MOP19.3. The pot size case.

The problem on 19.3 is resolved using geometric growth with
pot size bets.
Clare, the clairvoyant, will be dealt one card. If it's
an ace or king she wins, else she loses. Dean will be the
defender. There are three streets of betting. Clare may
bet or give up. Dean may call or fold. Both will ante
five units. Clare's bets will be pot size.

Question.
If both Clare and Dean are playing optimally, what's the
value of the game?

Answer.
Clare has a +EV of 0.19231 units.

The ex-showdown value of the game is -3.46. This is from
MOP 19.3. The game is solved by linking three matrices in
series.
First the three matrices are solved separately. On street
one Clare bluffs about 9% of her losers. If this were a
one street game, Dean would call 50% of the time. Since
this is a three street game, Dean can improve on his
-0.19231 EV by just folding to every bet. The game value
would be 5*(.76923)-5*(.23077)=2.6923. That's 2.6923
in Dean's favor.
To force Dean to call more often Clare must overbluff
street one. To produce +0.19231 EV Clare must bet so
that if Dean folds to every bet, she would still get
her +0.19231.

5*(x-(1-x))=0.19231
2x-1=0.19231/5
2x=1+.038462
x=.519231

Plug these numbers in and Clare is betting about 40% of
her losers instead of 9%.
On street two Clare had to overbluff again. She bets 35%
of her remaining losers instead of 21% suggesting by the
one street matrix.
By street three the game has been reduced to a one street
game. Clare bets losers at the suggested optimal strategy
frequency.
Clare overbluffs by over 300% on street one. This suggests
in a real game where Clare starts with 50-70% winners the
100% continuation bet may be viable. She only overbluffs
about 60% on street two.
Dean calls at the 50%(pot/{pot/bet}) frequency thruout all
three streets.

geogrowth overbluff
S1 Cgives 0.48077 __-5 ____-2.40385
S1 Dfolds 0.25962 __ 5 ____ 1.29808
S2 Cgives 0.11857 _-15 ____-1.77862
S2 Dfolds 0.07052 __15 _____1.05781
S3 matrix 0.07052 __28.63 __2.01888
____________________________0.19231
On street one Clare gives up 48% of the time. She loses
5 units on those. Dean folds about 26% of the time.
The street three matrix is played out as a one street
matrix game.