Wednesday, April 27, 2011

AK vs half-dead pair (User Request)

I got a fun question from a user today. "How does AK (suited or unsuited) fare against any pair assuming that one of the pair's set outs are dead?"

We can answer this with a little PQL hackery. I say "hackery" because there isn't a way to connect dead cards with other hand ranges in PQL at the moment. We will perform an all in equity simulation with AK vs any pair. If the pair gets quads by the river, we throw out the sim, since one of the set cards is supposed to be dead. If the pair does not get a matching card by the river, we keep the sim, since the dead card never appeared. If the pair hits exactly one of its set cards but doesn't have quads, we have a 50/50 chance that the sim should be thrown out. Here's where the hack comes in - we can just throw out all sims in this case where one of the pair cards is a heart, as 50% of pairs have a heart in them. Note that if the pair is Aces or Kings, then we should not be able to hit the board at all, so we need to exclude that as well.

Here is the PQL query I came up with:

select avg(riverEquity(hero))
from game='holdem', hero='AK', villain='AA-22', syntax='Generic'
case handBoardIntersections(villain, river)
when 0 then true
when 2 then inRange(villain,'*!h!AA-KK')
and not (handtype(villain, river) = quads)

Answer - AK has 48% equity.