Preflop Odds Heads Up 2

[SS] “Again you’re all-in against a single opponent”, Stan the Stat posed. “But this time you can select both your own hole cards and your opponent’s. What should you pick?”

[RR] “I thought the best was something like Aces against Ace-Nine offsuit, with the Nine matching the suit of one of your Aces.”

[SS] “Close.”

[FF] “Ace-Eight?” Figaro the Fish ventured.

[SS] “Nope.”

[HH] “Ace-Seven?” Harriet the Hazy attempted.

[SS] “Nope.”

[LL] “Ace-Six?” Leroy the Lion guessed.

[SS] “And nope. Oddly, the Ace-Nine is the best of those because King-Queen-Jack-Ten is only a push, but the Ace-Six is next.”1

[EE] “So, it’s not a pair of Aces at all! Then it must be Kings vs. King-Two”, Elias the Eagle deduced.

[SS] “Indeed, with nearly 95% equity.2 With an Ace, you can’t let your opponent have anything under a Five because that would permit too many straights. With the King, no such problem. The King-Deuce does tie a few more hands, but it wins many fewer because the Six through Nine all take part in five kinds of straights while the Two only makes two. Queens vs. Queen-Two is the next best.”3

Footnotes:

  1. Ace-Eight makes 12 more winning full houses than Ace-Seven, which in turn makes 12 more than Ace-Six.
  2. 94.92% from 1,612,287 wins and 26,192 ties out of 1,712,304 possibilities.
  3. 94.66%. Then Kings vs. King-Three (94.48%), Jacks vs. Jack-Two (94.35%), Queens vs. Queen-Three (94.22%), and finally Aces vs. Ace-Nine (94.08%), barely edging Kings vs. King-Four (94.04%) and Kings vs. King-Two with four suits (94.03%).

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