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.