brainwagon

While watching the World Poker Tour today, I saw Mike Madusow survive going all in against a pair of aces, and surviving by hitting three kings on the river. During the break, they had this question as a quiz:

Which hand has the best odds going up against A♦ A♣ in the hole?

• K♦ K♠
• 10♦ 9♦
• Q♣ J♦

It seems obvious that the third is right out, but what might be a teensy bit surprising is that you have a better shot with 10 ♦ 9♦ against a pair of aces than you do with the pair of kings. Apparently the additional chances to hit straights and flushes outweigh the additional rank which is mostly useless against the aces. You can use the GNU poker eval program to verify this:

[fishtank] % ./hcmp2 AD AC KH KS
1712304 boards
  cards      win  %win       loss  %lose       tie  %tie      EV
  Ac Ad  1388072  81.06    317694  18.55      6538   0.38     0.813
  Ks Kh   317694  18.55   1388072  81.06      6538   0.38     0.187
[fishtank] % ./hcmp2 AD AC TD 9D
1712304 boards
  cards      win  %win       loss  %lose       tie  %tie      EV
  Ac Ad  1338249  78.15    367143  21.44      6912   0.40     0.784
  Td 9d   367143  21.44   1338249  78.15      6912   0.40     0.216
[fishtank] % ./hcmp2 AD AC QC JH
1712304 boards
  cards      win  %win       loss  %lose       tie  %tie      EV
  Ac Ad  1450987  84.74    254763  14.88      6554   0.38     0.849
  Qc Jh   254763  14.88   1450987  84.74      6554   0.38     0.151

I thought it was cool.