Now,
both Greta and Opie know before each play which situation
they will be confronting. Opie bets optimally, in
proportion to her advantage, 2 units with a 2% advantage
and 6 units with the 6% edge, while Greta bets grossly,
4 units whenever the game is favorable. Thereby they
both achieve the same 3.6% of a unit expectation per
play. Starting with various bank sizes, their goals
are to double their stakes without being ruined. The
results of 2000 simulated trials in each circumstance
appear below.
Greta
is obviously the more often ruined woman, but since
they have the same expectation per play there must
be a compensating factor. This is, of course, timewhether
double or nothing, Greta usually gets her result more
quickly. This illustrates the general truth (pointed
out by Thorp in his Favorable Games paper) that optimal
betting systems tend to be "timid", perhaps
more so than a person who values her time would find
acceptable.1c] 
Let's
define the term narrowly and say that there are exactly
500 different skills available to master in poker.
Now, let's
take two local club players, each of whom is pretty
goodnot duffers but no threat to win the World Series
of Poker, either. Let's further say that these "advanced
intermediate" players have attained that status
because they have each mastered 300 of the 500 necessary
skills.
This might
make the two players equally talented and might mean
that against equal opponents, they rate to achieve
equivalent results over the long run, but it would
take an astounding coincidence for each player to
have mastered precisely the same 300 skills. They're
probably good at different things. Let's say that
Player X has mastered skills 51 through 350, while
Player Y has mastered skills 176475.
