Solitaire Card Games
Roger
potential win rate in the 80% range at the Solitaire Laboratory and
Pretty Good Solitaire websites. But players of Black Hole who have
reported their win rates to the Pretty Good Solitaire website have an
average win rate of 15.1%. Assuming the potential 80% win rate is
correct, a lot of players, myself included, are playing Black Hole
with the wrong strategy. Are there any Black Hole devotees out there
who can set us straight and free us from the downward spiral of this
formidable game?
Sevo Stille
> The solitaire card game called Black Hole is stated as having a
> potential win rate in the 80% range at the Solitaire Laboratory and
> Pretty Good Solitaire websites. But players of Black Hole who have
> reported their win rates to the Pretty Good Solitaire website have an
> average win rate of 15.1%. Assuming the potential 80% win rate is
> correct, a lot of players, myself included, are playing Black Hole
> with the wrong strategy.
Potential win rates usually are the games theoretically solvable playing
the right card every time, as opposed to games that cannot be solved
regardless of any player action. As such they do not take into account
that the player has to pick his choices among obscured cards/stacks. It
is not unusual for 100% solvable solitaire games to have a practical win
rate well below 25%.
Sevo
Roger
I agree that inept individuals can have a win rate well below 25% for
games that are nearly 100% winnable. But it seems to me that a 15%
average win rate for a multitude of players when 80% or more of the
games are winnable is unusual. Can you list any solitaire games with
this wide of a differential between games won and games winnable using
the statistics at the Pretty Good Solitaire website or any other
statistics source which averages a large number of individuals?
Michael Keller
player picking from facedown cards (as in Spider, e.g.). Black Hole
is probably one of the hardest and deepest open solitaires to win.
According to a paper "Search in the Patience Game �Black Hole�" by Ian
Gent et al., the win rate is about 7 out of 8 with perfect play. But
the authors report on a number of different computer solvers,
even the best of which sometimes took several minutes of computer time
(that's a long time for a solitaire solver) to solve some of the
deals.
I suspect that the best players are not so much using better strategy,
but able to look further ahead (as a strong chess or go player can).
While there are some obvious strategies (don't play the last card of a
pile if another card of the same rank, be careful how often and where
you change direction), I suspect that it will be very hard for human
players to match the ideal win rate.
Some deals can be won with no changes of direction, but most will
require several changes. One site about the game absurdly states
that you cannot win if you change direction at a point other than
after playing a multiple of 13 cards. But this is not so, e.g.:
A232A23456789TJQKA23456789TJQKQJT9876543456789TJQKAK.
I note that there are two players on Pretty Good Solitaire with very
high win rates, but I suspect they are being selective about which
games they attempt (PGS does not charge a loss if no cards are played,
and it is easy to examine a deal to make sure that at least a
reasonable number of cards can be played at the start).
Michael Keller
Solitaire Laboratory
On Sat, 06 Jun 2009 11:52:43 +0200, Sevo Stille <sevo...@radiox.de>
wrote: