Yes, you're on the right track. The 134,459 figure is the number of
5-card hands that are distinguishable assuming all ranks are
distinct
while all suits have equal priority. The payoff schedule isn't
taken
into account when breaking down the hands into these 134,459
equivalence classes.Jeff Lotspiech mistakenly claims that all 134,459 patterns must be
tested in order to guarantee that an optimal strategy is found, but
that isn't true. When finding an optimal strategy, we really only
care about the best possible draw for each hand -- the 31 other
ways to play the hand are irrelevant. You only have to look at
all 134,459 patterns if you need to attach some kind of relevance
to the 31 sub-optimal draws.If you ignore suits completely, there are only 6175 hands that
can be distinguished based on rank pattern. But for 9/6 JoB,
where we only need to distinguish high ranks (AKQJ) from
low ranks (T98765432) there are only 28 hands that include
a pair or bigger group, and 16 patterns with 5 distinct ranks.
So, for draws to "grouped" hands, there are only 44 distinct
starting hands.
Are these what I refered to earlier as hand "types"? E.g. Low pair,
High pair, 3 of a king, 4 of a kind, single high card, RF3, etc.
including penalty situations?
···
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote: