Notes on Morton's Poker Theorem and the Fundamental Theory of Poker

Overview

• Discussion about the potential flaws in the Fundamental Theory of Poker by David Slansky.
• The theory states:
  • When opponents make mistakes, you win.
  • When they play correctly, you lose.

Issues in Low Stakes Games

• Players often express frustration with low limit games.
• Common Scenario:
  • Opponents call with weak hands and chase unlikely draws.
  • Strong hands often get diluted due to multiple callers.
• The large number of players creates bigger pots, reducing the impact of individual mistakes.

Morton's Poker Theorem

• Morton's Theorem:
  • In multi-way pots, a player's profit can be maximized when opponents make the correct decisions.
  • Preferring opponents to fold even if they are making the right decision can lead to long-term gains.

Example Scenario

• Situation:
  • Player holds Ace of Diamonds and King of Clubs with a flop of King 9-3. (Top pair, best kicker)
  • Two opponents:
    • Opponent A: Nut Flush Draw (Ace-10 of Hearts)
    • Opponent B: Second Pair (Queen 9)
• After betting, the turn is a 6 of diamonds.
• Opponent A's Decision: Likely to call due to pot odds.
• Opponent B's Decision: Needs to calculate expected values based on the pot size.
  • Wins the pot 4 out of 42 times.
  • Pot size determines whether it's beneficial for B to call or fold.

Calculations

• Expected Value Calculations:
  • Opponent B's indifferent pot size: 7.5 big bets.
  • Player's indifferent pot size: 5.25 big bets.
• Paradoxical Region:
  • The range of pot sizes where it is correct for B to fold but profitable for the player when B folds.

Implications of Morton's Theorem

• Contradicts the Fundamental Theory of Poker due to multi-way dynamics.
• Involvement of multiple players means that not all profits from mistakes go to one player.
• Example of Implicit Collusion:
  • If opponents A and B benefit from B's incorrect call, they may seem to collude against the player holding the strong hand.

Strategic Takeaways

• Reduce Players in the Hand:
  • Strong hands are more vulnerable in multi-way pots.
  • Players with incorrect draws can inadvertently benefit other players.
• Value of Suited Hands Increases:
  • Suited hands benefit from implicit collusion in loose games.

Conclusion

• Need for a revised theory: Fundamental Theorem of Poker for Multi-Way Pots.
• Comments and Discussions:
  • Open for further thoughts on this topic.