Heads Up Poker Dealer Small Blind

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.

• However, in heads-up play, the person who has the button is the small blind, as well, and will subsequently be the first player to act pre-flop after the cards are dealt. Post-Flop: The player who is in the big blind (i.e. The player to the left of the poker dealer button) will be the first player to act on each post-flop betting round; betting.
• Big Blind Products 100 Piece Premium Poker Chip Set Set for Upscale Vegas-Style Poker Nights - Durable, Poker Chips with Denominations, Casino Weight Chips with Gift Box - Casino Chips 4.8 out of 5 stars 253.
• The button has the small blind when playing Texas Holdem heads up. The person who is the dealer has the button and also posts his/her small blind. This means that the other player (without the button) is the big blind. The small blind acts first on the first round of betting before the flop (pre-flop).

In heads-up play with two blinds, the small blind is on the button. A new player entering the game has the following options: (a) Wait for the big blind. (b) Post an amount equal to the big blind and immediately be dealt a hand. (In lowball, a new player must either post an amount double the big blind or wait for the big blind.) 5. In heads up poker games, the button pays the small blind (and is sometimes also referred to as the small blind position). The small-blind/button acts first on the preflop betting round but last on the postflop betting rounds. The other player is referred to as the big blind and pays the big blind amount preflop.

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.

1. The game is played with a single ordinary 52-card deck.
2. The player must make an equal bet on both the Ante and Odds.
3. Two cards are dealt face down to the player and dealer. The player may look at his own cards.
4. The player can check or make a Play bet equal to three times the Ante.
5. The dealer turns over three community cards.
6. 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.
7. Two final community cards are turned over.
8. 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.
9. The player and dealer will both make the best possible hand using any combination of their own two cards and the five community cards.
10. The dealer will need at least a pair to open.
11. 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

12. 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

13. 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

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

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

The next table shows four known pay tables for the Trips Plus.

Trips Plus Pay Tables

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

Pocket Bonus — Pay Table 2

Pocket Bonus — Pay Table 3

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.

Internal Links

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.

Stripper Stacks

Strippers are cards that are shaped in such a way as to allow them to be easily controlled by pulling them out of the deck, no matter where they are located.

A stripper stack uses this concept, along with carefully chosen cards, to enable a cheat to easily stack the deck in their favour.

A well known example of a stripper stack is the ten-card poker deal, which is a concept often used by magicians.

The Ten-Card Poker Deal

The ten-card poker deal came from the card table; it originally used nine cards and was specifically designed for a 5-card straight poker heads-up scenario.

The cheat would take nine cards from the deck, and cut them in such way that they could be stripped out when required.

In play, after the mark had shuffled, the deck would be passed to the cheat to be cut. The cheat would use the motion of cutting the cards to strip out the nine target cards and place them on top.

The result of this would be that the nine cards are dealt between the two players, with the mark's final card being a random card from the deck.

The nine cards consisted of three sets of three-of-a-kind, which we will denote A, B, and C.

So the nine cards are: AAABBBCCC. As such there are a relatively small number of possible outcomes:

The table shows the probabilities that either party will win, given the way the nine cards come out, and whether the random card is helpful to the mark or not.

In most cases the random card is not useful, and the cheat will win. But occasionally the random card will improve the marks hand, and in some cases that may be enough to beat the cheat.

Overall, the cheat will win 96.01% of the time, whereas the mark will only win 3.99% of the time.

The advantages of this particular method of cheating, are that

• It only requires a single 'cut' type action, which is built into the game's procedure,
• It's done on the opponent's deal,
• It has a very high success rate.

The main disadvantage is that it requires stripped cards, which need to be put into the game somehow.

Getting Strippers into the Game

Cutting cards to make strippers is not generally something that can be done at the table, which leaves three options:

• Making sure the deck in play has already had the cards doctored
• Switching the deck or the required cards during play
• Cutting the cards from the deck in-play

The first method could be achieved by stocking the local shop with a large number of doctored decks and then insisting that a new deck is purchased before the game begins. Another method would be to have an accomplice who pretends to purchase a deck, but in fact just provides a prepared deck.

Alternatively, the deck could be switched before the game; again with an accomplice that has access to where the decks are stored.

A deck switch could also be done by the cheat during the game, either when they handle the cards to deal, or when given the cards for a cut. In some cases an accomplice may be used to provide a distraction whilst the decks are switched.

Depending on the style of strippers used, it may actually be only the target cards that need to be gimmicked. In this case they could be slowly switched out, one at a time, throughout the night as game play continues.

Finally, the cards in play could be cut, which would require stealing them from the deck, taking them somewhere private to put the work in, and then reintroducing them back into the pack.

A Stripper Stack for Heads-Up Texas Hold'em

Currently, the most popular form of poker is Texas Hold'em, which has quite a different format to straight poker.

Two face down hole cards are dealt to each player, then between rounds of betting, five communal cards are dealt face up on to the table. The players must make the best 5-card hand using their hole cards and the communal cards.

The aim would be to find a set of cards that can be stripped to the top in a single cutting action, and provide a high win rate, when playing heads-up Texas Hold'em.

The introduction of communal cards means that in many cases the winning hand is not decided until the final card comes down. This means that, selecting a set of 11 cards, such that the river card is random, makes the final result highly variable. So this is not a particularly effective strategy.

If the rules were loosened slightly to allow two ‘moves', then 7 cards of one suit could be stripped to the top in the first action, and the ace of that suit stripped to the top in a second action. So, instead of ensuring that the mark is dealt a bad card, it's ensured that the cheat is dealt a good card. In this case, both players would make a flush, and the cheat would win with the ace. This scenario produces a 100% probability of the cheat winning, as the ace high flush can't be beaten, regardless of which cards are dealt on the turn or the river. However, there is the risk that the cards the mark ends up with are not good enough for them to want to bet on; so whilst the cheat will still win the hand, it may not be the biggest pot.

An alternative would be only controlling the hole cards, risking the fact that the 5 communal cards could completely change the winning hand.

By stripping three aces to the top on the mark's deal, the cheat will ensure a pair of aces for themselves and the mark will be dealt at least one ace.

There are two advantages to this; firstly, giving the mark an ace may entice them to stay in the hand longer, giving the cheat the opportunity to win more. Secondly, the cheat holds the other two aces, which makes it unlikely that the mark will pair their ace. Furthermore, if the mark makes a hand with their ace, then in many cases the cheat will at least be able to equal the hand, and in some cases beat it.

To illustrate this advantage, the cheat's pair of aces against any other two random cards, gives the cheat a win rate of 84.93%, the chances of drawing are 0.54%, and losing is 14.52% [results from wizardofodds.com]. Whereas, when the cheat's aces are up against an ace and any other card, the cheat's win rate is increased to 88.67%, the chances of drawing is increased to 3.17%, and crucially the probability of losing is now only 8.15% [results calculated with the help of cardplayer.com]. So by giving the mark an ace, the cheat's chances of winning are increased, as is the chance of the mark making a bet.

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. This strategy suggests that the only two moves in this scenario should be to jam or fold. The details of this strategy are described by a table, which give all possible hole card combinations, and assigns each a value. For the attacker, this value is the stack size in big blinds at which your play should switch from fold to jam. A second table is given for the defender, which dictates at what stack size their strategy should switch from fold to call.

When heads-up it's common for the order of play to change. In standard multiway tables the player to the left of the dealer posts the small blind, the next player puts up the big blind, and the next player is the first to act. In this manner when heads-up, the dealer would put in the big blind and their opponent would act first. However, the change in play for heads-up means that the dealer acts first and their opponent puts in the big blind.

Heads Up Poker Dealer Small Blind Girl

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.

• However, in heads-up play, the person who has the button is the small blind, as well, and will subsequently be the first player to act pre-flop after the cards are dealt. Post-Flop: The player who is in the big blind (i.e. The player to the left of the poker dealer button) will be the first player to act on each post-flop betting round; betting.
• Big Blind Products 100 Piece Premium Poker Chip Set Set for Upscale Vegas-Style Poker Nights - Durable, Poker Chips with Denominations, Casino Weight Chips with Gift Box - Casino Chips 4.8 out of 5 stars 253.
• The button has the small blind when playing Texas Holdem heads up. The person who is the dealer has the button and also posts his/her small blind. This means that the other player (without the button) is the big blind. The small blind acts first on the first round of betting before the flop (pre-flop).

In heads-up play with two blinds, the small blind is on the button. A new player entering the game has the following options: (a) Wait for the big blind. (b) Post an amount equal to the big blind and immediately be dealt a hand. (In lowball, a new player must either post an amount double the big blind or wait for the big blind.) 5. In heads up poker games, the button pays the small blind (and is sometimes also referred to as the small blind position). The small-blind/button acts first on the preflop betting round but last on the postflop betting rounds. The other player is referred to as the big blind and pays the big blind amount preflop.

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.

1. The game is played with a single ordinary 52-card deck.
2. The player must make an equal bet on both the Ante and Odds.
3. Two cards are dealt face down to the player and dealer. The player may look at his own cards.
4. The player can check or make a Play bet equal to three times the Ante.
5. The dealer turns over three community cards.
6. 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.
7. Two final community cards are turned over.
8. 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.
9. The player and dealer will both make the best possible hand using any combination of their own two cards and the five community cards.
10. The dealer will need at least a pair to open.
11. 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

12. 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

13. 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

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

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

The next table shows four known pay tables for the Trips Plus.

Trips Plus Pay Tables

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

Pocket Bonus — Pay Table 2

Pocket Bonus — Pay Table 3

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.

Internal Links

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.

Stripper Stacks

Strippers are cards that are shaped in such a way as to allow them to be easily controlled by pulling them out of the deck, no matter where they are located.

A stripper stack uses this concept, along with carefully chosen cards, to enable a cheat to easily stack the deck in their favour.

A well known example of a stripper stack is the ten-card poker deal, which is a concept often used by magicians.

The Ten-Card Poker Deal

The ten-card poker deal came from the card table; it originally used nine cards and was specifically designed for a 5-card straight poker heads-up scenario.

The cheat would take nine cards from the deck, and cut them in such way that they could be stripped out when required.

In play, after the mark had shuffled, the deck would be passed to the cheat to be cut. The cheat would use the motion of cutting the cards to strip out the nine target cards and place them on top.

The result of this would be that the nine cards are dealt between the two players, with the mark's final card being a random card from the deck.

The nine cards consisted of three sets of three-of-a-kind, which we will denote A, B, and C.

So the nine cards are: AAABBBCCC. As such there are a relatively small number of possible outcomes:

The table shows the probabilities that either party will win, given the way the nine cards come out, and whether the random card is helpful to the mark or not.

In most cases the random card is not useful, and the cheat will win. But occasionally the random card will improve the marks hand, and in some cases that may be enough to beat the cheat.

Overall, the cheat will win 96.01% of the time, whereas the mark will only win 3.99% of the time.

The advantages of this particular method of cheating, are that

• It only requires a single 'cut' type action, which is built into the game's procedure,
• It's done on the opponent's deal,
• It has a very high success rate.

The main disadvantage is that it requires stripped cards, which need to be put into the game somehow.

Getting Strippers into the Game

Cutting cards to make strippers is not generally something that can be done at the table, which leaves three options:

• Making sure the deck in play has already had the cards doctored
• Switching the deck or the required cards during play
• Cutting the cards from the deck in-play

The first method could be achieved by stocking the local shop with a large number of doctored decks and then insisting that a new deck is purchased before the game begins. Another method would be to have an accomplice who pretends to purchase a deck, but in fact just provides a prepared deck.

Alternatively, the deck could be switched before the game; again with an accomplice that has access to where the decks are stored.

A deck switch could also be done by the cheat during the game, either when they handle the cards to deal, or when given the cards for a cut. In some cases an accomplice may be used to provide a distraction whilst the decks are switched.

Depending on the style of strippers used, it may actually be only the target cards that need to be gimmicked. In this case they could be slowly switched out, one at a time, throughout the night as game play continues.

Finally, the cards in play could be cut, which would require stealing them from the deck, taking them somewhere private to put the work in, and then reintroducing them back into the pack.

A Stripper Stack for Heads-Up Texas Hold'em

Currently, the most popular form of poker is Texas Hold'em, which has quite a different format to straight poker.

Two face down hole cards are dealt to each player, then between rounds of betting, five communal cards are dealt face up on to the table. The players must make the best 5-card hand using their hole cards and the communal cards.

The aim would be to find a set of cards that can be stripped to the top in a single cutting action, and provide a high win rate, when playing heads-up Texas Hold'em.

The introduction of communal cards means that in many cases the winning hand is not decided until the final card comes down. This means that, selecting a set of 11 cards, such that the river card is random, makes the final result highly variable. So this is not a particularly effective strategy.

If the rules were loosened slightly to allow two ‘moves', then 7 cards of one suit could be stripped to the top in the first action, and the ace of that suit stripped to the top in a second action. So, instead of ensuring that the mark is dealt a bad card, it's ensured that the cheat is dealt a good card. In this case, both players would make a flush, and the cheat would win with the ace. This scenario produces a 100% probability of the cheat winning, as the ace high flush can't be beaten, regardless of which cards are dealt on the turn or the river. However, there is the risk that the cards the mark ends up with are not good enough for them to want to bet on; so whilst the cheat will still win the hand, it may not be the biggest pot.

An alternative would be only controlling the hole cards, risking the fact that the 5 communal cards could completely change the winning hand.

By stripping three aces to the top on the mark's deal, the cheat will ensure a pair of aces for themselves and the mark will be dealt at least one ace.

There are two advantages to this; firstly, giving the mark an ace may entice them to stay in the hand longer, giving the cheat the opportunity to win more. Secondly, the cheat holds the other two aces, which makes it unlikely that the mark will pair their ace. Furthermore, if the mark makes a hand with their ace, then in many cases the cheat will at least be able to equal the hand, and in some cases beat it.

To illustrate this advantage, the cheat's pair of aces against any other two random cards, gives the cheat a win rate of 84.93%, the chances of drawing are 0.54%, and losing is 14.52% [results from wizardofodds.com]. Whereas, when the cheat's aces are up against an ace and any other card, the cheat's win rate is increased to 88.67%, the chances of drawing is increased to 3.17%, and crucially the probability of losing is now only 8.15% [results calculated with the help of cardplayer.com]. So by giving the mark an ace, the cheat's chances of winning are increased, as is the chance of the mark making a bet.

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. This strategy suggests that the only two moves in this scenario should be to jam or fold. The details of this strategy are described by a table, which give all possible hole card combinations, and assigns each a value. For the attacker, this value is the stack size in big blinds at which your play should switch from fold to jam. A second table is given for the defender, which dictates at what stack size their strategy should switch from fold to call.

When heads-up it's common for the order of play to change. In standard multiway tables the player to the left of the dealer posts the small blind, the next player puts up the big blind, and the next player is the first to act. In this manner when heads-up, the dealer would put in the big blind and their opponent would act first. However, the change in play for heads-up means that the dealer acts first and their opponent puts in the big blind.

Heads Up Poker Dealer Small Blind Girl

As the cheat is stripping the cards on the mark's deal, then if the special heads-up order of play is enforced, the cheat is considered the defender. Whereas, if this change of play is not introduced, then the cheat would be considered the attacker.

Whilst the jam-fold strategy was developed for the alternate heads-up order of play, with the dealer acting first, results were calculated considering the cheat as both the attacker and the defender.

The following graph shows the cheat's probability of success for a given opponent's stack size. Where success would mean that the mark did not fold, and the pocket aces won the hand.

Heads Up Poker Dealer Small Blind Ball

The cheat's actions are clear, with their aces, they should jam if they are the attacker or call if they are the defender. However, the mark's actions will depend on their stack size and what random card they get with their ace.

The graph shows that the cheat is more likely to succeed if they are the defender, which suggests that the alternate heads-up order of play is beneficial for this method of cheating.

As an example, if the mark has a stack of 40 big blinds, then there is a 60.64% chance of the mark going all-in and the cheat winning the pot.

For a 50% or greater probability of success, the cheat should use this technique when their opponent has less than 42.6 big blinds in their stack. Or 29.2 big blinds if the alternate heads-up order of play is not used and the cheat is the attacker.

Conclusion

The nine-card poker deal was designed for a game of straight poker, and gave the cheat a 96.01% chance of winning the pot. The required cards could be stripped out in a single cutting action, meaning that the play would take place on the mark's deal.

Applying the same methodology to the game of Texas Hold'em is made more difficult with the introduction of communal cards. But by stripping only three aces, a similar outcome can be achieved; although the win rate drops to 88.67%.

Furthermore, using the near-optimal jam-fold strategy when the players are down to less than 50 big blinds, the cheats probability of success can be determined. These results suggest that the cheat has a greater than 50% success rate when their opponent has a stack of 42.6 big blinds or less.

As a final thought, after the mark calls all-in and the cards are flipped over, they will likely realise that they are a severe underdog. This opens up the opportunity for making a deal and potentially dividing up the pot in a cash game, or deciding finishing positions and prize money splits in a tournament. Making a deal negates the risk of running the board and losing, for both players.

Heads Up Poker Dealer Small Blind Bag

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