaging as possible for viewers, therefore offering more than just the normal bets on how the market plays out.
Therefore players are able to place bets on anything from ’Will Doug return to professional poker?’ to ’Will there be any slowrolling?’The Main Markets
McDonald says that PokerShares opened the markets ’very early’ within only a few minutes of the pair challenging each other to the match.
’The odds started out as even,’ said McDonald. ’I believe 1.93 on each player as we were only going by details on Twitter and didn’t even know the format of the match.’
However, at time of publication (November 2nd), Doug Polk has moved ahead as a strong favorite to win the match according to the odds:Poker Heads Up Odds AgainstDoug Polk vs Daniel NegreanuPlayerDecimalAmericanFractionalDaniel Negreanu5.40+44022/5Doug Polk1.17-5887/41Other Markets
There are several markets relating to the first session, scheduled to take place live on PokerGO on November 4th. These include whether a player will slowroll during Session 1 (No +105, Yes -128), the size of the biggest pot (Over $100k +105, Under $100k -128) and who will get stacked first (Polk +100, Negreanu -116).
Other markets relate to the potential fallout from the match including:Heads Up Poker Preflop Odds
*Will Doug Polk return to being a pro player after this challenge? (Yes +660, No -1000)
*Will Daniel Negreanu cease to be a poker player because of this challenge? (Yes +1400, No -5000)
*What date will the challenge conclude? (February 1st 2021 or later +105, January 31st 2021 or earlier -128)
Odds correct at time of publication - 2nd November 2020Timex Tells All
McDonald told PokerNews that he thinks the match has the potential to be ’the most exciting grudge match poker has ever seen.’Heads Up Poker Calculator
’What makes the challenge especially exciting, is that Daniel decided he wanted to beat Doug at his own game. Originally we expected them to each pick their best game and rotate what they play.
’..the most exciting grudge match poker has ever seen’
’On one hand, you’ve got Doug, once the clear number one Heads-Up No Limit (HUNL) player in the world, but he’s four years removed from competitive play.
’On the other hand, you’ve got Daniel. Not a heads-up specialist but the most famous and among the most successful all-around poker players of all time.’Poker Heads Up Odds Wild Card
McDonald says that there has been an interesting dynamic when it comes to those betting on either Negreanu or Polk.
’Generally the guys betting on Doug have never played live, and the guys betting on Daniel have never played online! It’s an interesting dynamic where I think online players tend to estimate Daniel, and live players tend to underestimate Doug.’Poker Heads Up Odds Nfl Week 11
However, he went on to say that PokerShares has seen ’shockingly little’ volume from any of the players who have substantial experience playing with both.
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