[pzhon]

AA is a solid favorite, even without the ace of the suit of the KQJs.

Here are two ways to see this:

[img]/images/graemlins/spade.gif[/img] KQs has an equity of .163 with the jack removed from the deck. KJs has an equity of .167. QJs has an equity of .185. These total .515. If the ways to win/tie were completely disjoint, KQJs might be a slight favorite, however, there is a huge amount of overlap. About 5% of the time, KQ wins with a flush, and so would KJs and QJs. When KQs hits trips, so would either QJs or KJs. That means the ways of winning are far from disjoint. From the flushes alone, the sum .515 overcounts the equity of KQJs by over .100.

[img]/images/graemlins/spade.gif[/img] I shuffled and dealt out 45 boards. AA won exactly 30, lost 15, and tied 0. That is more than 2 standard deviations away from breaking even, strong evidence that AA is the favorite.