Ultimate Texas Hold 'Em Collusion

Introduction

As Electric Table Games (ETGs) continue to gain popularity, players can easily exchange information regarding the cards they're holding. For instance, at a six-player table, participants could collectively be aware of ten cards that are already out of play. A common inquiry I encounter is regarding the usefulness of having knowledge of these ten dead cards. This article aims to provide clarity on that topic. Ultimate Texas Hold 'Em In order to investigate this, my trusted associate JB conducted a simulation with 40,000 rounds of Ultimate Texas Hold 'Em. Each round was composed of two random hole cards and ten random dead cards, assuming the player adhered to an optimal computer strategy throughout.

JB Analysis

Ultimately, the findings revealed that this player lost 0.0064 units for every unit wagered on the Ante, translating to a house edge of 0.64%. The risk element, defined as the ratio of anticipated loss to the total amount bet, stands at 0.15%.

In scenarios where dead cards are unknown, the house edge is 2.19%, with a risk element of 0.53%. This indicates a significant 71% decrease in the house edge.

Throughout the 40,000 hands played, the player diverged from traditional strategy before the flop on 3,613 occasions, representing a deviation rate of 9.0%.

The forum member known as Mental or Mental Block made remarkable contributions, developing his own simulation tool to analyze the effects of having 1 to 43 dead cards. The ensuing chart encapsulates his findings.

Mental Block Analysis

When this topic came up in my forum at Wizard of Vegas In the graph, blue dots represent the actual outcomes from the simulation, while orange dots illustrate data points along an exponential regression line. The formula determining player advantage (based on the Ante bet) in relation to the number of dead cards (d) is outlined as follows:

For 10 dead cards, his precise simulation results indicate a house edge of 0.58%. When applying the regression formula, the figure adjusts to 1.07%. Regardless, both figures fall within the acceptable error margin compared to JB's 0.64%.

Player advantage = 0.008034*e^0.0878d-0.03

According to Mental Block's regression analysis, players only start to gain an advantage when there are at least 16 dead cards.

In summary, engaging in collusion within Ultimate Texas Hold 'Em is not particularly advantageous. A straightforward and reliable strategy can slightly decrease the house edge. A link related to this topic is provided below.

Conclusion

I would like to express my gratitude to JB and Mental Block for their significant contributions to this discussion.

Acknowledgments

Practical Approaches to Collusion in Ultimate Texas Hold 'Em

External Links

• — An article on Discount Gambling proposes a collusion tactic for specific scenarios involving a 4x raise before the flop. — Explore discussions about collusion in Ultimate Texas Hold 'Em on my forum at Wizard of Vegas.
• Ultimate Texas Hold 'Em: Face Up Cards — Eliot Jacobson authored an article on this subject, concluding that a colluding player advantage in a six-player scenario is 2.5% based on a 500-hand simulation, a figure I personally contest.
• Ultimate Texas Hold 'Em Collusion Mathematically sound strategies and insights for various casino games including blackjack, craps, roulette, and many others are available.

Written by: Michael Shackleford