MOP Chap 19 simplified

X and Y start with stacks of 125 and each ante 5. Two streets of betting. Y is dealt a card marked winner or loser. 20% chance of the card is marked winner. Y wins the showdown if he holds the card marked winner.
Game A. Y bets 60 or gives up on each street. X may call or fold to a bet. On street one if Y gives up or X folds, game is over. If Y bets and X calls, street two is played.
Game B. Same as game A, accept Y bets 20 on street one and 100 on street two.

Matrix M
.... \ ...........X
....Y \_____call________fold
____VB___ f(S+b)-(1-f)b-S/2 ___S/2
__VCh_______f(S+b)-S/2______fS-S/2

V - Y value bets winner
B - Y bluffs loser
Ch - Y gives loser
f - 20% chance Y holds winner
(1-f) - chance Y holds loser
S - size of pot
b - size of bet
x - X calls
y - Y bluffs

Matrix N
----------Xcall----Xfold
Yvalue
Ybluff
Ycheck

Used matrix M to solve the strategy of the game and matrix N to calculate the value of the game.

A.
..\.............. X
Y \_____call______fold__
VB______-39________5__
VCh_______9_______-3

x = 1/7, (1-x) = 6/7
y = .2143, (1-y) = .7857

Y gives up... 62.86%
X folds value 17.14%
X folds bluff 14.69%
Game values
Y checks -3.1429
X folds 1.5918
GV at end of str1 -1.2857
game continues to street two
value 0.02857
bluff 0.02449
total 0.05316
ratio winners/total 7/13

.........\............ X
__Y__\_____call________fold__
__VB______9.615_______65__
__VCh____38.308________5

x = 13/19, (1-x)= 6/19
y = .36848, (1-y) = .63152
matrix value 27.11 times .05316 = 1.4386

Added to Ychecks and Xfolds of str1
Game value -0.1124

Game B.
..\........... X
Y \_____call________fold__
VB_______-1.5________.5__
VCh________.1_______-.3

x = 1/3, (1-x) = 2/3
y = 1/6, (1-y) = 5/6
Y gives up... 2/3
X folds value 4/30
X folds bluff 8/90
Game values
Y checks -3 1/3
X folds 1 1/9
GV at end of str1 -1.6667

.....\.......... X
_Y_\_____call___fold__
VB______25______25__
VCh_____65_______5

x = 1/3, (1-x) = 2/3
y is 100%
matrix value 25 times 1/9 = 2 7/9
Added to Ychecks and Xfolds of str1
Game value 5/9