Small incremental gains

This is the chart of Abe's EV in the full two alley game.
To rid the chart of negative EV's the units were changed.
The pot starts with 20 chips. These chips are treated like
free money so both Abe and Dan will have positive EV.
In a fair game both Abe and Dan will have an EV of ten.
The bet and raises are fixed at ten chips.
The x-axis is the hands Abe bets originally. At x Abe
bets x and all hands better than x. The y-axis is Abe's
EV when both Abe and Dan plays optimally after the
first alley bet.
By playing perfectly Abe improves his EV only one
third of a chip. The standard deviation is 13 to 16 big
bets. Think about THIS. The sd is 130 to 160 chips per
100 hands. Optimal strategy improves Abe's results by
1/3 of a chip. This is really a small incremental gain
for optimal strategy.



This new chart shows calling strategies plotted against
optimal strategy. Notice that optimal strategy DOES NOT
dominate all other strategies.
On the river against a habitual bluffer always calling
dominates all other strategies, including optimal. Against
a passive non-bluffer always folding dominates all other
strategies, including optimal.
This chart also approximates EVs between streets. Abe faces
a turn raise or check/raise. With TPTK to trips Abe is way
ahead or way behind. He doesn't know which. If way behind
Abe should fold. If way ahead Abe should raise. In fixed
limit optimal strategy is to call pot/(pot+bet). Online
poker utilities hints at the correct response. Look at opp's
aggression factor. High AF(over 2.5) raise. Low AF(under 1)
fold. Otherwise calldown. A incorrect calldown, calling
a passive opp unlikely to bluff, costs two bbs. Making one
of these mistakes every 100 hands can be the difference
between winning and breaking even.

This chart graphically shows that optimal strategy should
be reserved for unknown opponents. Unknown could be a
pro who is unpredictable or just a new opponent of unknown
style. In the future a best default strategy may be found.